LQG-LTR控制在無(wú)人機(jī)飛行控制中的實(shí)現(xiàn)及仿真

26

5

2009

5

:1006-9348(2009)05-0044-04

LQG/LTR

,

,

(

,

710072)

:

,

LQG/LTR

,

,

(LQG),

(LTR)

LQG

,

,

,LQG/LTR

,

,

,

:

;

;

;

:TP391.9;V249.1

:B

ImplementationandSimulationofLQG/LTRControl

MethodinUAVFlightControl

ZHOUZhi-jiu,YANJian-guo,ZHANGQiong-yan

(DepartmentofAutomaticControl,NorthwesternPolytechnicalUniversity,XianShanxi710072,China)

ABSTRACT:InviewoftheinfluencesofexternaldisturbancesandsensormeasurementnoiseintheUAVflight

course,aLQG/LTRrobustcontrolmethodisutilizedindesigningtheoptimalcontrollerandoptimalfilter(LQR)for

lateralflightcontrolofUAV.LoopTransferRecoverymethod(LTR)isalsousedtocompensatefordeficiencyofthe

LQGdesign.TheapplicationofLQG/LTRcontrolmethodaccomplishesthedesignforlateralcontrolofcertainUAV,

anditsolvestheproblemofinstabilityandinaccuracythatthecontrolsystemoftheaircraftmodelmightundergoby

randomdisturbances.Thesimulationofthecontrolmethodisgiven.SimulationresultsindicatethattheLQG/LTRro2

bustcontrolsystemisabletotrackthelateralinstructionsaccuratelywithgoodrobustness.Itsatisfiesthelateralcon2

trolrequirementsandisofgreatvalueinpracticalprojects.

KEYWORDS:Robustcontrol;UAV;Lateralcontrol;Simulation

1

,

,

2LQG/LTR

,

,

,

,

,

2.1

,

LQG

LQG/LTR(LinearQuadraticGaussianWithLoopTransfer

:

),

,

(LQR

)

Recovery)

,

(Kalman

LQG

(LTR)

LQG

,

LQG/LTR

,

LQG/LTR

Matlab

,

,

,

,

,

LQG

:2008-03-27

:2008-03-31

44

2.2LQG/LTR

LQG/LTR

,

3

1

,

,

,

,

,

,

,

1LQG

2000m

140km/h

:

,

,

q

x=Ax+Bu

,

y=Cx

,

q

:

<

x=[

u=[

p

r]

T

:

]

r

T

x(t)=Ax(t)+Bu(t)+T(t)

y(t)=Cx(t)+(t)

a

y=[

<]T

<pr,

,[A,B]

,[A,C]

(t)

(t)

,

,

,

a

r

:

2

E[(t)

E[(t)

(t)]=

(t)]=

0

T

T

T

>0

E[(t)

(t)]=0

E[x]

(t)

x

,E[xx

T

]

x

(t)

:

J=E{[z

(t)Qz(t)+u(t)Ru(t)]dt}

TT

0

2

z(t)=Kx(t)

Q

x(t)

,

,R

,

Q

=Q

T

0,R=R

>0

T

,

I

p

LQG/LTR

:

,

,

1)

LQG

Q

R

,

,

,

r

,

<

a

K(sI-A)-1

c

B

:

A

B

O

44

42

42

2)

LQG

K,

f

-100100

0-10010

q,

G(s)G(s)

c

A

=

=

Z

K(sI-A)-1

B

O

00

00

00

c

44

limG(s)G(s)

c

00

q

88

=limK(sI-A+BK+KC)-1KC(sI-A)-1

B

O

I

c

c

f

f

B

26

q

Z

=K(sI-A)-1

B

22

82

c

LQG/LTR

,

C

=[I

22

O

]

2628

Z

,

P=(C(-A)-1B)-1

60

45

10

K=R-

c

1

BTP,

c

Riccati

:

:

s+10

ABP+M

QM=0

TTT

P+PA-PBR-1

cccc

Kalman

:

,P=P

c

T

0

c

=mBB

z

T

,

=nI

22

Matlab

LQG/LTR

,

z

LTR

:

K,K:

c

f

R=pI,Q=qCC

22

T

[G,K,P]=kalman(G,

,

);

[p1,p2,l,p,wp,p]=aresolv(A,Q,R);

K=RB

z

z

kff

,

Kalman

,

RQ

T

p

,

m

n

c

LQG/LTR

G:

c

<

,

,

,

G=ltry(G,K,Q,R,q,)

f

,

,

;

c

q

p

5

,

m

,

m=10

,n=10,p=0.1,q=10

310

,

n

,

,q

,

LQG/LTR

KK:

c

f

2.2543

-0.5514

8.7762

-0.5514

3.3988

0.0036

4

LQG/LTR

-2.9103

0.9991

,

Kalman

:

K=

f

-0.9539-2.4528

-2.97050.9854

K=PC

f

T

-1,P

f

Riccati

:

f

PA

f

T

+AP-PC

f

T

-1CP+TT

f

T

=0

f

-0.9914-3.0028

,P=P

f

T

f

0

-3.0028

0.9914

82

x^(t)

,

LQG

u3(t)=-Kx^(t),

c

,

0.6639-0.0575

0.3150

0.0825

0.5745-0.2135

0.0666

3.3636

-0.4195

K=

c

0.7352-0.0016-0.0101-0.01560.0273

-0.4195

1.0749

28

3

,

60dB,

=0

<=5,

,

4

,

10%

5%

5

,

,

,3s

;

,

,3s

,

,

,LQG/LTR

,

,

3

46

6

,1998,30(1).

[J].

[6]

,

.

LQR

[J].

,2006,24(3).

,

LQG/LTR

,

,

,

5

[7]

,

,

.

LQG/LTR

[J].

,2004,(4).

<

4

[

]

:

(1982-),

,

(

),

,

[1]

[2]

.

.

[M].

:

,1984.

:

,

[M].

:

;

,2006.

(1956-),

:

(

),

,

,

[3]GStein,MAthans.TheLQG/LTRproced-ureformultivariable

feedbackcontroldesign[J].IEEETransactiononAutomaticCon2

trol,1987,AC-32(2).

;

(1983-),

(

),

,

,

[4]AAlonge,FDIppolito,CGrillo.TakeoffandLandingRobust

ControlSystemforaTandemCanardUAV[J].AIAA.2005.

3447.

:

,

[5]

,

,

.

LQG/LTR

(

24

)

[3]MalcolmHawkes,AryeNehorai.Acousticvector-sensorbeamform2

ingandcapondirectionestimation[J].Transactionsonsignalpro2

cessing,19