Chapter 6 Aircraft Dynamics and Control...飛行力学 Chapter I-6 Aircraft Dynamics and Control 13...

Chapter I-6 Aircraft Dynamics and Control飛行力学

1

Chapter 6 Aircraft Dynamics and Control

6.1 Aircraft Model


2


3


4


5

x

0

c k

m

u

< Review > Dynamics of Mass-Spring-Damper System (1/7)

(1) Laplace Transformation and Transfer Function

ukxxcxm

Laplace Transformation

susxkcsms 2

Transfer Function in terms of sx su

11

2 kcsmss

u

x

Characteristics Equation

0kscsm 2


for : Conjugate Complex Root

6


m

mkccs

2

42

Eigen Values (Roots of Characteristics Equation)

042 mkc

jss 21,m

c

2

m

cmk

2

4 2

2

2

1

1

21

/1

ss

c

ss

c

ssss

ms

u

x

Transfer Function


7


Inverse Transfer Function (Response in Time Domain)

tm

cmke

cmk

tjtec

tjtectu

x

tm

c

t

t

2

4sin

4

2

sincos

sincos

2

2

2

2

1

2121 ,s,s

for : Real Root042 mkc

ttecect

u

x21

21


8


(2) State Equation

vx

ukxcvvm then

BuAxx where

v

xx uu

m

c

m

k10

A

m

10

B

x

0

c k

m

u


9


Laplace Transformation

where

BuAxx s BuxAI s

BuAIx1

s

sm

km

cs

ss

111

AI

m

ks

m

csss 2det AI


u

m

smu

msm

km

cs

v

x

ss

11

101

1

10


Transfer Function in terms of sx su

kcsmsm

su

x

s

2

11

kcsms

ss

u

v

2

Transfer Function in terms of sv su


11


(3) Damping and Frequency of Mode/ Eigenvalue

ssReal 21 ssjImag

02 22 sss ss

jImagReal

jss ssss

2

21 1,

Eigen Values

where

Frequency :22 ImagReals

Damping :22 ImagReal

Reals


12

6.2 Characteristics of Aircraft Motion

(1) Longitudinal Characteristics

e

q

u

u

x

BuAxx

0

M~U

Z

X

e

e

e

o

B

where

0

0

0

0

0

0

~

sin~

1~

~

~

U

ZMMM

U

gMM

U

ZMMM

U

ZMMM

U

ZMMM

e

ee

q

qq

uuu

(4.2-15)

0100

~~~~

sin1

cos

0

0

000

00

MMMM

U

g

U

Z

U

Z

U

Z

gWXX

qu

qu

u

A


13

Aircraft Model C <Charlie> (Flight Condition 4)

Linearized Equation Eq.(4.2-15) assuming

Approximate Short Period Mode Eq.(5.2-1), Eq.(5.2-2)

Approximate Phugoid Mode Eq.(5.2-4)0o

Full State Equation Approximate Equations

Longitudinal Mode Characteristics

ＥｉｇｅｎｖａｌｕｅＤａｍｐｉｎｇＦｒｅｑ．：ｒａｄ/ｓ

0.0006 + 0.0512ｉ -0.0108 0.0512

0.0006 – 0.0512ｉ -0.0108 0.0512

-0.3785 + 0.8456ｉ 0.4085 0.9264

-0.3785 – 0.8456ｉ 0.4085 0.9264

Short Period Mode Approximation


-0.3780 + 0.8453ｉ 0.4082 0.9260

-0.3780 – 0.8453ｉ 0.4082 0.9260

Phugoid Mode Approximation


0.0001 + 0.0524ｉ -0.0019 0.0524

0.0001 – 0.0524ｉ -0.0019 0.0524


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Full Calculation

Approximate Calculation


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Full Calculation



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(2) Lateral and Directional Characteristics

r

a

r

p

u

x

BuAxx

00

NN

LL

00

''

''

ra

ra

B

where

r,a,r,p,i

II/I1

LI/INN

II/I1

NI/ILL

zzxx

2

xz

izzxzi'

i

zzxx

2

xz

ixxxzi'

i

: Primed Derivatives

0tan10

0NNN

0LLL

U

cosg1

U

W

U

Y

0

'

r

'

p

'

'

r

'

p

'0

0

0

0

0

A

(4.2-16)


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Aircraft Model C <Charlie> (Flight Condition 4)

Linearized Equation Eq.(4.2-16)

Approximate Dutch Roll Mode Eq.(5.2-5)

Approximate Roll Mode Eq.(5.2-6)

Approximate Spiral Mode Eq.(5.2-7), Eq.(5.2-8)

Full State Equations Approximate Equations

Lateral/ Directional Mode Characteristics


0.0120 -1.0000 0.0120

-0.0453 + 0.8088ｉ 0.0560 0.8100

-0.0453 - 0.8088ｉ 0.0560 0.8100

-0.5624 1.0000 0.5624

Dutch Roll Mode Approximation


-0.0855 + 0.7740ｉ 0.1098 0.7787

-0.0855 – 0.7740ｉ 0.1098 0.7787

Roll Mode Approximation


-0.4700 1.0000 0.4700


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Full Calculation



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Full Calculation



20

BuAxx

Cxy

0sdet AI

oc uyyKu

oc BuBKyxBKCAx

0sdet BKCAI

Eq.(6.3-1)

6.3 Feedback Control

State Equation

Observation Equation

Characteristics Equation

Eq.(6.3-2)

Eq.(6.3-3)

Eq.(6.3-4)

Eq.(6.3-5)

Eq.(6.3-6)

ＣｏｎｔｒｏｌｌｅｒＫ

ＡｉｒｃｒａｆｔＤｙｎａｍｉｃｓ

ＯｂｓｅｒｖａｔｉｏｎＣ

yc + u x

y

-

Command

Feedback Control Law

Closed Loop State Equation

Characteristic Equation of

Closed Loop State Equation


21

Control

Law

Stability

Augmentation

System

Pitch Rate SAS

Yaw Damper

Yaw Damper (Wash-out Filter)

Beta Dot Damper

Control

Augmentation

System

Pitch Rate Control

RSS Control

Bank Control

Bank Control for Directionally

Unstable Aircraft

Guidance

Law

Flight Path

Guidance

Altitude Control

Direction Control

Design of Guidance and Control Law

in General

Chapter 6 Aircraft Dynamics and Control...飛行力学 Chapter I-6 Aircraft Dynamics and Control 13...

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Transcript of Chapter 6 Aircraft Dynamics and Control...飛行力学 Chapter I-6 Aircraft Dynamics and Control 13...