8/19/2019 MEMS accelerometers
1/22
WARSAW UNIVERSITY OF TECHNOLOGY
FUCULTY OF POWER AND AERONAUTICAL ENGINEERING
ATTITUDE AND NAVIGARION SYSTEMS
Topic of project:
MEMS ACCELEROMETERS, PRINCIPLES OF
OPERATION, ERROR ANALYSIS
SUPERVISOR
ANTONI KOPYT, M. Sc., Eng
DONE BY
OLEH SHULIMOV, student
280738
WARSAW 2015
8/19/2019 MEMS accelerometers
2/22
2
CONTENT
1. INTRODUCTION ..................................................................................................... 4
2. BASIC THEORETICAL INFORMATION ............................................................. 5
2.1 MEMS Accelerometers Implementation ............................................................. 52.2 Architecture and operational principle of MEMS accelerometers ...................... 7
2.3 Error and noise analysis ..................................................................................... 10
3. MATLAB PROGRAMMING ................................................................................ 11
3.1 Problem description and method of problem solution ...................................... 11
3.2 Program code ...................................................................................................... 14
3.3 Input and output representation .......................................................................... 17
4. CONCLUSION ....................................................................................................... 21
5. REFERENCES ........................................................................................................ 22
8/19/2019 MEMS accelerometers
3/22
3
LIST OF SYMBOLS AND ABBREVIATIONS
MEMS – microelectromechanical systems
DVR – data video recorder
a – acceleration
F – force to compress or extend spring
m – mass of the proof mass
k – spring stiffness constant
x – displacement of the proof mass
– roll angle of the proof mass – pith angle of the proof mass
g – normalized accelerometer data
V – velocity of the proof mass
8/19/2019 MEMS accelerometers
4/22
4
1. INTRODUCTION
MEMS it is abbreviation that means “microelectromechanical systems”. These
are miniature devices that contain microelectronic and micromechanical components.
Daily we use variety of devices that are based on MEMS technology. The simplest
example of microelectromechanical systems is an accelerometer that is used in all
modern smart phones, gaming consoles and hard drives. At present MEMS
accelerometer has became important part of many systems. Its solution is used in the
automotive industry, military industry, medicine and particularly in aerospace
industry.
The aim of this project is considerable learning of MEMS accelerometers,
including knowledge acquisition relating its spheres of implementation, operational
principle, consideration of error and noise appearance. Also project included
modeling of real data from MEMS accelerometer and its simulation during addition
of noise and filtration.
The main idea of the project is to provide visualization of MEMS
accelerometer operation in real-time conditions and present the method of solution of
the problems that can appear during MEMS accelerometer exploitation.
8/19/2019 MEMS accelerometers
5/22
5
2. BASIC THEORETICAL INFORMATION
2.1 MEMS Accelerometers Implementation
Technologies have been advanced daily. To combine small size of
accelerometer and its effectiveness people started to invent something absolutely new
using microelectronics field. In 1979 at Stanford University there was developed
MEMS (micro electro-mechanical systems) accelerometer. Today MEMS
accelerometers revolutionized and uses in variety of technologies spheres to simplify
our routine life. This type of accelerometers is highly potential from technological
and commercial point of view. Less power – more efficiency. This is great advantage
of MEMS accelerometers over others. Also it has more benefits. Firstly, it has chip
and easy maintenance. Secondly, comparing with average electromechanical
accelerometer, it three times cheaper than price, for example, of piezoelectric
accelerometer. Similar, it has 1/100 size. Lastly, all electronic situates on the one chip
that gives high portability for users.
Fig. 2.1.1 Evolution of accelerometers
The most common device in MEMS technology is a MEMS accelerometer. As
mentioned above, the scope of its use is extremely broad. It covers mobile phones,
laptops, game consoles as well as more serious devices such as automobiles, aircraft
and rockets. The main purpose of the accelerometer is to measure the acceleration. In
the case of mobile phones, it is used for many goals. For example, it is used for
change of screen orientation or performance of some functions during the “shaking”
8/19/2019 MEMS accelerometers
6/22
6
of the device. However, the main area of implementation of MEMS accelerometers in
smart phones is game industry. Nowadays it is difficult to imagine smart phone
without installed accelerometer. By the way, first time it was installed in the mobile
phone Nokia 5500. It used as a pedometer. On the whole, interest in MEMS began to
grow with the development of platforms iOS and Android. Also accelerometers are
also available in variety of controllers, game consoles. For example, it can be used in
ordinary gamepad or in motion controllers. Especial importance MEMS
accelerometers have in laptops, precisely in its hard disks. It is known that hard disk
is brittle device that can be damaged easily. During the drop of laptop accelerometer
fixes sharp change in acceleration and sends command to parking of the head of a
hard disk preventing the damage of device and the losses of data. On a similar
principle accelerometer affects the car DVR. During hard acceleration, braking and
vehicle rebuild videotape marked with a special marker, which protects it from
erasing and rewriting, which greatly facilitates further parsing of road accidents.
In general, the largest and most promising market for accelerometers and other
MEMS is the automotive industry. In contrast to the market and mobile gaming
devices, where the accelerometers are used for entertainment purposes, in
automobiles any security system based on accelerometer working. With its help,
operating system of airbags deployment, anti-lock brakes, stability, adaptive cruise
control, adaptive suspension, Traction Control system. Taking into account that car
manufacturers are paying particular attention to safety, the number of employed
accelerometers and other MEMS will only grow. In mechanics and aerospace
industry, MEMS accelerometers is used to measure the level of vibrations of separate
parts. For example, in aviation this type of accelerometer is used for measurement the
level of engine vibration. Also it is actively implemented in aircraft control systems
and navigation.
8/19/2019 MEMS accelerometers
7/22
7
2.2 Architecture and operational principle of MEMS accelerometers
Design of the MEMS accelerometer. There are several types of devices
depending on their architectures. The work of the accelerometer can be based on the
capacitor principle. The movable part of such a system is a proof mass which shifts
depending on the inclination of the device. The capacitance changes because of shift
of proof mass and then change the voltage appears. From these data, it is possible to
obtain displacement of the proof mass and desired acceleration.
Fig. 2.2.1 Structure of capacitor MEMS accelerometer
The most common type of accelerometer is piezoelectric system
accelerometers. Just as in the capacitor accelerometers, they are based on proof mass,
pressure of which acts on the piezoelectric crystal. Under the pressure it generates an
electric current that allows calculating the required acceleration, knowing the
parameters of the entire system. There is another type of accelerometer that isfundamentally different from the capacitor and the piezoelectric accelerometer. These
accelerometers are called thermal. Their architecture involves the use of an air
bubble. During the acceleration the bubble is deflected from its initial position and
accelerometer fixes it. Knowing how much shifted bubble motion, the acceleration
can be calculated.
Simple mass spring system is the main key principle of MEMS accelerometer
working. Hooke’s law physically controls spring movement inside an accelerometer.
8/19/2019 MEMS accelerometers
8/22
8
“Hooke's law is a principle of physics that states that the force needed to extend or
compress a spring by some distance is proportional to that distance. That is: where is
a constant factor characteristic of the spring, its stiffness.”[7]. Mathematically
Hooke’s law has a form:
where
[] – stiffness of spring, its constant factor characteristic, N/m;[] – displacement of spring, m;[] – force to compress or extend spring, N;Another very important physical rule that underlies working of MEMS
accelerometer is Newton’s second law. It states that force acting on the accelerated
mass will produce the force with magnitude. Mathematically Newton’s second law
looks like:
where
[] – mass of the proof mass, g;[] – acceleration m/s2;
Fig. 2.2.2 Mass-spring system
Figure 2.2.2 demonstrates the mass connected to the spring. In accordance to
the Newton’s second law, if this system will be accelerated resulting force will
appear and will equal . This force causes expanding or compression of the massunder the constraint that
8/19/2019 MEMS accelerometers
9/22
9
Consequently, acceleration a will cause displacement of the proof mass that
can be expressed as:
Similarly, if we observe displacement that using following expression it is
possible to find acceleration:
This simple mathematical method solves a problem that relates to acceleration
finding using change of displacement of proof mass connected to the spring.
However, this system responds only along length of spring. Other words, it is
possible to measure acceleration only along one axis. To receive acceleration along
desirable axes, this system should be installed along each axis:
where
[ , – acceleration and displacement along axis x respectively;[ ] – acceleration and displacement along axis y respectively;[ – acceleration and displacement along axis z respectively.
Fig. 2.2.3 Capacitive MEMS accelerometer operation
8/19/2019 MEMS accelerometers
10/22
10
2.3 Error and noise analysis
However, MEMS accelerometers contain set of errors that can reduce its
accuracy of measurement. It is possible to characterize and divide errors into two
groups, deterministic and stochastic.
Deterministic errors are characterized by misalignment configurations. These
problems are possible to divide into two groups, external and internal. External
misalignment may appear during 2D MEMS accelerometers usage. Problem with
nonperpendicularity between two accelerometers may be present. Internal
misalignment occurs due to the manufacturing process. Also deterministic errors
include quantization errors. During digitalization for the convenience of processingand information transmission, discrete signal can contain quantization errors.
Generally stochastic errors in accelerometer is caused by some amount of noise
and created by thermal and mechanical fluctuations inside the accelerometer. Each
axis of accelerometer has different level of noise. It is explained by different
construction of each orientation of accelerometer. There are two basic types of noise,
namely white noise and random walk. White noise is created by means of random
charge motion made by the thermal agitation. Random walk, called drift, is
characterized by long-term noise that makes true values of samples not accurate. This
type of noise is not so significant for accelerometers with constant movement and fast
rate of sampling. However, accelerometers with long-term averaged measurements
suffer from influence of this type of noise.
8/19/2019 MEMS accelerometers
11/22
11
3. MATLAB PROGRAMMING
3.1 Problem description and method of problem solution
The practical part of the project is based on measurements of real-time data
using built-in 3-axis MEMS accelerometer of Samsung Galaxy Tab 4 tablet. To
measure input data there was downloaded from Play Market special application that
called Accelerometer. To model and simulate the inputs and outputs programming
software Matlab was used. Following diagram demonstrates algorithm of program:
2
1
3
4
5
6
7
8
9
Input data extraction.
Input of optimized parameters.
Gaussian white noiseaddition to measured
acceleration along each axis
Calculation of proof
mass displacement
Calculation of roll and
pitch angles of proof masschanged during displacement
Calculation of velocity
of proof mass
Calculation of proof
mass displacement with
Gaussian white noise
Filtration of acceleration
with added noise
Calculation of proof
mass displacement using
filtered acceleration
Plotting of graphs
8/19/2019 MEMS accelerometers
12/22
12
Basic part of the experiment was to move physically the tablet. This movement
caused displacement of accelerometer proof mass and acceleration was occurred.
During experiment there was decided to move tablet changing its pitch angle.
Following pictures represent initial and final position of tablet:
Fig 3.1.1 Initial and final position of the tablet
Than the data including acceleration along each of the axes and time of
displacement was recorded to tablet in txt format. Following steps describes process
in details:
1. The data was put to the laptop and extracted using functions of Matlab
software.
2. After the data were extracted, along each axis displacement of proof mass
was calculated using optimized design parameters of capacitive MEMS
accelerometer such as spring constant and mass of the proof mass. Optimized data
were taken from one of the scientific articles. Displacement along each of axis was
calculated from equation:
8/19/2019 MEMS accelerometers
13/22
13
3. Using accelerometer, it is possible to find roll and pitch angles which a
change during some period of time. It was achieved using following formulas:
where,
[, [ – roll and pitch angles respectively;[ [ – normalized data of accelerometer.4. Also the velocity along axis X was found using integration of acceleration
along axis X:
5. Using special function in Matlab, there was added Gaussian white noise to
measured acceleration. The signal-to-noise ratio per sample is 30 dB.
6. Then displacement with some error was computed. Method of calculation
remained the same as on step number 2.
7. To minimize the appearance of noise during the measurements, Gaussian
low pass filter with equiripple single-rate or multirate FIR filter design was applied. It
was used with some specifications such as frequency at the start of the pass band
equal 100 Hz, frequency at the end of the stop band equal 220 Hz, amount of ripple
allowed in the pass band is 60 dB and attenuation in the stop band is 0.5 dB. After it
implementation acceleration data along each axis were filtered.
8. In this step displacement in accordance to the filtered acceleration was
received. Method was used as on the previous steps.
9. Finally, after all computations graphs were built.
8/19/2019 MEMS accelerometers
14/22
14
3.2 Program code
This part of the project highlights program code with comments.
clc
clear all close all
%input data for optimized MEMS accelerometer m=0.42e-6;%g. optimized mass of proof-mass k=1.784;%n/m optimized stiffness of spring
%read data from text file a1=textread('D:\1\mmm_x.txt');ax=a1(:,1)';%acc tx=a1(:,2)';%time
a2=textread('D:\1\mmm_y.txt');ay=a2(:,1)';ty=a2(:,2)';a3=textread('D:\1\mmm_z.txt');az=a3(:,1)';tz=a3(:,2)';
%take each 2th element of acceleration vector ax1=ax(1:2:length(ax));ay1=ay(1:2:length(ay));az1=az(1:2:length(az));
tx1=tx(1:2:length(tx));ty1=ty(1:2:length(ty));tz1=tz(1:2:length(tz));
%calculation of displacement along x,y,z (10e-6 m = 1 micron) x=(m*ax1/k);y=(m*ay1/k);z=(m*az1/k);%calculation of roll and pitch angles r=atan(ay1./az1);
p=atan((-ax1.*cos(r))./az1);calculation in degrees roll=r.*180./3.14;% pitch=p.*180./3.14;
%velocity calculation Vx=cumtrapz(tx1,ax1);Vy=cumtrapz(ty1,ay1);Vz=cumtrapz(tz1,az1);
%addion of Gaussian white noise
a11 = awgn(ax1,30,'measured');a12 = awgn(ay1,30,'measured');a13 = awgn(az1,30,'measured');
8/19/2019 MEMS accelerometers
15/22
15
%calculation of displacement with noise along x,y,zx11=(m*a11/k);y11=(m*a12/k);z11=(m*a13/k);%Gaussian low pass filter design and filtration
d = fdesign.lowpass('Fp,Fst,Ap,Ast',100,220,60,0.5,1000);Hd = design(d,'equiripple');axf = filter(Hd,a11);ayf = filter(Hd,a12);azf = filter(Hd,a13);
xf=(m*axf/k);yf=(m*ayf/k);zf=(m*azf/k);
figure
plot3(x,y,z,'--')hold on plot3(x11,y11,z11,'--g')hold on plot3(xf(5:123),yf(5:123),zf(5:123),'r')grid on xlabel('X, m')ylabel('Y, m')zlabel('Z, m')legend('Measured displacement of mass','Measured displacementof mass with added noise','Filtered displacement of mass by
Gaussian low pass filter')
figureplot(tx1,Vx)grid ontitle('Velocity on time dependence along X axes')xlabel('Time, s')ylabel('Velocity, m/s')
figureplot(tx1,pitch)
grid on title('Tablet pitch angle on time dependence')xlabel('Time, s')ylabel('Pitch angle, deg')
figureplot(ty1,roll)grid on axis([0 5 -10 10])title('Tablet roll angle on time dependence')xlabel('Time, s')
ylabel('Roll angle, deg')
8/19/2019 MEMS accelerometers
16/22
16
figureplot(tx1, ax1)hold on plot(tx1,a11,'g')hold on plot(tx1,axf,'r')
grid on title('Acceleration on time dependence along X axis')xlabel('Time, s')ylabel('Acceleration, m/s.^2')legend('Measured acceleration','Measured acceleration withadded noise','Filtered acceleration by Gaussian low passfilter')
figureplot(tx1, ay1)hold on
plot(tx1,a12,'g')hold on plot(tx1,ayf,'r')grid on title('Acceleration on time dependence along Y axis')xlabel('Time, s')ylabel('Acceleration, m/s.^2')legend('Measured acceleration','Measured acceleration withadded noise','Filtered acceleration by Gaussian low passfilter')
figureplot(tx1, az1)hold on plot(tx1,a13,'g')hold on plot(tx1,azf,'r')grid on title('Acceleration on time dependence along Z axis')xlabel('Time, s')ylabel('Acceleration, m/s.^2')legend('Measured acceleration','Measured acceleration with
added noise','Filtered acceleration by Gaussian low passfilter')
8/19/2019 MEMS accelerometers
17/22
17
3.3 Input and output representation
Fig. 3.3.1 Displacement of proof-mass along X,Y,Z axis (NED frame)
Fig. 3.3.2 Velocity on time dependence along X axes
-50
510
1520
x 10-7
-1
-0.5
0
0.5
1
x 10-7
1
1.5
2
2.5
x 10-6
Y, m
X, m
Z , m
Measured displacement of mass
Measured displacement of mass with added noise
Filtered displacement of mass by Gaussian low pass filter
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2
0
2
4
6
8
10
12
Time, s
V e l o
c i t y , m / s
8/19/2019 MEMS accelerometers
18/22
18
Fig. 3.3.3 Pitch angle of proof mass on time dependence
Fig. 3.3.4 Roll angle of proof mass on time dependence
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-60
-50
-40
-30
-20
-10
0
10
Time, s
P i t c h a n g l e ,
d e g
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10
-8
-6
-4
-2
0
2
4
6
8
10
Time, s
R o l l a n g l e ,
d e g
8/19/2019 MEMS accelerometers
19/22
19
Fig. 3.3.5 Acceleration on time dependence along X
Fig. 3.3.6 Acceleration on time dependence along Y
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
0
1
2
3
4
5
6
7
8
Time, s
A c c e l e r a t i o n , m / s . 2
Measured acceleration
Measured acceleration with added noise
Filtered acceleration by Gaussian low pass filter
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Time, s
A
c c e l e r a t i o n , m / s . 2
Measured acceleration
Measured acceleration with added noise
Filtered acceleration by Gaussian low pass filter
8/19/2019 MEMS accelerometers
20/22
20
Fig. 3.3.7 Acceleration on time dependence along Z
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 54
5
6
7
8
9
10
11
12
13
Time, s
A c c e l e r a t i o n , m / s . 2
Measured acceleration
Measured acceleration with added noise
Filtered acceleration by Gaussian low pass filter
8/19/2019 MEMS accelerometers
21/22
21
4. CONCLUSION
MEMS technology has been advanced with time. One of the popular MEMS
technology device accelerometer has became important part of modern life. Although
first accelerometers were constructed for industrial and automotive purposes, today it
evolved to use for personal goals. Our ordinary devices use MEMS accelerometer
technology to make a lot of things easier and improve it. Moreover, scientists plan to
implement it more and more in the near future. Therefore, research in this topic is
very actual at present.
There was considered main areas of implementation of MEMS accelerometer,
its design and basic principle of operation. Possible errors and noise factor duringMEMS accelerometer usage were regarded. On the top of this, based on operational
principle of the accelerometer and methods of data calculation, there was written
computer program that read, analyze, compute and model data. Different graphs were
built. Results of all computations were displayed using simulation and visualization
method.
8/19/2019 MEMS accelerometers
22/22
22
5. REFERENCES
1. Matej Andrejaśić, MEMS accelerometers, pp. 2-3, March 2008
2. Kanchan Sharma, Isaac G. Macwan, Linfeng Zhang, Lawrence Hmurcik,
Xingguo Xiong, Design Optimization of MEMS Comb Accelerometer , p.8
3. http://www.phidgets.com/docs/Accelerometer_Primer
4. http://soundlab.cs.princeton.edu/learning/tutorials/sensors/node9.html
5. Der-Ming Ma, Jaw-Kuen Shiau, I.-Chiang Wang and Yu-Heng Lin, Attitude
Determination Using a MEMS-Based Flight Information Measurement Unit , p.5,
2012
6. http://www.ferra.ru/ru/techlife/review/mems-part-1/#.VmBkhnYvfIW
7. https://en.wikipedia.org/wiki/Hooke%27s_law
Top Related