Robust Flight Control System Design with Cerebellar Model ...w3.uch.edu.tw/control/download/SMC5.pdf · (PD) based cerebellar model articulation controller (CMAC) for vertical take-off

T. C. Kuo

Robust Flight Control System Design with Cerebellar Model Articulation Controller

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Contents

Abstract IntroductionSystem DynamicsVTOL Aircraft Control SystemControl System Performance Conclusion

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Abstract This paper presents a robust proportional-derivative

(PD) based cerebellar model articulation controller (CMAC) for vertical take-off and landing (VTOL)flight control systems.

CMAC that requires training patterns for tuning some

weighting factors can be used for robust control.

A novel CMAC incorporating with a PD controllerdesign is proposed in this paper. Successful on-line training and recalling process of CMAC accompanyingthe PD controller is developed.

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The advantage of the proposed method is mainly therobust tracking performance against aerodynamic parametric variation and external wind gust.

The effectiveness of the proposed algorithm is

validated through the application of a VOTL aircraft control system. Wonderful tracking controlperformance is demonstrated.

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Introduction Robust flight control is of interest to control engineers

because there are a lot of environmental changes during flightControlling a vertical takeoff and landing (VTOL) aircraft isnot simple.

PD control is used for steady-state tracking of step inputs or

slow time-varying reference trajectories. It is not sufficiently robust against system uncertainties and external disturbancesbecause the proportional and derivative coefficients in thecontroller are usually fixed.

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CMAC is an iterative learning controller that imitates thehuman cerebellum through iterative weight updating [13-17]. Learning behaviors and the convergence of the iterativelearning in a CMAC structure have been proved in [15],making CMAC useful in many applications.

In this paper, we propose the PD-based CMAC strategy

which achieves robust tracking control of VTOL aircrafts.

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System DynamicsConsider a typical flight condition with the nominal airspeed of 135knots [1, 2]. The simplified dynamic equations of this VTOL aircraftin the vertical plane can be described as

( )xvBuAxx ,t++=& (1)

Cxy = (2)

With airspeed ranging from 60 to 170 knots, significant changes

occur in the elements 32A and 34A , Assume that 2192.032 ≤ΔA

and 2031.134 ≤ΔA . The tracking error vector is defined as yye −= d ,

where Tddd yy ],[ 21=y .

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Fig1. VTOL aircraft in a vertical plane.

x4

x2

x1

pitchangle

x3pitch rate

weight

vertical velocity

horizontal velocity

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Fig2. VTOL aircraft control system .

VTOL Aircraft Control SystemThe configuration of the proposed control scheme is shown in Fig. 2.

cmacu

pdu uydy

−

++

+

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The control law is defined as follows.

cmacpd uuu += (6)

The PD controller is designed to stabilize the states of the VTOLaircraft control system. In this stage, the robustness is notguaranteed. Define the PD controller as

eKeKu &dppd += (7)

Adequate training patterns and training time in the learningprocess required by the CMAC are provided by the PD controller.Consequently, the PD controller and the CMAC are in aharmonizing status during learning and controlling cycles

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∑

1w

2w

3w

4w

5w

6w

7w

M

∑

jzy

jzdy ,

jz

M

M

jza 8w

9w

10w

11w

42w

Fig3. Structure of the CMAC.

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The whole input space is quantized by the discrete reference

states, 4021 ,,, zzz L . Every reference state jz is mapped into

the output jzy . Let the output of the CMAC be defined as

wajj zzy = . (8)

The on-line updating law is chosen to be

( ) ( ) ( )ki

ki

ki www Δ+=+1 ,

( ) ( ) ( )( )ktrainingcmaci

ki

kTi

iki uu _,

)(

3−+= aw φ (9)

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The PD controller is first designed to stabilize the VTOL aircraft control system. The initial memory weights of theCMAC are zero, i.e., cmacu is zero. The PD controller begins to work, a series of training patterns for the CMAC will beobtained, and the CMAC begins to learn and merge the control.

Case I. Vertical velocity ( )td ey 2

1 19.0 −−= and horizontal

velocity 02 =dy (normalized); Case II. Vertical velocity 01 =dy and horizontal velocity

( )td ey 2

2 19.0 −−= (normalized)

Control System Performance

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Fig 5. Vertical and Horizontal velocities in Case I.

0 2 4 6 8 10 12 14 16 18 20-0.01

-0.005

0

0.005

0.01

time (sec)

horiz

onta

l vel

ocity

(kno

ts)

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

time (sec)

verti

cal v

eloc

ity (k

nots

)

y2d, desired trajectoryy2, tracking trajectory

y1d, desired trajectoryy1, tracking trajectory

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Fig 6. Vertical and Horizontal velocities in Case II.

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

time (sec)

horiz

onta

l vel

ocity

(kno

ts)

y2d, desired trajectoryy2, tracking trajectory

0 2 4 6 8 10 12 14 16 18 20-0.04

-0.02

0

0.02

time (sec)

verti

cal v

eloc

ity (k

nots

)

y1d, desired trajectoryy1, tracking trajectory

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Fig 7. Pitch rate and angle in Case I.

0 2 4 6 8 10 12 14 16 18 20-2

-1

0

1

2

3

time (sec)

pitc

h ra

te (d

eg/s

ec)

0 2 4 6 8 10 12 14 16 18 20-1.5

-1

-0.5

0

0.5

1

time (sec)

pitc

h an

gle

(deg

)

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Fig 8. Pitch rate and angle in Case II.

0 2 4 6 8 10 12 14 16 18 20-4

-2

0

2

4

time (sec)

pitc

h ra

te (d

eg/s

ec)

0 2 4 6 8 10 12 14 16 18 20-2

-1

0

1

2

time (sec)

pitc

h an

gle

(deg

)

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Fig 9. Control inputs from PD controller in Case I.

0 2 4 6 8 10 12 14 16 18 20-2

-1

0

1

2

time (sec)

u pd1 (d

eg)

0 2 4 6 8 10 12 14 16 18 20-1

-0.5

0

0.5

time (sec)

u pd2 (d

eg)

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Fig 10. Control inputs from PD controller in Case II.

0 2 4 6 8 10 12 14 16 18 20-2

-1

0

1

2

3

time (sec)

u pd1 (d

eg)

0 2 4 6 8 10 12 14 16 18 20-1

-0.5

0

0.5

1

time (sec)

u pd2 (d

eg)

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Fig 11. Control inputs from CMAC controller in Case I.

0 2 4 6 8 10 12 14 16 18 20-2

-1

0

1

2

time (sec)

u cmac

1 (deg

)

0 2 4 6 8 10 12 14 16 18 20-1

-0.5

0

0.5

time (sec)

u cmac

2 (deg

)

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Fig 12. Control inputs from CMAC controller in Case II.

0 2 4 6 8 10 12 14 16 18 20-2

-1

0

1

2

3

time (sec)

u cmac

1 (deg

)

0 2 4 6 8 10 12 14 16 18 20-1

-0.5

0

0.5

1

time (sec)

u cmac

2 (deg

)

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Conclusion PD control is a simple and effective control method.

CMAC can be used for robust control. A novel CMAC used together with a PD controller

design is proposed in this paper. The PD controllerprovides the CMAC training patterns.

The CMAC assists the PD controller to ensure the robustness. The advantage of this method is that accuratesystem model is not required.

Further, when the PD controller is not designed well, theCMAC is capable of doing a good job of robust controlthrough on-line recalling and training procedures.