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공학박사학위논문
전륜 가속도 센서 기반 승차감 향상을
위한 능동 현가 시스템 예측 제어
Wheelbase Preview Active Suspension Control to
Improve Vehicle Ride Comfort based on Front-Wheel
Acceleration Sensing
2018년 8월
서울대학교 대학원
기계항공공학부
권 백 순
i
Abstract
Wheelbase Preview Active Suspension
Control to Improve Vehicle Ride
Comfort based on Front-Wheel Acceleration Sensing
Baek-soon Kwon
School of Mechanical and Aerospace Engineering
The Graduate School
Seoul National University
Active and semi-active suspension systems for passenger vehicles have been
a very active area of research for several decades owing to their potential to
improve the ride comfort and handling performance. It is well known that active
suspensions provide better performance and more functions compared to semi-
active suspensions. The main functions of active suspensions are vehicle height
adjustment, ride quality improvement, and attitude control. Some active
suspensions have been implemented and commercialized on high performance
and luxury vehicle these days. For example, Hydractive suspension by Citroen,
active body control (ABC) system by Mercedes-Benz, and anti-roll control
(ARS) system by BMW have been developed. Active suspensions have even
greater potential if preview information of the oncoming road height profile is
available. There are various ongoing projects which are trying to achieve better
driving performance using road preview information. Mercedes-Benz
introduced the world’s first actively preview controlled suspension system by
detecting road surface undulations in advance. BMW is trying to develop video
image processing system for suspension control. Volkswagen has undertaken
researches to prepare and operate suspension parts by road sensing with radar/
ii
laser sensors. Honda holds a patent for adaptive active suspension and aware
vehicle network system.
From a careful review of considerable amount of literature, active suspension
and preview control technology has the potential to promote both safety and
convenience of passengers. However, the current state-of-the-art in preview
active suspension technology has two main challenges. First, the developed
suspension control approaches require information on signals which may be
difficult to access such as suspension stroke speed or tire deflection. Second, it
requires precise, expensive sensors to detect road information such as a laser
scanner. While the cost of these sensors is going down, integrating these sensors
include special considerations and represent yet another barrier to adoption.
Therefore, this dissertation focused on developing a partial preview control
algorithm for low-bandwidth active suspension systems. In order to cope with
the unknown road disturbance, a novel vertical vehicle model has been adopted.
The state variables for suspension control were estimated using easily
accessible measurements. The vertical acceleration information of front wheels
is used to obtain preview control inputs for rear suspension actuators. From the
present driving mode by a mode selector, the control objective is determined to
be height control, attitude control, or ride comfort control.
In the remainder of this thesis, we will provide an overview of the overall
architecture of the proposed active suspension control algorithm. The
performance of the proposed algorithm has been verified via computer
simulations and vehicle tests. The results show the enhanced vehicle driving
performance by the proposed suspension control and state estimation algorithm.
Keywords: Active suspension control, Reduced vertical full-car model, Kalman
filter, Linear quadratic regulator, Optimal linear preview control, Model
predictive control, Electro-mechanical suspension
Student Number: 2013-23053
iii
List of Figures
Figure 2.1. Schematic diagram of the electro-mechanical suspension control
algorithm for a vehicle. The proposed control algorithm consists of mode
selector, upper-level and lower-level controllers, and suspension state
observer. .......................................................................................... 14
Figure 3.1. Quarter-car model of a high-bandwidth active suspension. ........ 16
Figure 3.2. Quarter-car model of a medium-bandwidth active suspension. ... 16
Figure 3.3. Quarter-car model of a low-bandwidth active suspension .......... 16
Figure 3.4. The 7-DOF vertical full-car model ........................................... 22
Figure 3.5. The height profile of the road for model validation ................... 26
Figure 3.6. Comparison of vehicle body motion of actual and simulated
vehicle ............................................................................................. 27
Figure 3.7. Comparison of suspension deflection of actual and simulated
vehicle ............................................................................................. 28
Figure 4.1. Block diagram of suspension state observer.............................. 30
Figure 4.2. Two sensor configurations for measurement............................. 32
Figure 4.3. The relation between the suspension velocity and the damping
force used in simulation given in Carsim® ......................................... 40
Figure 4.4. Comparisons of actual and estimated states by disturbance-
coupled observer and the proposed observer for single bump road test . 42
Figure 4.5. Comparisons of actual and estimated suspension velocities by
disturbance-coupled observer and the proposed observer for single bump
road test. .......................................................................................... 43
Figure 4.6. Semi-active suspension system of front side and mounted sensors
for the field test ................................................................................ 45
Figure 4.7. The damping force versus suspension velocity curves of the semi-
active damper prototype .................................................................... 45
Figure 4.8. Comparisons of reference data and estimated states for single
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bump road case................................................................................. 48
Figure 4.9. Comparisons of reference data and estimated suspension velocities
for single bump road case.................................................................. 49
Figure 4.10. Comparisons of reference data and estimated states for off-road
case ................................................................................................. 50
Figure 4.11. Comparisons of reference data and estimated suspension
velocities for off-road case ................................................................ 51
Figure 4.12. Comparisons of measured and estimated acceleration of rear
wheels for off-road case .................................................................... 52
Figure 5.1. Bode plots from symmetric road elevation input to delayed front
left wheel acceleration and that of rear left wheel acceleration in full-car
model .............................................................................................. 60
Figure 5.2. Delayed front left wheel acceleration and that of rear left wheel
acceleration generated by sinusoidal road disturbance simulation ......... 62
Figure 5.3. Wheelbase preview disturbance information. ............................ 64
Figure 5.4. Schematic of MPC concept ..................................................... 66
Figure 5.5. Frequency response of the passive vehicle at 10 kph ................. 71
Figure 5.6. Frequency response of the heave acceleration of the controlled
vehicle at 10 kph .............................................................................. 72
Figure 5.4. Frequency response of the pitch acceleration of the controlled
vehicle at 10 kph .............................................................................. 73
Figure 6.1. A quarter-car model with electro-mechanical actuator. .............. 76
Figure 6.2. Belt-driven ball screw actuator model ...................................... 77
Figure 6.3. Circuit diagram of the motor ................................................... 79
Figure 6.4. A vertical full-car model with EMS.......................................... 80
Figure 6.5. Accumulator spring stiffness to incorporate the actuator stroke
limit................................................................................................. 82
Figure 6.6. Mode and desired height level decision algorithm..................... 88
Figure 7.1. Comparison of ride comfort improvement simulation................ 97
Figure 7.2. Comparison of ride comfort improvement simulation...............101
Figure 7.3. Comparison of ride comfort improvement simulation for
v
unconstrained EMS system ..............................................................106
Figure 7.4. Comparison of ride comfort improvement simulation for
constrained EMS system .................................................................. 110
Figure 7.5. Simulation scenario for evaluation of the proposed EMS control
algorithm ........................................................................................ 111
Figure 7.6. Simulation scenario for evaluation of the proposed EMS control
algorithm ........................................................................................ 113
Figure 7.7. Heave acceleration of the vehicle body ................................... 114
Figure 7.8. Pitch angel of the vehicle ....................................................... 114
Figure 7.9. Roll angel of the vehicle ........................................................ 114
Figure 7.10. FL suspension displacement ................................................. 116
Figure 7.11. RR suspension displacement................................................. 116
Figure 7.12. FL actuator stroke ................................................................ 117
Figure 7.13. RR actuator stroke ............................................................... 117
Figure 7.14. Estimated FL suspension speed at double lane change ............ 117
vi
Contents
Chapter 1 Introduction ........................................................1
1.1. Background and Motivation ..................................................... 1
1.2. Previous Researches.................................................................. 4
1.3. Thesis Objectives .................................................................... 10
1.4. Thesis Outline ......................................................................... 11
Chapter 2 Description of an Electro-mechanical Suspension
(EMS) system ............................................ 12
Chapter 3 An Active Suspension System Model ................. 15
3.1. Model Reduction of a Quarter-car Suspension System .......... 17
3.1.1. Conventional quarter-car model ............................................... 17
3.1.2. Model reduction...................................................................... 19
3.2. A Reduced Vertical Full-car Model......................................... 21
3.2.1. Model reduction of 7-DOF full-car model................................. 21
3.2.2. Model validation ..................................................................... 26
Chapter 4 Suspension State Estimation .............................. 29
4.1. Design of a Suspension State Estimator ................................. 30
4.1.1. Sensor configurations .............................................................. 31
4.1.2. Estimation of rear wheel acceleration ....................................... 33
4.1.3. Suspension state estimator ....................................................... 35
4.1.4. Algorithm to estimate sensor bias............................................. 37
4.2. Performance Evaluation of Estimator ..................................... 39
4.2.1. Simulation results ................................................................... 39
4.2.2. Vehicle test results .................................................................. 44
Chapter 5 Design of Active Suspension Control Algorithm. 53
vii
5.1. Linear Quadratic Optimal Control .......................................... 54
5.2. Wheelbase Preview Control .................................................... 57
5.2.1. Wheelbase preview information ............................................... 57
5.2.2. Optimal preview control .......................................................... 63
5.2.3. Model predictive control ......................................................... 65
5.3. Frequency Response Analysis of Controlled Vehicle ............. 70
Chapter 6 An Electro-mechanical Active Suspension
System....................................................... 75
6.1. EMS system modeling ............................................................ 77
6.1.1. Electro-mechanical actuator modeling ...................................... 77
6.1.2. Reduced vertical full-car model with EMS................................ 80
6.2. EMS System Control Algorithm ............................................. 87
6.2.1. Driving mode decision ............................................................ 87
6.2.2. Desired suspension state decision............................................. 93
6.2.3. Desired motor voltage decision ................................................ 94
Chapter 7 Performance Evaluation .................................... 96
7.1. Ride Comfort Control Performance ........................................ 97
7.1.1. Carsim® simulation results ...................................................... 99
7.1.2. EMS system simulation results ...............................................102
7.2. Mode Control Performance....................................................111
Chapter 8 Conclusions and Future works ......................... 118
Bibliography .................................................................. 120
Abstract in Korean.......................................................... 128
1
Chapter 1 Introduction
1.1. Background and Motivation
An automotive suspension system is one of the major components in a
vehicle. In general, a vehicle has one suspension for each wheel; hence a vehicle
has four wheels, it also has four suspensions. Within the available suspension
travel, aims of a vehicular suspension are: (a) to isolate the vehicle body from
external disturbances coming from irregular road surfaces and internal
disturbances created by cornering, acceleration, or deceleration, in order to
have ride comfort; (b) to carry the weight of the vehicle body; (c) to
accommodate variations in load, due to changes in the number of passengers
and luggage, or from internal disturbances; and (d) to keep a firm contact
between the road and the tires, for good handling performance thus improving
drive safety. One can say that the suspension system plays major role in safety
and ride comfort of a vehicle [Williams'94, Appleyard'95, Cao'08]. Thereby,
research and development of vehicular suspensions have been being concerned,
in order to meet ever-strengthening user requirements on ride quality and drive
safety [Xue'11].
It is well known that conventional passive suspensions represent a trade-off
between conflicting performance metrics such as the ride comfort and the road
holding. Since the late 1960s, vehicle suspension systems have been widely
investigated and studied because of their potential to improve the ride quality
2
[Els'07, Huang'06, Yoshimura'01]. An ideal vehicle suspension system should
be able to reduce the acceleration and the displacement of the vehicle body to
achieve ride comfort. Meanwhile an acceptable level of suspension deflection
and tire deflection should also be maintained as handling measures.
Active suspension systems for passenger vehicles have been a very active
area of research for several decades owing to their potential to improve the ride
comfort and handling performance. This is because active systems offer
additional functionalities and therefore enlarge the full driving dynamics
potential of a vehicle by employing different types of actuator such as
magnetorheological actuators and hydraulic actuators. Although an active
system shows an outstanding performance, it consumes heavy amount of power
compared to a semi-active or a passive system.
Performance improvements and power consumption is a tradeoff in active
system [Singal'13]. Since active control requires extra energy compared to
passive and semi-active system, it has not been widely considered in the real
world. This challenge must be faced and solved due to the fact that the active
system is indispensable in the future to maximize ride quality and handling
performance [Yoshihiro'96].
Recently, Daimler AG introduced the world’s first actively controlled
hydraulic suspension system called active body control, which has been
successfully implemented in several Mercedes–Benz models [Rajala'11].
Another example is the system by BMW, which has developed an anti-roll
control hydraulic actuator in the center of the rear anti-roll bar [Strassberger'04].
3
Active suspensions have even greater potential if preview information of the
oncoming road height profile is available. There are various ongoing projects
trying to achieve better driving performance using road preview information.
Mercedes-Benz introduced the world’s first actively preview controlled
suspension system by detecting road surface undulations in advance. BMW is
trying to develop video image processing system for suspension control.
Volkswagen has undertaken researches to prepare and operate suspension parts
by road sensing with radar/ laser sensors. Honda holds a patent for adaptive
active suspension and aware vehicle network system.
From a careful review of considerable amount of literature, preview active
suspension control technology has the potential to promote passenger’s safety
and convenience simultaneously. However, the current state-of-the-art in
preview active suspension control technology has main challenge on obtaining
road preview information. It requires precise, expensive sensors to detect road
information such as a laser scanner. While the cost of these sensors is going
down, integrating them into series production vehicles will increase the price
and represent yet another barrier to market.
Therefore, this dissertation focused on developing a partial preview control
algorithm using road information with less detail. Still this would include
acceleration information of front wheels which was used to obtain preview
control inputs for rear suspension actuators.
4
1.2. Previous Researches
The main objective of active suspension systems is to reduce motions of the
sprung mass. Use of optimal control theory for designing active vehicle
suspension systems have been proposed by many researchers. Davis and
Thompson obtained optimal control by measurement of axle acceleration and
of axle to body displacement, and the incorporation of a term corresponding to
the integral of the axle to body displacement has achieved zero steady state
response to both static body forces and ramp road inputs [Davis'88]. Krtolica et
al. developed a complete analytical solution for a two-dimensional half-car
model in which the unsprung masses have not been included [Krtolica'90].
Shirahatt et al. obtained the optimal suspension parameters of a passive
suspension and active suspension for a passenger car which satisfies the
performance as per ISO 2631 standards by genetic algorithm [Shirahatt'08].
To understand the performance improvement more realistically, the existing
actuator limitation should be incorporated when designing the controller. For
active suspension systems, the bump stoppers mechanically constrain the
suspension deflections; thus constraining the actuator displacements at the
same time. Also the controller design should consider rate of the actuator
displacement, too. The linear quadratic regulator (LQR) controller design is
suitable at minimizing a linear cost function without explicitly incorporating
hard constraints. Köse et al. proposed state and output feedback scheduled
controllers with sufficient conditions to satisfy a parameter-dependent
performance measure, without violating the saturation bounds [KöSe'03]. Sun
5
et al. proposed a saturated adaptive robust control strategy to handle the
saturation constraints by anti-windup compensation approach [Sun'13].
It is shown that using a force control loop to compensate the hydraulic
dynamics can destabilize the system [Alleyne'98]. This full nonlinear control
problem of active suspensions has been investigated using several approaches
including optimal control. Moreover, several assumptions of linearity in the
parameters are needed, which actual systems may not satisfy. The use of fuzzy
logic systems has accelerated in recent years in many areas, including feedback
control. Cal and Konik proposed a fuzzy logic approach for the active control
of a hydro-pneumatic actuator [Cal'96]. Particularly important in fuzzy logic
control are the universal function approximation capabilities of the systems
[Kosko'92, Kosko'94]. Given these recent results, some rigorous design
techniques for fuzzy logic feedback control based on adaptive control
approaches have now been given [Wang'92, Wang'94]. Fuzzy logic systems
offer significant advantages over adaptive control, including no requirement for
linearity in the parameters assumptions and no need to compute a regression
matrix for each specific system. Fuzzy logic control schemes have been used to
control suspension systems. For example, Salem and Aly designed a quarter-
car system on the basis of the concept of a four-wheel independent suspension
system. They proposed a fuzzy control for active suspension system to improve
the ride comfort [Salem'09].
In active suspension systems, inevitable uncertainties often emerge. Roughly
speaking, the uncertainties can be classified into two categories: parametric
uncertainties and general uncertainties. Gaspar et al. have used a robust
6
controller for a full vehicle linear active suspension system using the mixed
parameter synthesis [Gaspar'03]. Chamseddine et al. developed a method for
the purpose of sensor fault diagnosis and accommodation [Chamseddine'06]. A
sliding mode technique is designed for a linear full vehicle active suspension
system. Yagiz et al. designed a sliding mode controller for a non-linear seven
degrees of freedom vehicle model [Yagiz'00]. Yagiz and Yuksek designed an
SMC for a linear model [Yagiz'01]. In these two studies, the robustness of the
controller has been shown by varying the vehicle parameters such as the vehicle
mass and the damper ratios.
Due to inherent strong nonlinearities in the damper and spring components,
inevitably the nonlinear effect must be taken into account in designing the
controller for practical active suspension systems. Suspension control design
mainly focuses on the following three motions of the vehicle: vertical
movement at center of gravity, pitching movement and rolling movement. An
intelligent controller can be used to design a control system for a full vehicle
nonlinear active suspension system such as neural controller. Neural networks
are capable of handling complex and nonlinear problems, process information
rapidly and can reduce the engineering effort required in controller model
development. These methods provide an extensive freedom for control
engineers to deal with practical problems of vagueness, uncertainty, or
imprecision. These intelligent methods are good candidates for alleviating the
problems associated with active suspension control systems [Rumelhart'86,
Narendra'90].
Active suspensions have even greater potential if preview information of the
7
oncoming road height profile is available. An optimal control for previewing
active suspension systems can be derived using the Hamilton function [Hac'92,
Balzer'81]. This is the common optimal preview control (OPC) approach in the
current literature and results in a LQR as a state feedback and a preview
feedforward term calculated from the oncoming road height profile
[Thompson'98, Louam'92, Youn'00, Kang'09, Martinus'96, Huisman'93a,
Huisman'93b, Marzbanrad'04, Senthil'96].
Furthermore, model predictive control (MPC) is a promising design scheme,
since information about the future is available and actuator constraints can be
explicitly incorporated [Mehra'97, Cho'99, Cho'05, Göhrle'12, Göhrle'13,
Göhrle'14, Göhrle'15].
Most of these researches above assume that all state variables are available.
However, implementation of these suspension control laws requires
information on states which may be difficult to access. Indeed, one of issues in
active / semi-active suspension control is to estimate states of the suspensions
from easily accessible and inexpensive measurements such as accelerations or
angular velocities for on-board suspension control applications. This requires
observer that can produce estimates of the states such as suspension deflection
and velocity using reduced number of sensors. The implementation of the
observer with low cost sensors is one of the main challenges to car
manufacturers that aim at equipping mass-produced cars with controlled
suspension systems.
Observers to estimate suspension states have been developed in many
researches. J.K. Hedrick et al. proposed disturbance-decoupled observers for
8
semi-active and fully active suspension systems [Hedrick'94]. R. Rajamani and
J.K. Hedrick proposed an adaptive observer for a class of nonlinear suspension
systems [Rajamani'93]. In deterministic case, K. Yi provided a bilinear observer
for semi-active suspension systems whose estimation error is independent of
the unknown disturbance [Yi'95]. The disturbance-decoupled observer for
semi-active suspension was developed in stochastic case by K. Yi and B.S.
Song [Yi'99]. N. Pletschen and K. J. Diepold proposed a nonlinear state
estimation approach which combines Kalman filter theory and Takagi-Sugeno
modelling and applied to a hybrid vehicle suspension [Pletschen'17]. In these
works, the observers were provided for estimation of quarter car model states
only.
However, relatively little work has been done about observers with full-car
model. L. Dugard et al. proposed a H∞ observer with 7-DOF full-car model
[Dugard'12]. In their work, the observer was designed by minimizing the
unknown disturbance effect on the estimated state variables. However, effects
of measurements noise were not considered in the design process. H. Ren et al.
proposed a suspension state observer based on unscented Kalman filter to
improve the robustness against parameters variation of the semi-active
suspension control strategy and to be adaptive to different types of unknown
road disturbances [Ren'16]. In their work, the road disturbance is considered as
system process noise, however, the sensitivity to unknown disturbance is not
discussed analytically.
From a careful review of considerable amount of literature, preview active
suspension control technology has the potential to promote both safety and
9
convenience simultaneously. However, the current state-of-the-art in preview
active suspension control technology has main challenge on obtaining road
preview information. It requires detailed road information that currently can be
obtained by only expensive sensors such as a laser scanner or a precision level
of road information from stereo vision sensors. While the cost of these sensors
is going down, integrating them into cars will increase the price and represent
yet another barrier to adoption. Moreover, a drawback of “look-ahead” sensor
is that they are vulnerable to water, snow, or other soft obstacles on the road.
For example, they recognize a heap of leaves as a serious obstacle, while a
pothole filled with water, will not detected at all.
Therefore, this dissertation would focus on developing a partial preview rear
suspension control algorithm without information. The measured vertical
acceleration information of front wheels is used to obtain preview control
inputs for rear suspension actuators. This wheelbase preview is relatively
reliable and economical compared with look-ahead sensor. A novel 3-DOF full-
car model is adopted to design a road disturbance-decoupled suspension state
observer. The vertical acceleration measurements of the front wheels and
estimated vertical acceleration of the rear wheels are regarded as system inputs
in the time process model. Two sensor configurations are considered to make
measurement information which is easily accessible and convenient to use for
active / semi-active suspensions.
10
1.3. Thesis Objectives
This dissertation focused on developing a partial preview control algorithm
with limited road preview information to improve the driving performance.
From a considerable amount of literature, preview active suspension control
technology has the potential to promote both ride comfort and safety of
passengers. However, the current state-of-the-art in preview active suspension
control technology has main challenge on obtaining road preview information
and state estimation.
Mainly three research issues are considered: how to cope with the unknown
road disturbance, how to estimate the suspension state variable, and how to
control the vehicle. In the remainder of this thesis, we will provide an overview
of the overall architecture of the proposed preview active suspension control
algorithm and the experimental results which shown the effectiveness of the
proposed state estimation algorithm. The effectiveness of the proposed preview
active suspension control algorithm has been evaluated via computer
simulations. The results show the improved ride comfort and handling
performance on scenarios such as bump, double lane change, J-turn, squat and
dive.
11
1.4. Thesis Outline
This dissertation is structured in the following manner. An overall
architecture of the proposed active suspension control algorithm is described in
Chapter 2. In Chapter 3, a conventional active suspension model is introduced
and model reduction is conducted. In Chapter 4, a suspension state estimator is
introduced and shows the experiment results for the evaluation of the estimation
performance. In Chapter 5, the concept of preview information for rear
suspension from front suspension is introduced. Then an algorithm for
wheelbase preview active suspension control is designed based on OPC and
MPC approaches. In Chapter 6, an electro-mechanical suspension (EMS)
system and control algorithm are introduced. The proposed modeling and
control methods in previous chapters are applied. Chapter 7 shows the
simulation results for the evaluation of the performance of the proposed EMS
control algorithm. Then the conclusion which describes the summary and
contribution of the proposed active suspension control algorithm and future
works is presented in Chapter 8.
12
Chapter 2 Description of an Electro-
mechanical Suspension (EMS) system
All active suspensions implemented in automobiles today are based on
hydraulic or pneumatic operation. Although hydraulic systems have already
proved their potential in commercial systems, there are three main
disadvantages: inefficiency due to the continuously pressurized system, a
relatively high system time constant and environmental pollution issues
because of hose leaks and ruptures. An electro-mechanical suspension system
can resolve the disadvantages of hydraulic systems since continuous power is
not needed, control is easy and no fluids are present. In this research, a control
algorithm for an electro-mechanical suspension system is proposed to improve
the driving performance of a vehicle.
From a considerable amount of literature, preview active suspension control
technology has the potential to promote not only safety of passengers but also
convenience. However, the current state-of-the-art in preview active suspension
control technology has main challenge on obtaining road preview information
and state estimation. It requires precise, expensive sensors to detect road
information such as a laser scanner or a stereo camera. While the cost of these
sensors is going down, integrating them into cars will increase the price and
represent yet another barrier to adoption. Moreover, a drawback of “look-ahead”
13
sensor is that they are vulnerable, potentially confused by water, snow, or other
soft obstacles.
Therefore, in this research, we focus on developing a partial preview control
algorithm without road information. As aforementioned, mainly three research
issues are considered: how to cope with the unknown road disturbance, how to
estimate the suspension state variable, and how to control the vehicle. The
system architecture of the algorithm is outlined in Figure 2.1. The proposed
control algorithm consists of mode selector, upper-level and lower-level
controllers, and suspension state observer. The mode selector determines a
present driving mode and desired height level of the vehicle. The upper-level
controller determines the desired suspension state considering the actuator
stroke limit. The electro-mechanical actuator is driven by a motor which is
controlled by a motor voltage controller, so the lower level controller calculates
the voltage at each actuator motor using estimated state by the observer and the
calculated desired state. A novel 3-DOF full-car model is adopted to design a
road disturbance-decoupled suspension state observer and lower level
controller. To improve the ride comfort performance, the vertical acceleration
information of front wheels is used to obtain preview control inputs for rear
suspension actuators.
In the remainder of this thesis, we will provide an overview of the overall
architecture of the proposed EMS control algorithm and the experimental and
simulation results which shown the effectiveness of the proposed algorithm.
14
Mode
Selector Lower
Level
Controller
Actuator
Vehicle
Sensor
State
Observer
EMS Control Algorithm
Upper
Level
Controller
Figure 2.1. Schematic diagram of the electro-mechanical suspension control
algorithm for a vehicle. The proposed control algorithm consists of mode
selector, upper-level and lower-level controllers, and suspension state observer.
15
Chapter 3 An Active Suspension System
Model
An active suspension is one including an actuator that can supply active force,
which is regulated by a control algorithm using data from sensors attached to
the vehicle. An active suspension is composed of an actuator and a mechanical
spring, or an actuator, a mechanical spring and a damper. It belongs to the high-
bandwidth active suspension controlling both the sprung mass and the unsprung
mass if the active actuator works mechanically in parallel with the spring. It is
the low-bandwidth active suspension controlling the sprung mass if the active
actuator works mechanically in series with the spring and the damper. In general,
the frequency of the unsprung mass lies in the range of 10 ~ 15 Hz, and the
frequency of the sprung mass lies in the range of 1 ~ 2 Hz. Due to supplying
active force control, active suspensions provide the possibility to fully
accomplish the aims of automotive suspensions. Three typical quarter-car
models of active suspensions according to the actuator bandwidth are illustrated
in Figure 3.1 ~ 3.3 [Xue'11]. The main objective of suspension systems is to
reduce motions of the sprung mass against to the uneven road surface. An
appropriate control input is calculated through modeling process.
16
ms
mu
Figure 3.1. Quarter-car model of a high-bandwidth active suspension.
ms
mu
Figure 3.2. Quarter-car model of a medium-bandwidth active suspension.
ms
mu
Figure 3.3. Quarter-car model of a low-bandwidth active suspension.
17
3.1. Model Reduction of a Quarter-car Suspension
System
In this section, a conventional quarter-car model is formulated for active
suspension control. Then, model reduction is conducted to cope with the
unknown road disturbance and state estimation.
3.1.1. Conventional quarter-car model
In many previous literature, the common approach is to use quarter-car
[Canale'06], half-car [Marzbanrad'04], or full-car models [Unger'11] with
sprung mass and unsprung mass. This approach can regulate motions of both
vehicle body and wheel because both dynamics are incorporated in model
representation. For example, equations of quarter-car model of a medium-
bandwidth active suspension shown in Figure 3.2 is given as follows:
s s s u s u a
u u s u s u t u r a
m z k z z c z z f
m z k z z c z z k z z f
(3.1)
where the subscript s, u, t, and r denote vehicle body, wheel, tire, and road,
respectively. m denotes the mass, k denotes the spring stiffness, c denotes the
damping coefficient, z denotes the vertical displacement which respect to the
static equilibrium position, and fa denotes the control force from actuator. The
state-space formulation from (3.1) is obtained as follows:
wx = Ax+ Bu + B w (3.2)
where the state vector consists of the vehicle body displacement from the wheel,
the wheel displacement from the road, absolute velocity of the body, and
18
absolute velocity of the wheel. The controlled input of the system is force from
actuator, and absolute velocity of the road surface is disturbance to the system
as follows:
T
s u u r s u
a
r
x z z z z z z
u f
w z
The system matrix, input matrix, and disturbance input matrix is given as
follows:
0 0 1 1 0
00 0 0 1 0
110 , ,
0
1 0
w
s s s s
t
uu u u u
k c cA B B
m m m m
kk c c
mm m m m
This conventional state-space representation for quarter-car model has two
limitations from a practical point of view. First, some state variables such as
suspension deflection, absolute velocity of the body and wheel are difficult to
access directly [Davis'88]. Second, the disturbance input, absolute velocity of
the road surface, is unknown or hard to know. It requires precise, expensive
sensors to detect road information such as a laser scanner or a stereo camera.
Moreover, a drawback of such sensor is that they are vulnerable, potentially
confused by water, snow, or other soft obstacles [Arunachalam'03]. In these
reasons, the conventional model is not suitable for controller implementation
of active suspension system.
19
3.1.2. Model reduction
A model reduction is conducted to overcome the limitation of conventional
quarter car model. The model reduction is proposed from the fact that the
electro-mechanical actuator considered in this research has a much lower
operating frequency (~ 5 Hz) than eigenfrequency of the wheel (10 ~ 15 Hz).
Using the conventional model, a suspension controller calculates high-
frequency control signals to influence wheel dynamics, which cannot be
realized by the actuator [Göhrle'14]. Hence, only the vehicle body dynamics is
considered and wheel dynamics is ignored. This approach has been hardly
proceeded in the literature [Krtolica'90, Göhrle'15]. In their works, however,
the unknown road disturbance still remains. A novel state-space representation
for reduced quarter-car model which is free from unknown disturbance is
proposed in this research.
From (3.1), using only the vehicle body dynamics equation, the state-space
representation for reduced quarter-car model is obtained as follows:
,reduced r reduced r w r reducedx = A x + B u + B w (3.3)
where the state vector consists of vehicle body displacement and its velocity
from the wheel. The controlled input of the system is force from actuator, and
the vertical wheel acceleration is disturbance to the system as follows:
T
reduced s u s u
a
reduced u
x z z z z
u f
w z
The system matrix, input matrix, and disturbance input matrix is given as
20
follows:
,
0 1 00
, ,11
r r w r
s s s
A B Bk c
m m m
When compared with the conventional model, the reduced one has half-size
system matrix because of ignoring wheel dynamics. Therefore, the wheel
deflection, absolute velocity of the body, and absolute velocity of the wheel are
no states of the reduced model and hence do not have to be observed for
controller implementation. Moreover, it is noted the disturbance input can be
measured easily by accelerometers on the wheel. From the measured
disturbance, it is possible to design a suspension state observer which is
independent from unknown road disturbance. Using the reduced model without
modeled wheel dynamics, the controller calculates control signals in a feasible
frequency range.
21
3.2. A Reduced Vertical Full-car Model
3.2.1. Model reduction of 7-DOF full-car model
The classical linearized 7-DOF full-car model considered heave, pitch, and
roll motions of the sprung mass and vertical motions of the four unsprung
masses [Esmailzadeh'97, ElBeheiry'96]. In Figure 3.4, a typical 7-DOF vertical
full-car model is shown. The variables of the model and nominal parameter
values of typical sedan given in Carsim® are given in Table 3.1. The equations
of body motion of the full-car model are given as follows:
1 1 1 2 2 2 3 3 3 4 4 4
1 1 1 2 2 2 3 3 3 4 4 4
1 2 3 4
1 1 1 2 2 2 3 3 3 4 4 4
1 1 1
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( )
s s s u s u s u s u
s u s u s u s u
xx s u f s u f s u r s u r
s u
m z k z z k z z k z z k z z
c z z c z z c z z c z z
f f f f
I k z z t k z z t k z z t k z z t
c z z
2 2 2 3 3 3 4 4 4
, , 1 2 3 4
1 1 1 2 2 2 3 3 3 4 4 4
1 1 1 2 2 2 3 3 3 4
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
f s u f s u r s u r
roll f roll r f f r r
yy s u f s u f s u r s u r
s u f s u f s u r
t c z z t c z z t c z z t
K K t f t f t f t f
I k z z l k z z l k z z l k z z l
c z z l c z z l c z z l c
4 4
1 2 3 4
( )
( ) ( )
s u r
f r
z z l
l f f l f f
(3.4)
The dynamic equations of bounce motion of wheels are given as follows:
1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4 4 4
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
u u s u s u t u r
u u s u s u t u r
u u s u s u t u r
u u s u s u t u r
m z k z z c z z k z z f
m z k z z c z z k z z f
m z k z z c z z k z z f
m z k z z c z z k z z f
(3.5)
22
X
Y
Z
zu1
zs1
zu2zu3
k1,c1
k2,c2
k3,c3
k4,c4
zs2
zs3
zs4
2tf
2tr
lf
lr
zs
zu4
ms,Ixx,Iyy
zr1
zr3
zr2
zr4
f1
f3
f2
f4
Figure 3.4. The 7-DOF vertical full-car model.
Table 3.1. The variables and nominal parameters of full-car model used in
simulation study.
Parameter/
variable Description Value
ms Sprung mass 1653 kg
mu Unsprung mass 45 kg
Ixx, Iyy Roll and pitch moment of inertia 614, 2765 kg∙m2
k1,2 Front suspension stiffness 25222 N/m
k3,4 Rear suspension stiffness 29220 N/m
k t Tire stiffness 230000 N/m
Kroll,f ,r Roll stiffness of front and rear axle 22000 N∙m/rad
c1,2 Front damping ratio 4721 N∙s/m
c3,4 Rear damping ratio 3979 N∙s/m
tf ,tr Distance from C.G. to front/rear left tire 0.8, 0.8 m
lf Distance from C.G. to front axle 1.402 m
lr Distance from C.G. to rear axle 1.646 m
L The wheel base 3.048 m
zs Vertical displacement of C.G. of sprung mass
zsi Vertical displacement of i-th point of sprung mass i=1…4
zui Vertical displacement of unsprung masses i=1…4
zri Vertical displacement of road under every wheel i=1…4
θ Sprung mass pitch angle
ϕ Sprung mass roll angle
fi Controlled force from i-th actuator i=1…4
23
The linearized kinematic equations involved with vertical displacement at
each corner of sprung mass and vertical displacement/attitude of C.G of the
sprung mass are given as follows:
1
2
3
4
s s f f
s s f f
s s r r
s s r r
z z l t
z z l t
z z l t
z z l t
(3.6)
In the proposed reduced full-car model, vertical motions of the four unsprung
masses are not considered as mentioned in chapter 3.1.2, but their vertical
accelerations are regarded as disturbance input to the system. From (3.4) and
(3.6), the state-space representation for reduced full-car model is obtained as
follows:
wx Ax Bu B w (3.7)
where the state vector consists of suspension displacement and its velocity at
each corner, and vertical, roll, and pitch velocity of the body. The controlle d
input vector of the system consists of force from each actuator, and the vertical
acceleration at each wheel is disturbance to the system as follows:
1 1 1 1 2 2 2 2
3 3 3 3 4 4 4 4
1 2 3 4
1 2 3 4
s u s u s u s u
T
s u s u s u s u
T
T
u u u u
z z z z z z z z
z z z z z z z z z
f f f f
z z z z
x
u
w
(3.8)
The system matrix, input matrix, and disturbance input matrix is given as
follows:
24
0 0 0 0
1 0 0 0
0 0 0 0
0 1 0 0
0 0 0 0
, , 0 0 1 0
0 0 0 0
0 0 0 1
0 0 0 0
0 0 0 0
0 0 0 0
1 1
2 2
3 3
4 4
5 5
w6 6
7 7
8 8
9 9
10 10
11 11
A B
A B
A B
A B
A B
A B BA B
A B
A B
A B
A B
A B
where
2 2 2 2 2 2
1 1 2 21 1 1 2 2 2
3 3 4 43 3 3 4 4 4
0 1 0 0 0 0 0 0 0 0 0
0 0 0
0 0 0 1 0 0
f f f f f f
s yy s xx yy s yy s xx yy
f r f r f r f r f r f r
s yy s xx yy s yy s xx yy
l t l l t lk c k ca k c c a k c c
m I m I I m I m I I
l l t t l l l l t t l lk c k cb k c c b k c c
m I m I I m I m I I
1
2
3
A
A
A
2 2 2 2 2 2
1 1 2 21 1 1 2 2 2
3 3 4 43 3 3 4 4 4
0 0 0 0 0
0 0 0
0 0 0 0 0 1 0 0 0 0 0
f f f f f f
s yy s xx yy s yy s xx yy
f r f r f r f r f r f r
s yy s xx yy s yy s xx yy
l t l l t lk c k ca k c c a k c c
m I m I I m I m I I
l l t t l l l l t t l lk c k cb k c c b k c c
m I m I I m I m I I
4
5
6
A
A
A
1 1 2 21 1 1 2 2 2
2 2 2 2 2 2
3 3 4 43 3 3 4 4 4 0 0 0
0 0 0 0 0 0 0 1 0 0 0
f r f r f r f r f r f r
s yy s xx yy s yy s xx yy
r r r r r r
s yy s xx yy s yy s xx yy
l l t t l l l l t t l lk c k cc k c c c k c c
m I m I I m I m I I
k cl t l k l c t ld k c c d k c c
m I m I I m I m I I
7A
25
1 1 2 21 1 1 2 2 2
2 2 2 2 2 2
3 3 4 43 3 3 4 4 4
1 1 2 2
0 0 0
f r f r f r f r f r f r
s yy s xx yy s yy s xx yy
r r r r r r
s yy s xx yy s yy s xx yy
s s s s
l l t t l l l l t t l lk c k cc k c c c k c c
m I m I I m I m I I
k cl t l k l c t ld k c c d k c c
m I m I I m I m I I
k c k c
m m m m
8
9
A
A 3 3 4 4
1 2 3 4
1 1 2 2 3 3 4 4
0 0 0
0 0 0
0 0 0
s s s s
f f r r
f xx f xx f xx f xx
f f f f r r r r
yy yy yy yy yy yy yy yy
k c k c
m m m m
t c t c t c t ca a b b
t I t I t I t I
l k l c l k l c l k l c l k l c
I I I I I I I I
10
11
A
A
, ,, ,
1 3 1 32 2 2 2
f roll f f roll froll r roll rr rf r f r
xx f xx r xx f xx r
t K t KK Kt ta k t b k t c k t d k t
I t I t I t I t
2 2 2 2
2 2 2 2
0 0 0 0
1 1 1 1
1 1 1 1
1
f f f f f r f r f r f r
s xx yy s xx yy s xx yy s xx yy
f f f f f r f r f r f r
s xx yy s xx yy s xx yy s xx yy
f r f
s xx
t l t l t t l l t t l l
m I I m I I m I I m I I
t l t l t t l l t t l l
m I I m I I m I I m I I
t t l l
m I
1 3 5 7
2
4
6
B B B B
B
B
B2 2 2 2
2 2 2 2
1 1 1
1 1 1 1
1 1 1 1
r f r f r r r r r
yy s xx yy s xx yy s xx yy
f r f r f r f r r r r r
s xx yy s xx yy s xx yy s xx yy
s s s s
f f r r
xx xx xx xx
t t l l t l t l
I m I I m I I m I I
t t l l t t l l t l t l
m I I m I I m I I m I I
m m m m
t t t t
I I I I
8
9
10
B
B
B
f f r r
yy yy yy yy
l l l l
I I I I
11B
26
3.2.2. Model validation
The derived vehicle model (3.7) is validated via simulation with vehicle
software Carsim® and MATLAB/Simulink. Therefore, it is driven with the test
vehicle in Carsim® with actuator force equal to zero over a road, where the
height profile was pre-defined. The measured vertical wheel acceleration from
the test vehicle was input to the proposed model simultaneously. Hence,
simulated heave, roll, and pitch motion and suspension state are compared to
the values measured in the vehicle.
An irregular and asymmetric road height profile used in model validation is
shown in Figure 3.5. The speed of test vehicle was 20 kph. Figure 3.6 and 3.7
show that the vehicle body motion and suspension deflection calculated from
the proposed vertical full-car model. It is shown that the results from the model
correspond well with the actual values. A small error is occurred mainly from
nonlinear damping characteristics of the test vehicle which is not considered in
the linear model. However, the error is tolerable for suspension control in the
interesting frequency range up to about 5 Hz.
Figure 3.5. The height profile of the road for model validation.
27
Figure 3.6. Comparison of vehicle body motion of actual and simulated
vehicle. (a) vertical displacement, (b) roll angle, and (c) pitch angle
28
Figure 3.7. Comparison of suspension deflection of actual and simulated
vehicle. (a) FL, (b) FR, (c) RL, and (d) RR suspension
29
Chapter 4 Suspension State Estimation
In recent decades, many suspension control approaches to improve ride
quality and handling performance were developed assuming that all states are
available. Implementation of these suspension control laws requires
information on states which may be difficult to access. Indeed, one of issues in
active / semi-active suspension control is to estimate states of the suspensions
from easily accessible and inexpensive measurements such as accelerations or
angular velocities for on-board suspension control applications. This requires
observer that can produce estimates of the states such as suspension deflection
and velocity using reduced number of sensors. The implementation of the
observer with low cost is one of the main challenges to car manufacturers aim
at equipping mass-produced cars with controlled suspension systems.
In this chapter, a road disturbance-decoupled suspension state observer is
designed based on the reduced full-car model. Two sensor configurations are
considered to make measurement information which is easily accessible and
convenient to use for active / semi-active suspensions. The estimation
performance of the proposed observer has been examined via simulation study
and field tests.
30
4.1. Design of a Suspension State Estimator
The overall structure of suspension state observer with reduced full-car model
is shown in Figure 4.1. The proposed system involves three elements:
measurement of body and front wheel motion, estimation of rear wheel
acceleration, and suspension state observer. The functions and relationship
between the three elements can be summarized as follows.
The suspension states (x) and acceleration of wheels (�̈�𝒖) are influenced by
the vertical road displacement input (𝒛𝒓). The body motion is measured by
accelerometers or gyroscopes which is represented by y in Figure 4.1. The
acceleration of front wheels is measured by accelerometers which is
represented by �̈�𝒖,𝒇∗ in Figure 4.1. These measurements are utilized in
suspension state observer and rear wheel acceleration estimator. Two sensor
configurations are introduced in subsection 4.1.1.
Vehicle
Reduced full car model
Body and front wheel motion sensors
Measurement update
Rear wheel acceleration estimator
Suspension state observer
Figure 4.1. Block diagram of suspension state observer.
31
The acceleration of rear wheels should be estimated because no
accelerometer is mounted at rear wheels in this research. The estimated
acceleration of rear wheels (�̂̈�𝒖,𝒓) is utilized in suspension state observer. This
estimator can be replaced by additional accelerometers, but using the least
sensors is one of goal in this work. The estimation algorithm and its analysis
are described in subsection 4.1.2.
The suspension state observer utilizes measured acceleration of front wheels
and estimated acceleration of rear wheels in time process model. The measured
body motion is utilized in measurement update to estimate the suspension state.
The priori state estimate and posteriori estimate are represented by �̂�− and �̂�+,
respectively in Figure 4.1. The Kalman filter to minimize the estimation error
covariance is designed in subsection 4.1.3.
4.1.1. Sensor configurations
As shown in Figure 4.2, two sensor configurations which are inexpensive to
be mounted are introduced in this section. Two accelerometers at front wheels
are used for the road disturbance input measurements in all sensor
configurations. The road disturbance input measurements are given in (4.1).
* * *
1 2 3 4
1 1 2 2 3 3 4 4
ˆ ˆ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
T
u u u u
T
u u u u
t z t z t z t z t t t
z t t z t t z t t z t t
w w ξ (4.1)
where ξi, i=1…4, are assumed to be zero mean stationary white noise processes.
32
X
Y
Z3 point body acceleration
Front wheel acceleration
X
Y
Z
Front wheel acceleration
Z-axis acceleration
X, Y-axis Angular velocities
(a) sensor configuration 1 (b) sensor configuration 2
Figure 4.2. Two sensor configurations for measurement.
From the sensor configuration 1, the body motion is measured from three
accelerometers mounted at three corners of the sprung mass. The measurement
equation is given in (4.2).
1 2 3( ) [ ( ) ( ) ( )] ( )
( ) ( ) ( )
( ) ( ) ( )
T
s s s
T TT T T T T T
t z t z t z t t
t t t
t t t
1 1
2 4 6 2 4 6 1
1 1 1
y v
A A A x B B B u v
H x J u v
(4.2)
From the sensor configuration 2, the body motion is measured from two gyros
and one accelerometers mounted at center of gravity point of the sprung mass.
The measurement equation is given in equation (4.3).
2 9 2 2
( ) [ ( ) ( ) ( )] ( )
( ) ( ) ( )0
( ) ( ) ( )
T
s
TT T T
t z t t t t
t t tI
t t t
2 2
9
9 10 11 2
2 2 2
y v
Ax B B B u v
H x J u v
(4.3)
where the measurement noise vectors v1 and v2 are assumed to be zero mean
stationary white noise processes.
33
4.1.2. Estimation of rear wheel acceleration
In the reduced full-car model as written in (3.7), each acceleration of wheels
is applied to the system as disturbance input and should be obtained. The exact
way to obtain the disturbance information is the acceleration measurement by
accelerometers mounted at each wheels. To reduce the number of sensors, only
two accelerometers at front wheels are used for the road disturbance input
measurements. Then the acceleration of the rear wheels should be estimated
and two estimation methods are proposed in this research.
The first method for estimation of acceleration of rear wheels is time delaying
of measured acceleration of front wheels. This time delay concept was proposed
in many previous work [Marzbanrad'04, Marzbanrad'02]. In these work, the
road disturbance input to front wheels is delayed equally to rear wheels. This
can be reasonable when the vehicle speed is constant. On the additional
assumption that the tire grip on the road is keeping with no tire deflection, the
acceleration of front wheels would be delayed to rear wheels as follows:
3 4 1 2ˆ ˆ( ) ( ) ( ) ( )
T T
u u u delay u delayz t z t z t t z t t (4.4)
where �̂̈�𝒖𝟑(𝒕) and �̂̈�𝒖𝟒(𝒕) are estimated rear left and right wheel acceleration,
respectively. tdelay is the delayed time which is represented with the longitudinal
velocity vx and the wheel base L as written in (4.5).
delay
x
Lt
v (4.5)
The time delaying method for estimation of acceleration of rear wheels is
based on the assumption of constant speed. When the vehicle speed is low, the
delayed time step is strongly influenced by the slight change of the speed. In
34
this case, the time delay method is not suitable and another method is proposed
to reduce the estimation error.
The second method for estimation of acceleration of rear wheels is using
estimated suspension velocity and body motion. For example, the rear left
suspension velocity which is the 6-th state variable in the reduced full-car
model as defined in (3.8) can be represented as (4.6) from the time derivative
of equation (3.6).
6 3 3
3
s u
s r r u
x z z
z l t z
(4.6)
From time derivative of equation (4.6), the acceleration of rear left wheel is
represented as follows:
3 6u s r r
dz z l t x
dt (4.7)
The estimated acceleration of rear left wheel can be written with the estimated
state variables as follows:
3 6
ˆ ˆˆ ˆ ˆu s r r
dz z l t x
dt (4.8)
In the same way, the estimated acceleration of rear right wheel can be
obtained as follows:
4 8
ˆ ˆˆ ˆ ˆu s r r
dz z l t x
dt (4.9)
If the present vehicle speed is higher than threshold value, the rear wheel
acceleration is estimated with the first method. Otherwise, the second method
is used in the rear wheel acceleration estimator.
35
4.1.3. Suspension state estimator
Considering the computing period of ECU, the discrete-time Kalman filter is
designed to minimize the estimation error covariance matrix. The continuous
system represented in (3.7) is transformed into a discrete-time system of which
the time step is T as follows:
k k-1 k-1 w k-1x Fx Gu G w (4.10)
where
1
1
T
T
T
e T
e T
e T
A
A
A
w w w
F I A
G F I A B B
G F I A B B
In this process, the real road disturbance input vector wk is substituted by the
measured and estimated wheel acceleration vector w* in (4.1). The
measurement noise vector ξk-1 is regarded as the process noise vector and then
the time process equation is represented as follows:
* k k-1 k-1 w k-1 k-1
x Fx Gu G w ξ (4.11)
The measurement equation (4.2), and (4.3) are also transformed into
discretized equations.
i i i i ,k k k ,ky H x J u v (4.12)
where the subscript i means the i-th sensor configuration hereinafter. The noise
processes ξk and vi,k are white, zero-mean, uncorrelated, and have known
covariance matrices Q and Ri, respectively:
36
, , ,
,
~ 0, ,
~ 0, ,
T
k j
T
i i i i i k j
T
i
E
E
E
k k j
k k j
k j
ξ Q ξ ξ Q
v R v v R
ξ v 0
After a posteriori estimated states �̂�𝟎+ and a posteriori error covariance
matrix 𝐏𝟎+ are initialized, the following equations are computed for each time
step [Simon'06]. A priori error covariance matrix 𝐏𝐤− is updated as follows:
T - +
k k-1P FP F Q (4.13)
The optimal Kalman gain is obtained by (4.14).
1T T
i i i i
- -
k k kK P H H P H R (4.14)
A time update, a posteriori estimation, and a posteriori error covariance
matrix are obtained by (4.15).
*
,
ˆ ˆ
ˆ ˆ ˆi i i
i
- +
k k-1 k-1 w k-1
k k k k k k
+ -
k k k
x Fx Gu G w
x x K y H x J u
P I K H P
(4.15)
The optimal Kalman gain is computed each step and the real-time matrix
inversions are conducted. This is a drawback of Kalman filter when the system
matrix size is large such as the full-car model. The steady-state Kalman filter is
not optimal, however, this can save a lot of computational effort and the
estimation performance is nearly indistinguishable from that of the optimal
Kalman filter. One way to determine the steady-state Kalman gain is finding
the steady-state value of the estimation error covariance matrix as written in
(4.16) which called a discrete algebraic Riccati equation (DARE).
37
1
T T T T
i i i i i
P FP F FP H H P H R H P F Q (4.16)
Once 𝐏∞ is obtained, the steady-state Kalman gain 𝐊∞ is obtained by
substitution of 𝐏∞ for 𝐏𝐤− in (4.14) as follows:
1T T
i i i i
K P H H P H R (4.17)
4.1.4. Algorithm to estimate sensor bias
In our work, because the sensor measurement is used for system disturbance
input, the sensor bias generates drift of the estimated states. To deal with the
unknown but constant sensor bias, a recursive algorithm to estimate the sensor
bias is considered. In B. Friedland’s work, the optimum estimate of the state
and constant bias for linear system is proposed [Friedland'69]. The main results
can be summed up as follows.
The dynamic equations and observation equation are written as (4.18).
1
1
k k k k k k
k k
k k k k k k
x A x B b
b b
y H x C b
(4.18)
where xk is the original process state, bk is the bias vector, ξk is process noise
vector, and ηk is observation noise vector. The ξk and ηk are white, zero-mean,
and uncorrelated.
The optimum estimate of the state can be expressed as
ˆˆ ( )k k x kx x V k b (4.19)
Where �̃�𝒌 is the bias-free estimate, computed as if no bias were present, �̂�𝒌
is the optimum estimate of the bias, and 𝑽𝒙(𝒌) is a matrix which can be
38
interpreted as the ratio of the covariance of �̃�𝒌 and �̂�𝒌. The bias-free state and
the bias estimation equations are written as follows:
1 1 1 1
1 1 1 1 1 1
( )
ˆ ˆ ˆ ˆˆ( ) ( )
k k k x k k k k
k k b k k k k k k k k
x A x K k y H A x
b b K k y H A x B b C b
(4.20)
where �̃�𝒌(𝒌) is the bias-free gain and 𝑲𝒃(𝒌) is the bias gain.
The results presented in his work are based on expressing the solution of the
estimation error variance equation of the problem with bias present in terms of
the solution of the variance equation for bias-free estimation and other matrices
which depend only on the bias-free computations. By this technique the
estimation of the bias is essentially decoupled from the computation of the bias-
free estimate of the state.
39
4.2. Performance Evaluation of Estimator
To evaluate the estimation performance of proposed observer, a simulation
study has been conducted by using the vehicle software Carsim® and
MATLAB/Simulink. Then the observer and semi-active damper prototype have
been implemented on a test vehicle.
4.2.1. Simulation results
Passing a single bump without actuator control scenario has been simulated
to evaluate the performance of the observer. The single bump road height
profile described by equation (4.21) is applied to the right wheels only so that
the roll and pitch motions are generated simultaneously.
2
1 cos ( 10) 10, 10( )
0
r b
r b
h X for X Lz X L
otherwise
(4.21)
where zr is road elevation, X is longitudinal displacement, hr is a half of the
bump height, and Lb is the bump width. In this study, hr =0.05 m and Lb=3.6 m
were used. The simulated vehicle speed was 20 kph. The nominal parameters
of simulated vehicle given in Carsim® are shown in Table 3.1 which is used to
design the observer. The nonlinear relation between the suspension velocity and
the damping force used in simulation study is shown in Figure 4.3.
40
Figure 4.3. The relation between the suspension velocity and the damping
force used in simulation given in Carsim® .
The proposed observer described in section 4.1 was designed to completely
decouple the unknown road disturbance. In other works, the road disturbance
was not completely removed and was considered as unknown input
[Pletschen'16, Dugard'12, Ren'16]. A disturbance-coupled observer with full-
car model has been designed to compare the estimation performance as written
as follows:
ˆ ˆ ˆ
o o o o o
o o o o
o o o o o o o o o
x A x B w
y H x v
x A x B w K y H x
(4.22)
where the state xc and disturbance input wc are defined as follows:
1~4 1~4 1~4
1 2 3 4
T
u s u u r
T
r r r r
z z z z z z
z z z z
o
o
x
w
The states are composed with bounce, roll, pitch velocities of the body, each
41
unsprung mass velocity, each suspension deflection, each tire deflection. The
unknown disturbance input is the derivative of road elevation, which is
considered as system process noise when the Kalman gain Ko is computed.
In Figure 4.4 and 4.5, comparison of some estimated states by the proposed
disturbance-decoupled observer (DDO) and disturbance-coupled observer
(DCO) and actual states (heaving acceleration, heaving, rolling, pitching
velocities, and suspension velocities) for the single bump simulation are shown.
The legend “actual” indicates that the signals have been obtained by Carsim®
outputs, and the legends “estimated, DDO” and “estimated, DCO” indicate that
the signals have been computed by the proposed disturbance-decoupled
observer and disturbance-coupled observer, respectively. The titles FL, FR, RL,
and RR represent the front left, front right, rear left, and rear right suspensions,
respectively. Both observers are designed with the sensor configuration 1. The
RMS noise value of accelerometer used in simulations are 0.049 m/s2. It is
illustrated that the estimation performance of the proposed DDO is much better
than that of the DCO because the proposed observer completely removes the
effect of unknown road disturbance on the estimation error. It is shown that the
estimated states by the proposed DDO are quite close to the actual states. In
Figure 4.5, it is also shown that the front suspension velocity is estimated more
accurately than rear suspension velocity by DDO. This estimation error is
mainly caused by the assumption that the road disturbance input is equally
delayed from front to rear wheels.
42
Figure 4.4. Comparisons of actual and estimated states by disturbance-
coupled observer and the proposed observer for single bump road test. (a)
heaving acceleration, (b) heaving, (c) rolling, and (d) pitching velocities.
43
Figure 4.5. Comparisons of actual and estimated suspension velocities by
disturbance-coupled observer and the proposed observer for single bump road
test. (a) FL, (b) FR, (c) RL, and (d) RR suspension.
44
4.2.2. Vehicle test results
In Figure 4.6, prototype of semi-active suspension system and sensors
mounted on front side of the test car are shown. Four semi-active damper
prototypes have been installed at each corner of the test car. The semi-active
damping force curves used in field test are shown in Figure 4.7. The damping
rate of each damper was controlled by unknown control strategy in real time
during the experiment. The proposed observer in this work would be used for
semi-active suspension control strategy, but the experiment has been conducted
to evaluate the estimation performance only. Therefore, the control logic was
assumed to be unknown. The measurement from accelerometers at three
corners of the sprung mass was used for state estimation and the measurement
from linear variable differential transformer (LVDT) was used for getting
reference data only. Using the LVDT data for state estimation is not suitable for
mass-produced cars because the deflection sensor is expensive and has a short
life-time. One accelerometer and two gyros have been mounted on the center
of gravity point of the sprung mass for measurement of heaving acceleration,
pitching and rolling velocity, respectively. These three body-mounted sensors
were used for getting reference data or state estimation.
Two test cases, single bump and low speed off-road, have been used to
evaluate the performance of the observer. In single bump case, the vehicle speed
was about 30 kph and the acceleration of rear wheels was estimated from time
delaying of measured acceleration of front wheels. In off-road case, the vehicle
speed was less than 5 kph and the acceleration of rear wheels was estimated by
using estimated suspension velocity and body motion.
45
Sprung mass
LVDT
Accelerometer
Semi-active damper prototype
Spring
Accelerometer
Figure 4.6. Semi-active suspension system of front side and mounted sensors
for the field test.
Figure 4.7. The damping force versus suspension velocity curves of the semi-
active damper prototype.
46
In Figure 4.8 ~ 4.11, comparisons of some estimated and measured states for
the single bump case and the off-road case are shown. The “reference” indicates
that the signals have been obtained by additional sensors, and the legends
“estimated1” and “estimated2” indicate that the signals have been computed by
the observers using the sensor measurements with the sensor configuration 1
and 2, respectively. In Figure 4.8 and 4.10, the reference data of heaving
velocity was obtained by numerical integration of measured acceleration from
body-mounted sensor. In Figure 4.9 and 4.11, the reference data of suspension
velocity was obtained by numerical differentiation of measured suspension
deflection from LVDT. In both test cases, it is illustrated that the estimated
states are quite close to the actual states for all sensor configurations and
therefore the estimation results can be used for semi-active suspension control
strategy in real-time. The root-mean-square errors of estimated states by
observers with the sensor configuration 1 and 2 are compared in Table 4.1. The
estimation performance of heaving, rolling, and pitching motion by observer
with sensor configuration 2 is better than that of observer with sensor
configuration 1 because the body motion measurement is used for state
estimation directly. The vertical acceleration measurement from accelerometers
at three corners of the sprung mass is distorted as rolling or pitching motion is
generated, while the measurement from accelerometer and gyros mounted on
the center of gravity point of the sprung mass is not influenced. The suspension
velocity is the most important state because many semi-active control strategies
are based on this signal. In general, the estimation performance of front
suspension velocity is better than that of rear suspension velocity because the
47
front wheel acceleration is measured directly whereas the rear wheel
acceleration is estimated to reduce the number of sensors. The suspension
velocity estimation performance of observer with the sensor configuration 1 is
similar to that of observer with the sensor configuration 2, relatively.
Table 4.1. The experimental estimation results
Estimated state
RMSEa
Single bump case Off-road case
S.C.b 1 S.C. 2 S.C. 1 S.C. 2
Heaving acceleration (m/s2) 0.297 0.053 0.309 0.013
Heaving velocity (m/s) 0.030 0.002 0.012 0.001
Rolling velocity (deg/s) 1.026 0.393 1.107 0.488
Pitching velocity (deg/s) 1.589 0.697 0.577 0.296
Suspension velocity, FL (mm/s) 42.2 28.5 37.7 28.4
Suspension velocity, FR (mm/s) 42.1 49.1 35.5 25.6
Suspension velocity, RL (mm/s) 58.8 61.6 39.0 41.3
Suspension velocity, RR (mm/s) 48.6 52.8 30.1 37.1
a Root-mean-square error
b Sensor configuration
48
Figure 4.8. Comparisons of reference data and estimated states for single
bump road case. (a) heaving acceleration (b) heaving velocity, (c) rolling
velocity, and (d) pitching velocity.
49
Figure 4.9. Comparisons of reference data and estimated suspension velocities
for single bump road case. (a) FL, (b) FR, (c) RL, and (d) RR suspension.
50
Figure 4.10. Comparisons of reference data and estimated states for off-road
case. (a) heaving acceleration (b) heaving velocity, (c) rolling velocity, and
(d) pitching velocity.
51
Figure 4.11. Comparisons of reference data and estimated suspension
velocities for off-road case. (a) FL, (b) FR, (c) RL, and (d) RR.
52
In Figure 4.12, the estimated acceleration of rear wheels by the two methods
discussed in subsection 4.1.2 for the off-road case is shown. The legends
“delayed” and “estimated” indicate that the signals have been computed by the
time delaying method and by the proposed method using estimated suspension
velocity and body motion, respectively. The reference data has been acquired
from additional accelerometers mounted on rear wheels. Because the vehicle
speed is low and not constant, the phase and magnitude of front wheel
acceleration is not equally delayed to rear wheel. In this case, the proposed
estimation algorithm has improved the estimation performance of the rear
wheel acceleration and suspension states.
Figure 4.12. Comparisons of measured and estimated acceleration of rear
wheels for off-road case. (a) RL, (b) RR
53
Chapter 5 Design of Active Suspension
Control Algorithm
From a careful review of considerable amount of literature, preview active
suspension systems have even greater potential than feedback systems.
However, the current state-of-the-art in preview active suspension control
technology has main challenge on obtaining road preview information. It
requires precise, expensive sensors to detect road information such as a laser
scanner or a stereo camera. Moreover, a drawback of “look-ahead” sensor is
that they are vulnerable, potentially confused by water, snow, or other soft
obstacles.
In this Chapter, active suspension control algorithm based on the reduced
vertical full-car model is introduced. The main control objective of low-
bandwidth active suspension control is ride comfort improvement such as
isolation of the vehicle body from external disturbances coming from irregular
road surfaces and internal disturbances created by cornering, acceleration, or
deceleration. A feedback control approach for ride comfort is considered, then
a partial preview control without road information is developed. The wheel base
preview is relatively reliable and economical when compared with look-ahead
sensor. The vertical acceleration information of front wheels was used to obtain
preview control inputs for rear suspension actuators.
54
5.1. Linear Quadratic Optimal Control
A time invariant linear system can always be stabilized by a linear feedback
if it is controllable or stabilizable. A linear quadratic (LQ) optimal control for
the reduced quarter-car model is introduced before it is extended to the reduced
vertical full-car model.
The reduced quarter-car suspension system in (3.3) is controllable. It can be
easily proved from that the controllability matrix written as (5.1) has full rank.
.
2
10
1
s
cont r r r
s s
mR B A B
c
m m
(5.1)
Therefore, the system can be stabilized by LQ optimal control. To find an
input that suffices both the requirement of fast control and does not require
infinite control power, an optimization problem has to be solved. A very useful
criterion is the quadratic integral criterion as follows:
0
lim
f
f
t
T T
c ct
J y t Qy t u t Ru t dt
(5.2)
where yc is the interested output variable and Q and R is a diagonal non-negative
weighting matrix containing the weighting factors. For ride comfort
improvement and regulation of the suspension rattle space, the yc can be
formulated as follows:
s
c reduced
s u
zy Cx Du
z z
(5.3)
55
where C and D is written as follows:
1
,
1 0 0
s s s
k c
m m mC D
Now consider (5.3), substituting this into (5.2) results in
0
0
0
lim
lim
lim
f
f
f
f
f
f
t
T T
reduced reducedt
t T T
T T
reduced reducedT Tt
t
c cT T
reduced reducedTt
c c
J Cx Du Q Cx Du u Ru dt
C QC C QDx u x u dt
D QC D QD R
Q Nx u x u dt
N R
(5.4)
If (Ar, C) is observable, then the optimal closed loop control system written
in (5.5) is stable.
1 T T
reduced r r c c r reducedx A B R N B P x (5.5)
where P (strictly positive definite) is the solution of the Riccati equation as
follows:
1 1
1 1 0
TT T
r r c c r r c c
T T
r c r c c c c
P A B R N A B R N P
PB R B P Q N R N
(5.6)
The control law is obtained as a state feedback
c reducedu K x (5.7)
with feedback gain, 1 T T
c c c rK R N B P .
The LQ optimal control can be applied to the reduced vertical full-car model
in (3.7). In reduced full-car model, the heave, roll, and pitch motion of the body
56
and suspension motion are interested output for ride comfort as follows:
1~4 1~4( ) ( )T
s s u s uz z z z z
cy Cx Du
(5.8)
with
TT T T T T T T T T T T
TT T T
9 10 11 1 3 5 7 2 4 6 8
9 10 11
C A A A Π Π Π Π Π Π Π Π
D B B B 0 0
where iΠ denotes a 𝟏 × 𝟏𝟏 matrix with a unity located in the i-th columns
and with remaining elements equal to zero. The output can be incorporated into
the quadratic integral criterion as follows:
0
0
lim
lim
f
f
f
f
t
T T
t
t
T T
t
J t t t t dt
dt
c c
c c
T
c c
y Qy u Ru
Q Nx u x u
N R
(5.9)
From a similar process, the feedback control law for the reduced full-car
suspension system is obtained as follows:
cu K x (5.10)
The feedback gain can be given as follows:
1 T T
c
c c
K R N B P (5.11)
Where P is the solution of the Riccati equation as follows:
1 1
1 1
TT T
T T
c c c c
c c c c c
P A BR N A BR N P
PBR B P Q N R N 0 (5.12)
57
5.2. Wheelbase Preview Control
In order to develop a preview control algorithm without road information,
the road disturbance delay between the front and the rear wheels is considered.
The wheelbase preview control algorithm using delayed disturbance has been
introduced before [Moran'93, Marzbanrad'02, Marzbanrad'03]. However, in
their work, the algorithm still has limitations from a practical point of view such
as assumption that suspension state and road disturbance is available. In our
work, the vertical acceleration information of front wheels can be used to obtain
preview control inputs for rear suspension actuators because it is the
disturbance input of the proposed reduced full-car model.
5.2.1. Wheelbase preview information
In (4.4), the vertical acceleration of front wheels is delayed equally to rear
wheels with assumptions that the vehicle speed is constant and the tire grip on
the road is keeping with no tire deflection. Considering the tire dynamics in
(3.5), an analysis of the time delay method is conducted on frequency domain.
Taking Laplace transforms for (3.4) and (3.5) without control input, the
following equation (5.13) and (5.14) can be obtained.
58
2
1 1 1 2 2 2 3 3 3
4 4 4 1 1 1 2 2 2
3 3 3 4 4 4
2
1 1 1 2 2 2 3 3 3
4 4
( ) ( ) ( ) ( ) ( ) ( ) ( )
( s ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( s ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( )
( )
s s s s s
s u u
u u
xx f s f s r s
m s Z s c s k Z s c s k Z s c s k Z s
c k Z s c s k Z s c s k Z s
c s k Z s c k Z s
I s s c s k t Z s c s k t Z s c s k t Z s
c s k
4 1 1 1 2 2 2
3 3 3 4 4 4
2
1 1 1 2 2 2 3 3 3
4 4 4 1 1 1 2 2 2
3 3
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( )
r s f u f u
r u r u
yy f s f s r s
r s f u f u
r u
t Z s c s k t Z s c s k t Z s
c s k t Z s c s k t Z s
I s s c s k l Z s c s k l Z s c s k l Z s
c s k l Z s c s k l Z s c s k l Z s
c s k l Z
3 4 4 4( ) ( ) ( )r us c s k l Z s
(5.13)
2
1 1 1 1 1 1 1 1
2
2 2 2 2 2 2 2 2
2
3 3 3 3 3 3 3 3
2
4 4 4 4 4 4 4 4
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
u t u s t r
u t u s t r
u t u s t r
u t u s t r
m s c s k k Z s c s k Z s k Z s
m s c s k k Z s c s k Z s k Z s
m s c s k k Z s c s k Z s k Z s
m s c s k k Z s c s k Z s k Z s
(5.14)
With parameter assumptions of k i = k (i=1…4), ci = c (i=1…4), tf = tr, and lf
= lr, for simplicity, Laplace transformation of bounce, roll, and pitch position
of center of sprung mass with respect to road disturbance can be expressed as
follows:
1 2 3 42
1 2 3 42
1 2 3 42
( )( ) ( ( ) ( ) ( ) ( ))
( ) B( )
( ) /( ) ( ( ) ( ) ( ) ( ))
( ) B( )
( ) /( ) ( ( ) ( ) ( ) ( ))
( ) B( )
s r r r r
s
f
r r r r
x
f
r r r r
y
C sZ s Z s Z s Z s Z s
m s A s s
C s ts Z s Z s Z s Z s
m s A s s
C s ls Z s Z s Z s Z s
m s A s s
(5.15)
where
2 2
2 2
( ) , ( ) 4( )( )
( ) , / , /
u t u t
t t x xx f y yy f
A s m s cs k k B s m s k cs k
C s ck s kk m I t m I l
59
Laplace transformation of wheel accelerations with respect to road
disturbance can be expressed as follows:
11 12 13 14 11
21 22 23 24 22
31 32 33 34 33
41 42 43 44 44
( ) ( ) ( ) ( ) ( )( )
( ) ( ) ( ) ( ) ( )( )
( ) ( ) ( ) ( ) ( )( )
( ) ( ) ( ) ( ) ( )( )
ru
ru
ru
ru
G s G s G s G s Z sZ s
G s G s G s G s Z sZ s
G s G s G s G s Z sZ s
G s G s G s G s Z sZ s
(5.16)
where
11
2
11 12
13 14
23 14 24 13 34 12
( ) ( ), 1,...,4
( ) ( ), , 1,...,4
( ) ( ) ( ) ( ) , ( ) ( ) ( ) ( )( )
( ) ( ) ( ) ( ), ( ) ( ) ( ) ( )
( ) ( ), ( ) ( ), ( ) ( )
ii
ij ji
t
G s G s for i
G s G s for i j
k sG s D s E s F s G s D s E s F s
A s
G s D s E s F s G s D s E s F s
G s G s G s G s G s G s
where
2 2
2 2
2
2
( ) / ( ) /( ) ( )( ) , ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) / ( )( )
( ) ( ) ( )
t t
s x
t
y
s C s k s C s kC s C sD s E s
A s m s A s B s A s m s A s B s
s C s k C sF s
A s m s A s B s
The validation of the time delayed method can be conducted by analysis of
transfer functions. For example, from equation (5.16), the Laplace
transformation of time delayed front left wheel acceleration can be expressed
as follows:
1
2
1 11 12 13 14
3
4
( )
( )( )( ) ( ) ( ) ( ) ( )
( )
( )
delay
r
t s r
u delay
r
r
Z s
Z sZ t t s e G s G s G s G s
Z s
Z s
(5.17)
On the assumption that symmetric road disturbance of left and right wheels,
the road input can be expressed as follows:
60
1 2
3 4
(s) Z ( ) Z ( )
(s) (s) (s)delay
r r r
t s
r r r
Z s s
Z Z e Z
(5.18)
In this case, the transfer function of delayed front left wheel acceleration and
that of rear left wheel acceleration can be expressed as follows:
1
11 12 13 14
1_
331 32 33 34 3
( )( )( ( ) ( ) ( ) ( ))
( )
( )
( )( ( ) ( ) ( ) ( )) ( )
( )
delay delay delay
delay delay
t s t s t su delay
r
delay
t s t su
r
Z t t se G s G s e G s e G s
Z s
G s
Z sG s G s e G s e G s G s
Z s
(5.19)
The Bode plot of transfer functions in (5.19) is shown in Figure 5.1.
Figure 5.1. Bode plots from symmetric road elevation input to delayed front
left wheel acceleration and that of rear left wheel acceleration in full-car
model.
61
It is noted that magnitude gap between delayed front wheel acceleration and
rear wheel acceleration is caused by the frequency of road disturbance, but their
phase gap is negligible. As shown in figure 5.1, the magnitude of delayed front
wheel acceleration is expected to be larger than that of actual rear wheel
acceleration under 2.5 Hz road disturbance situation. An opposite result is
expected under 9 Hz road disturbance situation. The acceleration magnitude
gap according to the road disturbance was found by simulation with Carsim®.
In Figure 5.2, delayed front wheel acceleration and rear wheel acceleration
generated by symmetric sinusoidal road disturbance input in simulation are
compared. The simulation result shows the expected acceleration magnitude
gap and little phase gap. From the analysis of the acceleration time delay from
front to rear wheels, it is reasonable that the vertical acceleration information
of front wheels can be used to preview control for rear active suspension.
62
Figure 5.2. Delayed front left wheel acceleration and that of rear left wheel
acceleration generated by sinusoidal road disturbance simulation. (a) 2 Hz and
(b) 9 Hz road disturbance input, respectively.
63
5.2.2. Optimal preview control
The optimal linear preview control problem for active suspension was
considered by Bender, Tomizuka, and Foag. Solution of the problem calls for
linear feedback of the full state vector and feedforward of another variable that
depends on the future road inputs measured directly in the preview scheme. The
main results can be summed up as follows [Hac'92].
Consider the suspension system pre-defined by (3.7) where the state vector
x(t) is fully available, x0 is deterministically given and w(t) can be measured
exactly up to tp time units ahead of time t (i.e. 𝐰(𝝉), 𝛕 ∈ [𝒕, 𝒕 + 𝒕𝒑] is known).
Consider also the quadratic integral criterion as follows:
01 12 2
1( ) ( )
2
1[ ]
2
T
T
TT T T T T
p pt
J T T
dt
x P x
x Q x 2x N u u R u 2x Q w w Q w
(5.20)
where Q1, Rp, PT, and Q2 are symmetric, time-invariant weighting matrices such
that Rp is positive definite and 1
1
T
n p p p
Q Q N R N nonnegative definite. Then
the problem of determining an input which minimize the criterion (5.20),
0 0( ) [ ( ), ( ), , ]pt f t t t t t u x w , is called the deterministic
linear optimal preview control problem. Suppose now that the problem duration,
T, approaches infinity. In this case, instead of J, consider the cost rate 𝑱′ = 𝑱 𝑻⁄ .
When T is finite, the optimal control that minimizes J also minimizes J'. Then
the optimal control uo(t) that minimize 𝑱∞′ = 𝐥𝐢𝐦
𝑻→∞𝑱 𝑻⁄ is given by
1( ) [( ) ( ) ( )]T T T
o p pt t t u R N B P x B r (5.21)
64
where P is a nonnegative definite symmetric solution of the algebraic Riccati
equation as follows:
1T T
n n p n
0 PA A P PBR B P Q (5.22)
where 1 T
n p p
A A BR N and the preview control vector r(t) is given by
120
( ) ( ) (p
ct
t t d
TA
wr e PB Q w (5.23)
where 1 T
c n p
A A BR B P is asymptotically stable if the pair (A, B) is
stabilizable and (An, T) is detectable where T
n Q T T .
The concept of wheelbase preview disturbance information is shown in
Figure 5.3. No preview information for front suspension is provided and
vertical acceleration history of front wheels is used to preview information for
rear suspension as equation (5.24).
1
2
0
0( ) , [0, ]
( )
( )
delay delay
u delay
u delay
t tz t t
z t t
w (5.24)
65
Figure 5.3. Wheelbase preview disturbance information.
Using the same quadratic integral criterion in (5.9), the wheelbase preview
control input using optimal preview control approach is obtained as follows:
1
1
( ) [( ) ( ) ( )]
( ) ( )
T T T
opc delay
T
delay
t t t
t t
c c
c c
u R N B P x B r
K x R B r (5.25)
where the wheelbase preview control vector rdelay(t) is given by
0( ) (
delayd
t
delay delayt t d
TA
wr e PB w (5.26)
where P is the solution of the Riccati equation above in (5.12), and
1 1T T
d c
c c
A A BR N BR B P (5.27)
5.2.3. Model predictive control
In LQ optimal control approach, hard constraints cannot be explicitly
incorporated and hence have to be minimized in the cost function. For active
suspension systems, the constraints on suspension rattle space in order not to
reach the bump stoppers, the mechanically limited actuator displacements and
also the constrained of the actuator force should be considered in controller
design. Since vertical acceleration history of front wheels can be used to
preview information for rear suspension, furthermore constraints on control
variables should explicitly be incorporated and the optimization has to be
carried out in real-time, model predictive control (MPC) seems to be the
appropriate controller design scheme. MPC approaches for active suspensions
with preview road information based on a quarter-car model [CHO'99], a half-
car model [Mehra'97], and full-car model [Göhrle'15] were introduced. The
66
main results can be summed up as follows.
y(k)
past future
k k+1 k+2 k+N k+P
yr(k+i)
yp(k+i)
wp(k+i)
u*(k+i)
... ...
Control horizon, N
Prediction horizon, P
Figure 5.4. Schematic of MPC concept.
Consider the discretized suspension system pre-defined in (4.10) and (5.8).
( 1) ( ) ( ) ( )
( ) ( ) ( )
k k k k
k k k
wx Fx Gu G w
y Cx Du (5.28)
At each sample time, a set of N control moves u(k), u(k+1), …, u(k+N-1) are
computed by solving the following optimization problem:
2
( ), ( 1)... ( 1)1
12
0
min [ ( ) ( )]
[ ( )]
P
i p rk k k N
i
N
i
i
Q k i k i
R k i
u u uy y
u
(5.29)
such that
EU b (5.30)
67
where yp(k+i) are the predicted values of the controlled variable at the i-th future
sample time. The inequalities in (5.30) represent constraints such a rate and/or
absolute bounds on control/output variables.
The optimization problem in (5.29) can be represented as the following
equivalent vector space quadratic programming (QP) formulation.
minT TJ Q R
uy y u u (5.31)
where
[ ( 1) ( )]
[ ( ) ( )]
[ ( ) ( 1)]
( ( 1) ( ))
( ( ) ( ))
T
T
T
k k P
k k N
k k P
Q diag Q k Q k P
R diag R k R k N
y y y
u u u
w w w
and relationship among �⃗⃗� , x(k), �⃗⃗⃗� , and �⃗⃗� is given by
( ) u wk y x u w (5.32)
where Λ, Γu, and Γw are all matrices that can be constructed from the state space
model given by (5.28). Then the equation (5.31) is represented as follows:
min ( ( ) ) ( ( ) )
( )
2 2 2
T T
u w u w
T T T T T T
u u w w
T T T T T
w u w u
J k Q k R
Q Q R Q
Q Q Q
ux u w x u w u u
x x u u w w
x w x u w u
(5.33)
In the above, we can drop the terms not containing �⃗⃗� since they have no
effect on the minimization problem. We can now write the minimizat ion
problem in the standard QP formulation as follows:
1min ( ) ( )
2
T T T T T
u u u w uJ Q R Q Q u
u u x w u (5.34)
Input constraints are immediately addressed in QP algorithms which allow
68
for bounds on the design variable, i.e. the elements of �⃗⃗� . State and output
constraints may be incorporated in the following manner. Define an output
vector of constraints as follows:
, ,( )c c u c w ck y x u w (5.35)
where �⃗⃗� 𝒄, Δc, Γu,c, and Γw,c is obtained similar to (5.32).
Consider constraints of the form,
c cL U cy (5.36)
which implies
, ,
, ,
( )u c w cc c
u c c c w c
U k
L
xu
w (5.37)
The equation (5.34) and (5.37) are the standard QP optimization problem
formulation which allows us to utilize available generic QP algorithms. In the
absence of constraints, �⃗⃗� 𝒎𝒑𝒄 is immediately found by setting 𝝏𝑱
𝝏�⃗⃗� to zero and
solving for �⃗⃗� as follows:
1( ) ( ( ) )T T
mpc u u u wQ R Q k u x w (5.38)
The control law at each time step k is obtained as follows:
1 2 3 4 0 1( ) [ , , , ] ( ) [ ]pk k u x w (5.39)
where
1
1 2 3 4
1
0 1
[ , , , ] [1,0 0]( )
[ ] [1,0 0]( )
T T
u u u
T T
p u u u w
Q R Q
Q R Q
For the wheelbase preview control, the �⃗⃗⃗� in the above is constituted with
69
the wheelbase preview disturbance given in (5.24). In this research, to solve
MPC problem in MATLAB, CVXGEN which is designed to be utilizable in
MATLAB is used as solver [Mattingley'12].
70
5.3. Frequency Response Analysis of Controlled
Vehicle
The Laplace transformation of bounce, roll, and pitch position of the passive
(uncontrolled) vehicle model with respect to road disturbance can be expressed
as (5.15). With assumptions that the vehicle goes straight with constant speed
and the tire grip on the road is keeping, the delayed out-of-phase road elevation
inputs into the vehicle front and rear wheels. On the assumption that symmetric
road disturbance of left and right wheels written in (5.18), the vehicle model is
converted from a multi-input multi-output (MIMO) system to a single-input
multi-output (SIMO) system. Then transfer functions between the road input,
Zr(s), and the body motions can be obtained.
The frequency responses of the heave and pitch acceleration of the passive
vehicle at 10 kph is illustrated in Figure 5.5. It is noted that the heave and pitch
acceleration humps are occurred alternately in the magnitude plot due to phase
difference of the delayed road elevation inputs to front and rear wheels. The
acceleration magnitude has humps when the phase difference corresponding to
the multiple of one wavelength is occurred, while the pitch acceleration
magnitude has humps when the phase difference corresponding to the multiple
of a half-wavelength is occurred. The modal peak frequencies are speed-
dependent because the delayed time is a speed function (tdelay = L/vx).
71
Figure 5.5. Frequency response of the passive vehicle at 10 kph.
With some controlled forces, the Laplace transformation of the body motions
can be expressed as (5.40). To analyze the frequency response of the controlled
vehicle, the LQ optimal feedback control and the wheelbase preview control
for ride comfort improvement based on the reduced vertical full-car model
proposed in chapter 5.1 and 5.2 have been adopted. With the same assumptions
above, the frequency responses of the heave and pitch acceleration of the
controlled vehicle at 10 kph are illustrated in Figure 5.6 and 5.7, respectively.
72
1 2 3 42
2 2
1 2 3 42
1 2 3 42
2 2
1 2 3 42
( )( ) ( ( ) ( ) ( ) ( ))
( ) B( )
( ) ( ) ( ) ( )( ) B( )
( ) /( ) ( ( ) ( ) ( ) ( ))
( ) B( )
/( ) ( ) ( ) (
( ) B( )
s r r r r
s
u t
s
f
r r r r
x
u t f
s
C sZ s Z s Z s Z s Z s
m s A s s
s m s kF s F s F s F s
m s A s s
C s ts Z s Z s Z s Z s
m s A s s
s m s k tF s F s F s F s
m s A s s
1 2 3 42
2 2
1 2 3 42
)
( ) /( ) ( ( ) ( ) ( ) ( ))
( ) B( )
/( ) ( ) ( ) ( )
( ) B( )
f
r r r r
y
u t f
s
C s ls Z s Z s Z s Z s
m s A s s
s m s k lF s F s F s F s
m s A s s
(5.40)
Figure 5.6. Frequency response of the heave acceleration of the controlled
vehicle at 10 kph.
73
Figure 5.7. Frequency response of the pitch acceleration of the controlled
vehicle at 10 kph.
The magnitudes of both heave and pitch acceleration of the feedback
controlled vehicle are reduced compared to the passive vehicle within the
frequency range of about 0.5 to 50 Hz. This means that even with control
algorithm ignoring the wheel dynamics, vehicle ride comfort can be improved.
For performance comparison, the results of full preview controlled vehicle are
also shown assuming that 1-seconds of future road information is available. It
is shown that a significant ride comfort improvement is achieved by the full
preview control algorithm. The performance of the proposed wheelbase
74
preview control is superior to that of the feedback control but inferior to the full
preview control performance as expected. It is noted that the body motion
cannot be influenced by any control algorithms around the frequency of about
12 Hz which is known as a wheel-hop frequency [Hedrick'90]. The ride comfort
can be improved significantly by the proposed control algorithm within the
frequency range of about 0.5 to 5 Hz which is appropriate to low-bandwidth
actuators.
75
Chapter 6 An Electro-mechanical Active
Suspension System
All active suspensions implemented in automobiles today are based on
hydraulic or pneumatic operation. Although hydraulic systems have already
proved their potential in commercial systems, there are three main
disadvantages: inefficiency due to the continuously pressurized system, a
relatively high system time constant and environmental pollution issues
because of hose leaks and ruptures. An electro-mechanical suspension (EMS)
system can resolve the disadvantages of hydraulic systems since continuous
power is not needed, control is easy and no fluids are present.
Over the last decade, EMS systems for automobiles has been proposed
[Suda'00, Suda'03]. The electro-mechanical actuator consists of DC motor and
the ball screw mechanism. The tunable damping force on an electromagnetic
damper allows high controllability to be achieved [Kawamoto'07]. The
performance of the EMS has been discussed on the energy consumption,
vibration isolation, and vehicle maneuverability [Kawamoto'08]. J. Seo et al.
proposed a control algorithm for the motorized active suspension damper
(MASD). In their work, the MASD system significantly improves the ride
comfort compared with conventional CDC [Seo '14]. D. Shin et al. reduces the
actuator power consumption by changing its control mode according to the
driving conditions [Shin'16].
76
In this chapter, a control algorithm for an electro-mechanical suspension
system is proposed to improve the driving performance of a vehicle. A vehicle
height adjustment is one of the main salient features of EMS systems. The EMS
system lifts the sprung mass to improve ride comfort and to protect the vehicle
bottom during off road driving and lowers the sprung mass to reduce air drag
and to enhance safety during high-speed driving. Another main function of the
EMS system is isolation of the body against to road disturbance and roll, pitch
compensation.
A quarter-car model with the EMS in this research has been illustrated in
Figure 6.1. A typical low-bandwidth active suspension has been adopted in this
research which is primarily concerned with dominant (body) modes and
associated characteristics because the electro-mechanical actuator has a low
operating frequency (~ 5 Hz).
ms
mu
mb
Figure 6.1. A quarter-car model with electro-mechanical actuator.
77
6.1. EMS system modeling
6.1.1. Electro-mechanical actuator modeling
As shown in Figure 6.1, the actuator is inserted between sprung mass and
unsprung mass. An accumulator spring parallel to the actuator is necessary to
minimize the actuator loads in steady-state. The bottom of actuator is mounted
on the unsprung mass and the top of actuator, a ball nut, is attached in series to
the main spring and damper. A free body diagram of belt-driven ball screw
mechanism is shown in Figure 6.2 and parameters of the model are given in
Table 6.1. The motor and ball screw are attached at the unprung mass. The ball
nut is driven by the motor with a belt whose gear ratio is n, so that the driven
torque at ball nut is amplified as n times as much than output torque of motor.
A stroke motion of the actuator can be described by 1) rotary to axial
transformation of the ball screw and 2) rotor dynamics of the ball nut.
Motorrotor
Ball nut
Ball screw
Fixed to Unsprung mass
Figure 6.2. Belt-driven ball screw actuator model.
78
Table 6.1. The variables and nominal parameters of rotor dynamics of actuator
and quarter car model.
Parameter/variable Description Value
ωm Angular velocity of motor
ωb Angular velocity of ball nut
�̇�𝒃 − �̇�𝒖 Actuator stroke speed
Jm Moment of inertia of motor rotor 0.00025 kg∙m2
Jb Moment of inertia of ball nut 0.0025 kg∙m2
l Lead of the ball screw 0.01 m
n Reduction gear ratio of the belt 5
Efficiency of the belt 0.95
fr Coefficient of dynamic friction
In the following modelling procedure, the following items are assumed
[Kawamoto'07].
∙ Motor rotor and ball screw mechanism are assumed to be rigid.
∙ Backlash and torsion of ball screw are not considered.
From these assumptions, equation of rotary to axial transformation of the ball
screw is written as follows:
2( )b b uz z
l
(6.1)
The equation of rotor dynamics of ball nut with reduction gear ratio of the
belt is written as follows:
b b m aJ n (6.2)
where τm is the motor output torque, and τa is output torque of the actuator.
Using the equilibrium of force, the output force in the axial direction, fa, is
written as follows:
2a af
l
(6.3)
Considering the dynamic friction of the actuator and substituting (6.1) and
(6.3) into (6.2) yields following the output force [Seo '14].
79
2
( )a m r b u rf n m z z f f xl
(6.4)
where
2 sgn( ) 0.01 /
2,
0.01 /0.01 2
b u b u
r b b ub u
z z when z z m s
m J f x z zl sin when z z m s
Figure 6.3 shows that the motor circuit is modelled as the equivalent DC
motor circuit, while Table 6.2 gives the parameters of the model. The motor is
connected to a power supply, and the voltage is controlled. The circuit equation
is obtained as (6.5). The limit for the variable voltage of power supply is ±12
V.
motor motor e
diV L R i V
dt (6.5)
where Ve is the electromotive force which is proportional to the motor speed (=
n times the angular velocity of the ball nut) as written in (6.6).
+
-
M
Figure 6.3. Circuit diagram of the motor.
Table 6.2. The variables and nominal parameters of circuit model.
Parameter/variable Description Value
i Current
V Variable voltage of power supply ±12 V
Lmotor Inductance 0.01523 H
Rmotor Resistance 0.1523 Ω
Kt Motor torque constant 0.0455 Nm/A
Ke Induced voltage constant 0.0349 V∙sec/rad
80
2( )e e m e b e b uV K K n K n z z
l
(6.6)
Assuming that the output torque of the motor is proportional to the motor
current, i, it is obtained as (6.7).
m tK i (6.7)
6.1.2. Reduced vertical full-car model with EMS
Figure 6.4 shows that to design the EMS control algorithm, the EMS system
described in the above is modelled in a vertical full-car model. Throughout the
paper, the subscript i ∈{1,2,3,4} stands for front left, front right, rear left, and
rear right corner, respectively, of the vehicle. Table 6.3 gives the supplementary
to variables and nominal parameters in Table3.1. The equations of body motion
are given in (6.8) ~ (6.10).
x
y
z
zr1
zu1
zs1
zr3
zu3
k1,c1
k2,c2 k3,c3
k4,c4
zs2 zs3
zs4
2tf
2tr
lf
lr
zs
zr2
zu2
ka
kaka
ka
zb1
zb3zb2
kt
kt
kt
kt
fa1
fa2
fa3
fa4
Mx My
Figure 6.4. A vertical full-car model with EMS.
81
Table 6.3. The supplementary variables and nominal parameters of the full-car
model used in the simulation study.
Parameter/
variable Description Value
mb Ball nut mass 1 kg
ka Spring stiffness of accumulator spring 25000 N/m
zbi Displacement of i-th corner of ball nut i=1…4
ax, ay Longitudinal and lateral acceleration of sprung mass
1 1 1 2 2 2 3 3 3 4 4 4
1 1 1 2 2 2 3 3 3 4 4 4
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
s s b s b s b s b
s b s b s b s b
m z k z z k z z k z z k z z
c z z c z z c z z c z z
(6.8)
1 1 1 2 2 2 3 3 3 4 4 4
1 1 1 2 2 2 3 3 3 4 4 4
, ,
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
xx s b f s b f s b r s b r
s b f s b f s b r s b r
roll f roll r s roll y s roll
I k z z t k z z t k z z t k z z t
c z z t c z z t c z z t c z z t
K K m h a m gh
(6.9)
1 1 1 2 2 2 3 3 3 4 4 4
1 1 1 2 2 2 3 3 3 4 4 4
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
yy s b f s b f s b r s b r
s b f s b f s b r s b r
s pitch x s pitch
I k z z l k z z l k z z l k z z l
c z z l c z z l c z z l c z z l
m h a m gh
(6.10)
The equation of ball nut motion is given as follows:
( ) ( ) ( ) , 1, 4b bi i si bi i si bi a bi ui aim z k z z c z z k z z f for i (6.11)
where fai is the output force of each actuator, which is given as follows:
2( ) sgn( ), 1, 4ai t i r bi ui r bi uif nK i m z z f z z for i
l
(6.12)
where ii is the current of each motor from the circuit equation given as follows:
2( ), 1, 4i
i motor motor i e bi ui
diV L R i K n z z for i
dt l
(6.13)
The operational range of the ball screw mechanism is about ±30 mm. Figure
6.5 shows that to incorporate this stroke limit in the model, the accumulator
spring stiffness is dramatically increased beyond the range.
82
Actuator stroke [mm]
Accumulator spring
stiffness
30 33-33 -30
ka
40·ka
Figure 6.5. Accumulator spring stiffness to incorporate the actuator stroke limit.
The state-space representation for reduced full-car model with EMS is
obtained as follows:
a a a a a wa ax A x B u B w (6.14)
where the state vector consists of displacement between body and ball nut and
its velocity, the actuator stroke and its velocity at each corner, and the motor
current at each actuator. The controlled input vector of the system consists of
motor voltage at each actuator, and the vertical acceleration at each wheel and
longitudinal, lateral acceleration of the body is disturbance to the system as
follows:
1 1 1 1 2 2 2 2 3 3 3 3
4 4 4 4 1 1 1 1 2 2 2 2
3 3 3 3 4 4 4 4 1 2 3 4
1 2 3 4
1 2 3 4
s b s b s b s b s b s b
s b s b b u b u b u b u
T
b u b u b u b u
T
T
u u u u x y
z z z z z z z z z z z z
z z z z z z z z z z z z
z z z z z z z z i i i i
V V V V
z z z z a a
a
a
a
x
u
w
(6.15)
The system matrix, input matrix, and disturbance input matrix is given as
83
follows:
, ,
a1 a1 wa1
a2 a2 wa2
a a wa
a20 a20 wa20
A B B
A B BA B B
A B B
where
, 1,3,5,7,9,11,13,15for ai iA Π i
where iΠ denotes a 𝟏 × 𝟐𝟎 matrix with a unity located in the i-th columns
and with remaining elements equal to zero.
2 2 2 2
1 1 1 1 21 1 1 2
2 2
3 32 42 2 3 3 3 4
44 4
f f f f
f
s yy b r s xx yy b r s yy
f f f r f r f r f r
f
s xx yy s yy s xx yy s yy
f r f r a
s xx yy b
l t l lk k c c ka k l e c c a k
m I m m m I I m m m I
t l l l t t l l l lk cc kc c b k l e c c b k
m I I m I m I I m I
t t l l kcc c
m I I m
a2A
1 3 1 3
2 2 2 2
1 1 2 21 1 1 2
2 2
3 32 22 2 3
20 0 0 0
2 2
T
s roll s roll tf f
r xx xx b r
f f f f
f
s yy s xx yy s yy b r
f f f r f
f
s xx yy b r s yy s
m gh m gh nKl e l e
m I I l m m
l t l lk c k ka k l e c c a k
m I m I I m I m m
t l l l t tk cc cc c b k l e
m I I m m m I m
a4A
43 3 4
44 4 1 4 1 2
1 1 2 21 1 1 2
20 0 0 0
2 2
r f r f r
xx yy s yy
T
f r f r s roll a s roll tf f
s xx yy xx b r xx b r
f r f r f r f r
r
s yy s xx yy s yy s
l l l lkc c b k
I I m I
t t l l m gh k m gh nKcc c l e l e
m I I I m m I l m m
l l t t l l l l tk c k cc k l e c c c k
m I m I I m I m
a6A
2 2
2 2 2 2
3 3 3 3 43 3 3 4
2 2
44 4 1 5
20 0 0 0
2 2
f r f r
xx yy
r r r rr
s yy b r s xx yy b r s yy
T
s roll r s roll r a tr rr r
s xx yy xx f xx f b r b r
t l lc c
I I
k k c cl t l k ld k l e c c d k
m I m m m I I m m m I
m gh t m gh t k nKc t lc c l e l e
m I I I t I t m m l m m
84
1 1 2 21 1 1 2 2 2
2 2 2 2
3 3 343 3 3 4
2 2
344 4
f r f r f r f r f r f r
r
s yy s xx yy s yy s xx yy
r r r rr
s yy s xx yy s yy b r
sr r
s xx yy b r
l l t t l l l l t t l lk c k cc k l e c c c k c c
m I m I I m I m I I
k c kl t l k ld k l e c c d k
m I m I I m I m m
c m gc t lc c
m I I m m
a8A
1 4
, ,,
1 3 1
,
3
0 0 0 02 2
2
, ,2 2 2
2
roll r s roll r ar r
xx f xx f b r
T
t
b r
f roll f s roll f roll f s rollroll r rf r f
xx f xx r xx f
roll rrr
xx r
h t m gh t kl e l e
I t I t m m
nK
l m m
t K m gh t K m ghK ta k t b k t c k t
I t I t I t
Ktd k t
I t
1 1
2 2
3 3
,
0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
20 0 0 0 0 0 0
s pitch
yy
a
b r b r b r
T
t
b r
b r b r
T
a t
b r b r
b r b r
a t
b r
m ghe
I L
kk c
m m m m m m
nK
l m m
k c
m m m m
k nK
m m l m m
k c
m m m m
k nK
m m l m
a10
a12
a14
A
A
A
4 4
0
0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
T
b r
b r b r
T
a t
b r b r
e
motor
T
motor
motor
m
k c
m m m m
k nK
m m l m m
K n
lL
R
L
a16
a17
A
A
85
0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0
T
e motor
motor motor
T
e motor
motor motor
T
e motor
motor motor
K n R
lL L
K n R
lL L
K n R
lL L
a18
a19
a20
A
A
A
0 0 0 0 , 1,2,...,16
10 0 0
10 0 0
10 0 0
10 0 0
0 0 0 0 , 1,3,5,7,9,11,13,15,17,18,19,20
0 0 0
motor
motor
motor
motor
s pitch f s roll fr
b r yy xx
for
L
L
L
L
for
m h l m h tm
m m I I
ai
a17
a18
a19
a20
wai
a2
B i
B
B
B
B
B i
B
0 0 0
0 0 0
0 0 0
0 0 0 0 0
0 0 0 0 0
s pitch f s roll fr
b r yy xx
s pitch r s roll rr
b r yy xx
s pitch r s roll rr
b r yy xx
b
b r
b
b r
m h l m h tm
m m I I
m h l m h tm
m m I I
m h l m h tm
m m I I
m
m m
m
m m
a4
a6
a8
a10
a12
B
B
B
B
B
86
0 0 0 0 0
0 0 0 0 0
b
b r
b
b r
m
m m
m
m m
a14
a16
B
B
87
6.2. EMS System Control Algorithm
In this section, vehicle height levelling and ride comfort control algorithm of
the EMS as shown in Figure 2.1 is designed. The mode selector determines a
present driving mode and desired height level of the vehicle. The upper-level
controller determines the desired suspension state considering the actuator
stroke limit. The lower level controller calculates the target motor voltage at
each actuator using estimated state by the observer.
6.2.1. Driving mode decision
As shown in Figure 6.6, the mode selector determines a present driving mode
and desired height level of the vehicle, (𝒛𝒔 − 𝒛𝒖)𝒅, from the vehicle sensor
signals of longitudinal speed (vx), SWA, APS, BPS, and vertical acceleration of
wheels (�̈�𝒖). To reflect the driver’s intention and the road disturbance, the mode
selector classify the current situation into six modes: normal mode, attitude
control mode, bump mode, off-road mode, high-speed straightway mode, and
high-speed attitude control mode. Also, to prevent the chattering phenomenon
of the mode conversion, the driving mode in the previous step is used at the
same time. The mode decision condition and target height level are given in
Table 6.4.
88
Attitude control
mode
Bump mode
Normal mode
Mode Decision
Off-road mode
High-speed
attitude control
mode
High-speed
straightway mode
Figure 6.6. Mode and desired height level decision algorithm.
Table 6.4. Driving mode decision condition and desired height level.
mode situation Mode decision condition height level
1 Normal
vx ≤ 90 kph &
�̈�𝒖_𝑹𝑴𝑺 ≤ 2 m/s2 &
(APS & BPS & SWA)_RMS ≤ threshold_1
0 mm
2 Attitude control
vx ≤ 90 kph &
�̈�𝒖_𝑹𝑴𝑺 ≤ 2 m/s2 &
(APS | BPS | SWA)_RMS > threshold_1
0 mm
3 Bump vx ≤ 40 kph &
�̈�𝒖_𝑹𝑴𝑺 > 2 m/s2 0 mm
4 Off-road Staying at mode 3 for 2 sec + 30 mm
5 High-speed
straightway
vx > 90 kph &
(APS & BPS & SWA)_RMS ≤ threshold_2 - 30 mm
6 High-speed
attitude control
vx > 90 kph &
(APS | BPS | SWA)_RMS > threshold_2 - 30 mm
89
Each driving mode and corresponding situation is described as follows:
1) Normal mode, mode 1
The normal mode is a mild driving situation in which the driver's input is
small on a general flat road, not on a highway road. As a condition for
determining the non-high speed region and the flat road, the value of vehicle
speed is selected to be 90 kph or less, and the root mean square (RMS) value of
the vertical acceleration of the unsprung mass, �̈�𝒖, is selected to be 2 m/s2 or
less. As a condition for determining the mild driving situation, the RMS values
of APS, BPS, and SWA are less than 0.1, 0.1, and 30°, respectively. In the
normal mode, the target height level is selected as 0 mm, at which the vehicle
height is maintained by suspension spring and accumulator spring without
control to reduce the amount of control input.
2) Attitude control mode, mode 2
The attitude control mode is acceleration or cornering situation by the driver
on a general flat road, not on a highway road. The condition for determining
the non-high-speed region and the flat road is the same as in the case mode 1,
and the condition for making decision that the vehicle attitude control is
necessary due to the driver's input is that either of the RMS value of APS, BPS,
and SWA is greater than 0.1, 0.1, and 30°. In the attitude control mode, a
relatively large amount of control input is used to reduce roll and pitch angles
during cornering or acceleration. In order to secure both the negative and
positive range of the actuator, the target height level is selected as 0 mm.
3) Bump mode, mode 3
The bump mode is a situation in which the vehicle passes through the bump
90
and a large heave motion is instantaneously generated. Under the assumption
that the driver runs at low speed on the bump, the speed condition for
determining the bump road is selected as 40 kph or less. Also, the condition for
making decision that the ride control is required against the road disturbance is
that the RMS value of the �̈�𝒖 is larger than 2 m/s2. In the bump passing mode,
a relatively large amount of control input is used to reduce the vertical
acceleration of the sprung mass or reduce roll and pitch angles to improve ride
comfort. In order to secure both the negative and positive range of the actuator,
the target height level is selected as 0 mm.
4) Off-road mode, mode 4
The off-road mode is a situation in which the vehicle passes through the
rough road and a persistent irregular heave motion is generated. The perception
condition for the rough road is selected as the duration of the mode 3 is greater
than 2 seconds. The target height is selected as +30 mm to protect the vehicle
bottom.
5) High-speed straightway mode, mode 5
It is a high-speed straight-ahead driving situation in which the driver's input
is small on the highway. As a condition for determining the high speed region,
the vehicle speed is selected to be higher than 90 kph. As a condition for
determining the mild driving situation, the RMS values of APS, BPS, and SWA
are less than 0.2, 0.1, and 15°, respectively. The target height level is selected
to be -30 mm to reduce the air resistance and to improve fuel efficiency.
6) High-speed attitude control mode, mode 6
It is acceleration or cornering situation by the driver on the highway. The
91
condition for determining the high-speed region is the same as in the mode 5,
but the condition for making decision that the vehicle attitude control is
necessary due to the driver's input is that either of the RMS value of APS, BPS,
and SWA is greater than 0.2, 0.1, and 15°. The target height level is selected to
be -30 mm to reduce the air resistance and to enhance safety.
Some threshold values of the signal are used in the mode conversion
algorithm given in Table 6.4. This simple mode conversion algorithm can cause
unintentional chattering phenomenon of mode and height level near the
threshold value. Therefore, the chattering prevention algorithm considering the
driving mode in the previous step and the conservative threshold value is added
as Table 6.5. The added hysteresis of threshold value prevents the mode from
changing rapidly. Also, when the switching between the mode 2 and the mode
6 occurs, the previous target height level is maintained to ensure safety.
92
Table 6.5. Driving mode chattering prevention algorithm.
Previous
mode
Present
mode condition Mode decision height level
2 1 (APS & BPS & SWA)_RMS
≤ 0.5×threshold_1 1 0 mm
2 1 (APS & BPS & SWA)_RMS
> 0.5×threshold_1 2 0 mm
3 1 or 2 �̈�𝒖_𝑹𝑴𝑺 ≤ 0.5 m/s2 1 or 2 0 mm
3 1 or 2 �̈�𝒖_𝑹𝑴𝑺 > 0.5 m/s2 3 0 mm
4 1 or 2 �̈�𝒖_𝑹𝑴𝑺 ≤ 0.5 m/s2 1 or 2 0 mm
4 1 or 2 �̈�𝒖_𝑹𝑴𝑺 > 0.5 m/s2 4 +30 mm
4 3 - 4 +30 mm
5 1 vx ≤ 60 kph 1 0 mm
5 2 vx ≤ 60 kph 2 -30 mm
5 1 or 2 vx > 60 kph 5 -30 mm
6 1 vx ≤ 60 kph 1 0 mm
6 2 vx ≤ 60 kph 2 -30 mm
6 1 or 2 vx > 60 kph 6 -30 mm
6 5 (APS & BPS & SWA)_RMS
≤ 0.5×threshold_2 5 -30 mm
6 5 (APS & BPS & SWA)_RMS
> 0.5×threshold_2 6 -30 mm
93
6.2.2. Desired suspension state decision
The upper-level controller determines xad, the desired suspension state
variable of equation (6.15). If the target height level, h, is determined from the
mode selector, the xad is expressed as equation (6.16) except for the case of the
high-speed attitude control mode.
,2
, , , , 9,11,13,15,
Ta
ijkl h h h h h
t
k lk h k h k h k h k
nK
for i j k l respectively
adx Π (6.16)
where ijklΠ denotes a 𝟏 × 𝟏𝟔 matrix with the target height value h located
in the i,j,k ,l-th columns and with remaining elements equal to zero. hk h
denotes a steady state current to maintain the actuator stroke, h.
The xad in equation (6.16) is the steady-state variable to keep the height level
at h. In case of the high-speed attitude control mode, actuator is driven
restrictively due to the actuator stroke limit of -30 mm. In this case, an
additional target displacement within operational range, (ha)1~4, is applied to the
operable actuator for attitude control. The (ha)1~4 is obtained by multiplying
linear gains on the longitudinal and lateral accelerations of the vehicle as
follows:
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3
0& 0 : 0, , ,
0& 0 : , 0, ,
0& 0 : , , 0,
0& 0 : , , ,
y x y x
y y x x
x y x y
y x x y
y x a a a y a a x a a y a x
y x a a y a a a y a x a a x
y x a a x a a y a x a a a y
y x a a y a x a a x a a y
a a h h G a h G a h G a G a
a a h G a h h G a G a h G a
a a h G a h G a G a h h G a
a a h G a G a h G a h G a h
4 0a
(6.17)
94
where the gain values are determined as the magnitude of the longitudinal and
lateral accelerations, which generate suspension displacement by 30 mm of a
passive vehicle. Using the compensation as described in equation (6.17), the xad
in the case of the high-speed attitude control mode is expressed as (6.18).
1 8 1 2 3 4
1 2 3 4
0 0 0 0a a a a
T
h a h a h a h a
h h h h h h h h
k h h k h h k h h k h h
adx 0 (6.18)
6.2.3. Desired motor voltage decision
The LQ optimal control can be applied to the reduced vertical full-car model
with EMS system in (6.14). The heave, roll, and pitch motion of the body are
related to ride comfort control. The actuator stroke at each corner is related to
vehicle height and attitude control. The interested output of the model can be
represented in (6.19) and incorporated into the quadratic integral criterion as
follows:
1~4( )T
s b uz z z ay (6.19)
0
2 2 2 2 2
0
lim
lim ( )
f
f
f
sf
t
T T
t
t
z s i bi ui j jt
J t t t t dt
z z z V dt
a a a a a ay Q y u R u
(6.20)
where 𝝆𝒛𝒔, 𝝆𝝓, 𝝆𝜽, 𝝆𝒊, 𝝆𝒋 are weighting factors that are diagonal elements
of the Qa and Ra matrix. If the current driving mode is 1, 4 or 5, the control
objective is a smooth vehicle height adjustment, so the values of 𝝆𝒊 and 𝝆𝒋 is
tuned to be relatively large. If the current driving mode is 2 or 6, the control
95
objective is roll and pitch compensation, so the values of 𝝆𝒊 is tuned to be
relatively large. If the current driving mode is 3, the control objective is ride
comfort improvement, so the values of 𝝆𝒛𝒔 , 𝝆𝝓 , and 𝝆𝜽 are tuned to be
relatively large. Table 6.6 gives the sets of weights using in simulation study.
The solution to the optimal control problem that minimizes the cost (6.20)
using the estimated suspension state is written as follows:
1 2 3 4ˆ
TV V V V
a a a adu K x x (6.21)
At ride comfort control mode, the wheelbase preview control algorithm
proposed in section 5 is also adopted in the simulation study. The state variable
of the EMS system is estimated by proposed observer in section 4 with using
measurement of suspension deflection, motor voltage, vertical wheel
acceleration, longitudinal and lateral acceleration of the body.
Table 6.6. Weighting factors for each driving mode.
Mode
Value of weighting factors
𝝆𝒛𝒔 𝝆𝝓 𝝆𝜽 𝝆𝒊 𝝆𝒋
1, 4, 5 (height control) 0 0 0 1 1×10-1
2, 6 (attitude control) 0 0 0 1×101 1×10-2
3 (ride comfort control) 1×102 1×101 1×101 1 1×10-2
96
Chapter 7 Performance Evaluation
To evaluate the EMS system control algorithm, simulation studies have been
conducted. The computer simulation was conducted using MATLAB/Simulink
and vehicle software Carsim®. The fully nonlinear vehicle model used in
simulation consists of engine model, transmission model, steering model,
suspension model, brake model, tire model, and vehicle body model. The
samling time to calculate the overall vehicle motion was 0.001 sec, while the
control input was computed every 0.01 sec. The proposed wheelbase preview
control algorithm has been evaluated through bump test. The proposed mode
control algorithm has been evaluated through various driving situation test such
as acceleration/deceleration, double lane change, J-turn, and off-road. The
driving performance of controlled vehicle with EMS system is compared with
that of passive vehicle which has a passive suspension system, composed of the
non-controlled spring and the shock-absorbing damper.
97
7.1. Ride Comfort Control Performance
The vertical acceleration of a human is a good indication of the ride comfort.
The international standard ISO 2631-1 specifies a method of evaluation of the
ride comfort by weighting the root-mean square (r.m.s) acceleration with
human vibration sensitivity curves [ISO'97]. The human vibration sensitivity
curve is shown in Figure 7.1. As it shown, humans are most sensitive to
vibrations in frequncy range from 4 to 10 Hz.
Figure 7.1. The human sensitivity to vertical vibrations.
98
In Zuo’s work [Zuo'02], this acceleration weighting filter is approximated by
a quasi-least-fifth order continuous-time filter as (7.1).
4 3 2(5)
5 4 3 2
87.72 1138 11336 5453 5509( )
92.6854 2549.83 25969 81057 79783
s s s sW s
s s s s s
(7.1)
The magnitude frequency response of the approximated acceleration
weighting filter is also shown in Figure 7.1. The weighted r.m.s. acceleration is
expressed as (7.2).
1/2
2
,0
1 T
w rms wa a t dtT
(7.2)
where aw and T denote the weighted acceleration and the duration of the
measurement, respectively.
In Table 7.1, the following values give approximate indications of ride
comfort in public transport proposed by ISO 2631-1. Quantitative evaluation of
the ride comfort improvement according to the criteria given in Table 7.1 would
be conducted through single bump test in subsections below.
Table 7.1. Criteria for evaluation of the ride comfort in public transport.
The r.m.s value of the frequency-weighted acceleration Evaluation
Less than 0.315 m/s2 not uncomfortable
0.315 m/s2 to 0.63 m/s2 a little uncomfortable
0.5 m/s2 to 1 m/s2 fairly uncomfortable
0.8 m/s2 to 1.6 m/s2 uncomfortable
1.25 m/s2 to 2.5 m/s2 very uncomfortable
Greater than 2 m/s2 extremely uncomfortable
99
7.1.1. Carsim® simulation results
Passing a single bump at a speed of 30 kph scenario has been simulated with
vehicle software Carsim® and MATLAB/Simulink to evaluate the performance
of the ride comfort enhancement. The single bump road height profile described
by equation (4.21) was applied to the left and right wheels. The feedback
controller was designed based on the system model descried as equation (3.7)
and the optimal preview control algorithm described in subsection 5.2.2 was
adopted to ride comfort improvement.
In Figure 7.2, the simulation results of proposed ride comfort improvement
control algorithms have been compared. The figures are indicating the heave
acceleration of the body, pitch angle, front and rear actuator forces. The legends
“passive”, “feedback”, “wheelbase preview”, and “full preview” indicate the
signals obtained by the passive vehicle, by the LQ optimal feedback control in
(5.10), by the proposed wheelbase preview control (WPC) in equation (5.25),
and by the full preview control (FPC) assuming that 0.3-seconds of future road
information is available. It is shown that noticeable reduction of heave
acceleration and pitch angle is achieved by both the feedback and preview
control input, compared to the passive vehicle. Regarding ride comfort, these
simulation results are indicating a huge potential for improvement, which
would be obvious by the driver. The FPC has the best potential to promote ride
comfort by driving actuator 0.3 seconds (preview time) earlier than the
feedback and WPC algorithms. The performance of proposed WPC algorithm
without preview road information is superior to that of the feedback control. In
Figure 7.2-(c) and (d), the controlled actuator force has been shown. For
100
comparison, the damping force of the passive vehicle has been also indicated.
It is evident that both the front and rear control forces by the FPC algorithm are
driven earlier than the others due to preview road information. The front
actuator forces of feedback control and WPC algorithms are similar to each
other, but the rear actuator force of the WPC is generated by the wheelbase
preview information from front wheels. As a results, the rear actuator forces of
FPC and WPC algorithms are similar to each other.
101
Figure 7.2. Comparison of ride comfort improvement simulation. (a) heave
acceleration, (b) pitch angle, (c) front and (d) rear actuator force
While the vehicle is fully passed through the bump, the weighted r.m.s.
values of vertical acceleration of drivers, aw,rms, have been compared and given
in Table 7.2. From the simulation results above, the proposed wheelbase
preview control algorithm has shown a better potential for ride comfort
improvement than the feedback control, but not better than full preview control
algorithm.
102
Table 7.2. Evaluation of the ride comfort improvement.
aw,rms [m/s2] Evaluation
Passive 1.175 Uncomfortable
Feedback 0.4235 A little uncomfortable
Wheelbase preview 0.2974 Not uncomfortable
Full preview 0.2017 Not uncomfortable
7.1.2. EMS system simulation results
In LQ optimal control approach, hard constraints cannot be explicitly
incorporated and hence have to be minimized in the cost function. For the EMS
systems, the constraints on actuator stoke and actuator voltage can cause
performance deterioration of the LQ optimal controller. In this case, the
constraints on control variables should explicitly be incorporated and the
optimization has to be carried out in real-time, therefore the MPC is the
appropriate controller design scheme.
To evaluate the improvement of ride comfort performance of the proposed
EMS system, the same bump scenario above has been simulated with the
nonlinear vehicle model constructed in MATLAB/Simulink. For comparison, a
feedback controller and an optimal preview control with wheelbase preview
information were designed based on the system model descried as equation
(6.14) and the model predictive algorithm described in subsection 5.2.3 was
adopted to ride comfort improvement. The simulation has been carried out in
two different cases. In the first simulation case, no constraint on the actuator
stoke and the actuator voltage is assumed, so it is an ideal case. And the second
simulation case, the limit for the variable voltage of power supply is ±12 V, and
103
the ±30 mm operational range of the ball screw mechanism is assumed as
shown in Figure 6.5.
a) Unconstraint case
In Figure 7.3, the simulation results of proposed ride comfort improvement
control algorithms for the vehicle with EMS system without constraint case
have been compared. The figures are indicating the heave acceleration of the
body, pitch angle, actuator stroke and voltage, and actuator stroke speed vs axial
force. The legends “passive”, “LQR”, “OPC”, and “MPC” indicate the signals
obtained by the passive vehicle, by the LQ optimal feedback control (LQR), by
the proposed wheelbase optimal preview control (OPC), and by the proposed
wheelbase model predictive control (MPC). It is shown that noticeable
reduction of heave acceleration and pitch angle is achieved by both the
feedback and preview control input, compared to the passive vehicle. The
performance of proposed OPC and MPC algorithm without preview road
information is superior to that of the LQR. In Figure 7.3-(c) and (d), the
controlled actuator strokes have been shown. It is noted that all actuator strokes
are over the operational range of ± 30 mm. In Figure 7.3-(e) and (f), the
controlled motor voltages have been shown. It is also noted that all desired rear
motor voltages are beyond the operational range of ±12 V. In Figure 7.3-(g)
and (h), the actuator stroke speeds vs axial forces have been shown. The bold
lines in the first and third quadrant represent the boundary of the modeled
actuator power constraint. In the first and third quadrant, further region from
the origin than the boundary line cannot be reached by the performance of the
104
motor under consideration. Due to the constraints, actual performance of ride
comfort improvement is not expected as Figure 7.3-(a) and (b).
105
106
Figure 7.3. Comparison of ride comfort improvement simulation for
unconstrained EMS system. (a) heave acceleration, (b) pitch angle, (c) front,
(d) rear actuator stroke, (e) front, (f) rear actuator voltage, (g) front, and (h)
rear actuator stroke speed VS axial force.
b) Constraints on actuator stoke and voltage case
In Figure 7.4, the simulation results of proposed ride comfort improvement
control algorithms for the vehicle with EMS system with constraint case have
been compared. The figures are indicating the same properties in Figure 7.3.
The legends “passive”, “LQR”, “OPC”, and “MPC” indicate the signals
obtained by the passive vehicle, by the LQ optimal feedback control (LQR), by
the proposed wheelbase optimal preview control (OPC), and by the proposed
107
wheelbase model predictive control (MPC). In this MPC design, hard
constraints on actuator stroke (±30 mm) and voltage (±12 V) are considered.
It is shown that reduction of heave acceleration and pitch angle is achieved by
both the feedback and preview control input, compared to the passive vehicle.
However, less performance improvement of ride comfort is achieved by the
controller, compared to the unconstrained case because of less actuator power.
The performance of proposed OPC and MPC algorithm without preview road
information is still superior to that of the LQR, however the performance gap
is reduced, compared to the unconstrained case. The weighted r.m.s. values of
vertical acceleration of drivers, aw,rms, have been compared and given in Table
7.3. It is noted that both ride comfort evaluations of vehicles controlled by the
LQR and OPC approaches are same each other as fairly uncomfortable. The
proposed MPC algorithm has shown a better potential for ride comfort
improvement than LQ optimal approaches due to considering hard constraint
in the design process.
In Figure 7.4-(c) and (d), the controlled actuator strokes have been shown.
It is noted that actuator strokes of the MPC are within the operational range of
±30 mm, while those of the LQR and OPC are enlarged to the boundary of the
range. Near the operating range boundary, the actuator stoke cannot be
increased or decreased due to the dramatically increased accumulator spring
stiffness as shown in Figure 6.5. As shown in Figure 7.4-(a), the actuator stroke
limitation causes huge acceleration chattering phenomenon of the LQR and
OPC in which the hard stroke constraint cannot be explicitly incorporated. In
Figure 7.4-(e) and (f), the controlled motor voltages have been shown. It is also
108
noted that all desired rear motor voltages are within the operational range of
±12 V. The MPC algorithm finds the optimal control input in the accessible
control region, but the OPC does not. In Figure 7.4-(g) and (h), the actuator
stroke speeds vs axial forces have been shown. In the first and third quadrant,
as expected, the actuators are driven by the all control algorithms within the
actuator power boundary.
Table 7.3. Evaluation of the ride comfort improvement by the EMS system.
aw,rms [m/s2] Evaluation
Passive 1.376 Very uncomfortable
LQR 0.7941 Fairly uncomfortable
OPC 0.6391 Fairly uncomfortable
MPC 0.4868 A little uncomfortable
109
110
Figure 7.4. Comparison of ride comfort improvement simulation for
constrained EMS system. (a) heave acceleration, (b) pitch angle, (c) front, (d)
rear actuator stroke, (e) front, (f) rear actuator voltage, (g) front, and (h) rear
actuator stroke speed VS axial force.
111
7.2. Mode Control Performance
A scenario for evaluation of the proposed EMS control algorithm is shown
in Figure 7.5. In the scenario, a vehicle starting at a low speed of 30 kph passes
through a bump. After passing the bump, the vehicle accelerates to above 90
kph and performs double lane change simultaneously. After that, the vehicle
decelerates to 50 kph to perform a J-turn. At the end, the vehicle decelerates to
10 kph and passes over a rough road.
30 [kph] 90 [kph] 50 [kph]
50 [
kp
h]
Off-road
Bump Acceleration & DLC Deceleration
J-turn
Deceleration
60 [kph]30 [kph]
10
[k
ph
]
Figure 7.5. Simulation scenario for evaluation of the proposed EMS control
algorithm.
112
Figure 7.6 shows the driving mode change and target height level according
to each driving condition in the simulated situation. The results comparison of
passive vehicle and controlled vehicle are shown in Figure 7.7 ~ 7.11. The
legend “passive” and “control” means the signals obtained by passive
suspension system and EMS system, respectively. Vertical acceleration, pitch
angle, and roll angle of the body are shown in Figure 7.7 ~ 7.9. The vertical
acceleration of the body in Figure 7.7 shows that the vehicle travels through the
bump from 15 to 17 sec and travels over the off-road from 80 to 100 sec. The
pitch angle of Figure 7.8 shows that the vehicle accelerates from 20 to 39.5 sec,
decelerates from 50 to 57 sec, and decelerates from 72 to 77 sec. The roll angle
of Figure 7.9 shows that the vehicle performs double lane change from about
26 to 34 seconds, performs J-turn from 58 to 68 sec.
The driving mode begins with mode 1 and it is converted to mode 3 by
passing through the bump. It can be seen that the driving mode changes to mode
2 due to acceleration after passing the bump. Then, the mode is converted to
mode 6 when the vehicle speed exceeds 90 kph at about 38 sec, and the mode
is changed to mode 5 due to mild driving from 39.5 to 50 sec. When the vehicle
speed drops below 90 kph at about 50 sec, the mode is not directly converted
from mode 6 to mode 2 by the mode chattering prevention algorithm. After the
speed drops below 60 kph, the mode is converted mode 2 at about 55 sec. From
55 to 80 sec, the mode is changed between mode 1 and 2 due to J-turn and
deceleration. After the vehicle passes over the rough road, the driving mode is
converted to mode 3 firstly, then the mode is switched to mode 4 by staying in
mode 3 for more than 2 seconds.
113
The target height level starts at 0 mm, which corresponds to mode 1, and is
maintained until the mode is changed to mode 5 by the chattering prevention
algorithm. Although the mode is changed from mode 2 to mode 6 at about 38
sec, the target height level is lowered to -30 mm at about 39.5 sec. The lowered
target height is restored to 0 mm after changing to mode 1 at about 57 sec. This
prevents undesirable intervention of control input during the attitude control by
maintained target height from 50 to 57 sec. The target height is kept at +30 mm
from 82 sec when the mode is changed to mode 4 to protect the lower end of
the vehicle.
For the acceleration, deceleration, double lane change, and J-turn situations,
it can be seen that the pitch and roll angle of the vehicle with the controlled
EMS are reduced by about 30% compared to the passive vehicle.
Figure 7.6. Simulation scenario for evaluation of the proposed EMS control
algorithm.
114
Figure 7.7. Heave acceleration of the vehicle body.
Figure 7.8. Pitch angel of the vehicle.
Figure 7.9. Roll angel of the vehicle.
115
Figure 7.10 and 7.11 show the suspension displacement and target height
levels of the front left (FL) and rear right (RR) corners of the vehicle. It can be
seen that the controlled vehicle is lowered and raised at the high-speed driving
and passing the off-road. At the time about 37.5, 57, and 82 sec, the suspension
displacement is controlled to gradually reach the target height within three
seconds. It can be also seen that when the pitch and roll angle are generated by
acceleration or turning, the suspension displacement is less generated by the
attitude control as compared with the passive vehicle.
Figures 7.12 and 7.13 show the actuator strokes of the FL and RR corners.
Suspension displacement occurs as much as the actuator stroke in height control
on the flat road. In mode 2, the phase of the actuator stroke is opposite to that
of the suspension displacement, so that the roll and pitch angle is generated less
than the passive vehicle.
In the case of the deceleration while the height level is lowered to -30 mm
from 50 to 57 sec (mode 6), an additional target displacement is applied to the
front actuator by the upper level controller as written in the above equation
(6.17) to reduce the pitch angle. Figure 7.10 and 7.12 show that the front
actuator is operated to push the body during the simulation time of 50 to 57 sec,
so that the front suspension displacement is maintained unchanged relatively
than the passive vehicle. On the other hand, the rear actuator stroke is kept close
to limit of -30 mm, so that the shape of the rear suspension displacement is
similar to that of the passive vehicle.
Representatively, the estimated FL suspension speed used in controller at
the double lane change is detailed in Figure 7.14. The numerical differentiation
116
value of the deflection sensor signal is also illustrated. While the differentiation
value is too noisy to be used in controller because of sensor noise, the estimated
value calculated by the state observer is quite similar to the actual value and the
noise is reduced.
Figure 7.10. FL suspension displacement.
Figure 7.11. RR suspension displacement.
117
Figure 7.12. FL actuator stroke.
Figure 7.13. RR actuator stroke.
Figure 7.14. Estimated FL suspension speed at double lane change.
118
Chapter 8 Conclusions and Future works
This dissertation has proposed a feasible active suspension control
algorithm to improve the driving performance. The reduced full-car model
which is free from unknown disturbance has been proposed to design the
control algorithm and the suspension state observer. The reduced model is
appropriate for a low-bandwidth controller design to concern primarily with
dominant (body) modes and associated characteristics. To improve the ride
comfort performance, a partial preview control algorithm without road
information has proposed. The wheelbase preview is relatively reliable and
cheap when compared with look-ahead sensor. The vertical acceleration
information of front wheels was used to obtain preview control inputs for rear
suspension actuators.
Finally, the reduced model and control algorithm has been adopted to the
electro-mechanical suspension (EMS) system. The main function of the EMS
system is ride height adjustment, roll and pitch compensation, and ride comfort
improvement. The proposed EMS control algorithm consists of the mode
selector, upper-level and lower-level controllers, and the suspension state
observer. The mode selector determines a present driving mode and the desired
height level of the vehicle. The upper-level controller determines the desired
suspension state considering the actuator stroke limit. The lower level controller
calculates the voltage at each actuator motor using the estimated state by the
observer and the calculated desired state. From the present driving mode, the
119
control objective is determined to be height control, attitude control, or ride
comfort control.
The effectiveness of the proposed estimation and control algorithm has been
evaluated via vehicle tests and simulations. It has been proven that the proposed
observer could estimate the suspension state well without regard to the effect
of unknown road disturbance by the field tests. From the simulation study, it
has been shown that the driving mode and target height level are changed
adaptively according to each driving condition. It has been proven that
suspension state can be estimated with good accuracy by the proposed observer.
The vehicle height was controlled to gradually reach the target height in height
control mode. The roll and pitch angle was reduced by actuator holding control
in attitude control mode. The ride comfort enhancement performance of the
proposed wheelbase preview control algorithm was superior to that of the
feedback control. The model predictive control algorithm could consider hard
constraints on control variables in design process, as a result, the higher
performance could be achieved than LQ optimal control algorithm in the case
of the actuator limitation.
In the future intelligent transportation system environment, an active
suspension control with preview information through vehicle-to-vehicle (V2V)
or vehicle-to-infrastructure (V2I) communications is imperative to achieve
further improvement of the driving performance.
120
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초 록
전륜 가속도 센서 기반 승차감 향상을
위한 능동 현가 시스템 예측 제어
승용차의 능동 및 반 능동 현가 시스템은 승차감 향상과 핸들링
성능을 개선해 주는 효과 때문에 지난 수십 년간 매우 활발히
연구되어 왔다. 반 능동 현가 시스템에 비해 능동 현가 시스템은 더
향상된 성능과 더 많은 기능을 제공한다는 것은 잘 알려 진
사실이다. 능동 현가 시스템의 주요 기능은 차량 높이 조정, 승차감
향상 및 자세 제어다. 최근 능동 현가 시스템이 장착된 고성능 차량
및 고급 세단이 대량 생산되어 판매되고 있는 추세이다. 예를 들어
Citroen 사의 Hydractive 시스템, Mercedes-Ben 사의 Active Body Control
(ABC) 시스템, BMW 사의 anti-roll control (ARS) 시스템이 개발되어
양산화 되었다. 능동 현가장치의 성능은 전방 도로 정보가 주어지게
되면 크게 향상 될 수 있다. 이러한 전방 도로 정보를 이용한
승차감 향상을 목표로 전세계 다양한 연구 개발이 진행되고 있다.
Mercedes-Benz 사는 세계 최초로 전방 도로 표면을 인식하여 예측
제어하는 능동 현가장치가 장착된 차량을 선 보였다. BMW 는 능동
현가 제어를 위한 비디오 영상 처리 시스템 개발에 노력하고 있다.
129
Volkswagen 사는 레이더 / 레이저 센서를 이용해 전방 도로를
감지하고 현가 시스템을 이에 미리 대비하고 작동시키기 위한
연구를 진행 중에 있다. Honda 사는 적응 형 현가 시스템 및 차량 간
네트워크 시스템에 대한 특허를 보유하고 있다.
다수의 참고 문헌을 심도 있게 검토한 결과, 능동 현가 시스템의
예측 제어 기술은 승객의 안전뿐만 아니라 편의도 증진시킬 수
있을 것으로 기대된다. 하지만 현재 개발되고 있는 최첨단 예측
현가 시스템 기술은 두 가지 주요 문제에 당면해 있다. 첫째, 현재
다수 개발된 현가 시스템 제어 방식에서는 서스펜션 변위 속도
또는 타이어 변위 량과 같이 습득하기 어려운 신호에 대한 정보가
필요하다. 둘째, 전방 도로 정보를 감지하기 위해서는 레이저
스캐너와 같은 정밀하고 비싼 센서가 필요하다. 비록 이러한 센서의
가격이 하락하고 있는 추세이긴 하지만 센서를 자동차에
추가적으로 장착함으로 인해 가격이 상승하고 이는 시스템 양산에
또 다른 장벽이 되고 있다.
따라서 본 논문에서는 현재 양산된 차량용 센서들을 이용하여
낮은 작동 주파수 대역의 능동 현가 시스템 제어를 위한 부분적인
예측 제어 알고리즘을 개발하는 것을 목표로 하고 있다. 알 수 없는
도로 가진 입력에 대처하기 위해, 새로운 수직방향 전 차량 모델이
개발되었다. 이를 통해 쉽게 습득할 수 있는 측정값을 이용한 현가
시스템 상태 변수 추정기를 개발하였다. 전륜에서 발생하는 수직
가속도 정보는 후륜 능동 현가장치의 예측 제어를 위한 제어 량
결정에 사용된다. 차량 신호로부터 현재 주행 모드 판별에 의해
130
현가 시스템 제어 목표는 차고 조절, 자세 제어 및 승차감 향상
제어로 나뉜다.
제안된 능동 현가 시스템 제어 및 상태 변수 추정 알고리즘의
성능은 컴퓨터 시뮬레이션과 차량 테스트를 통해 검증되었다. 그
결과 제안된 제어 및 추정 알고리즘으로 향상된 차량 주행 성능을
확보함을 확인하였다.
주요어: 능동 현가 시스템, 수직방향 전 차량 축소 모델, 칼만 필터,
선형 제차 레귤레이터, 최적 선형 예측 제어 기법, 모델 예측 제어
기법, 전자 기계식 현가 시스템
학 번: 2013-23053