ICICIC 2006

Multiple Models Adaptive Decoupling Multiple Models Adaptive Decoupling Controller Using Dimension-By-Controller Using Dimension-By-

Dimension TechnologyDimension Technology

Xin WANGXin WANGwangxin26@sjtu.edu.cnwangxin26@sjtu.edu.cn

Center of Electrical & Electronic TechnologyCenter of Electrical & Electronic TechnologyShanghai Jiao Tong UniversityShanghai Jiao Tong University

ICICIC 2006

OutlineOutline

1. Introduction

2. Description of the system

3. Multiple Models Adaptive Decoupling Controller with DBD Technology

4. Global convergence analysis

5. Application

6. Conclusions

ICICIC 2006

1. Introduction1. Introduction

Multiple models adaptive control

Indirect MMAC

Problems

Our research work

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MMACMMAC

Direct MMAC– Newcastle University Prof. Fu– switching sequence is predetermined

Indirect MMAC– Yale University Prof. Narendra– switching is determined only by switching index

Weighting MMAC– France Prof. Binder– input is weighted

ICICIC 2006

Indirect MMACIndirect MMAC

Multiple adaptive models Multiple fixed models Multiple fixed models

+ 1 free-running adaptive model Multiple fixed models

+ 1 free-running adaptive model

+ 1 re-initialized adaptive model

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MMACMMAC

y

2my

Fixed model 2

Fixed model 1

System

Re-initalized

adaptive model m＋2

Fixed model m

Free-running

adaptive model m＋1

1y

1my

1e

2me

2e

Sw

itching Index J

Fired M

odel j

ICICIC 2006

ProblemsProblems

Single input single output system Indirect adaptive algorithm Too many models

– 4 parameters, 100models each parameter

– 1004 = 100,000,000 models

ICICIC 2006

Our Research WorkOur Research Work

Multivariable system – feedforward decoupling control

Nonminimum phase system

Direct adaptive algorithm– reduce computations

Global convergence analysis

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Linear time-varying system

)()(),()(),( 11 tktzttzt duByA

2 Description of System2 Description of System

1 11( , ) ( ) ( ) a

a

nnt z t z t z A I A A

b

b

nn ztzttzt )()()(),( 1

101 BBBB

ICICIC 2006

Assumptions

– infrequent large jumps parameters.

– minimum phase system

DARMA model

duByA )()()()( 11 tzktz

Description of SystemDescription of System

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DBD Principle of MMADC

Foundation of system models

DBD MMADC

3 DBD MMADC Design3 DBD MMADC Design

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DBD PrincipleDBD Principle

According to the prior information, determine the interval where the first dimension parameter changes;

Partition the above interval into n1 sub-intervals, then choose a center from each sub-interval and compose them into n1 fixed models of the first dimension parameter.

According to the switching index, choose the optimal value of the first dimension parameter whereas the other parameters are kept constant.

Repeat the above procedures until the optimal model of the last dimension, i.e. hth dimension, is chosen out.

ICICIC 2006

System parameter subsets

– divide the system parameter set into m

subsets

– satisfy

– system parameter set is covered by m subsets

s

m

ss

1

Fixed System ModelsFixed System Models

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Fixed system models

– select the model

– satisfy

– system parameter subset is covered by the

models and their neighbors

s

ssr

s

s

Fixed System ModelsFixed System Models

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DBD MMADCDBD MMADC

DBD fixed models– cover the system changing area

one free-running adaptive model (m+1)– guarantee the stability

one reinitialized adaptive model (m+2)– improve the transient response

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SwitchingSwitching

Switching index

Model selection

)()(1

)()(

)()(1

)(

T

2

T

2

ktkt

tt

ktkt

tJ s

fs

s

XX

yy

XX

e

)min(arg sJj

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Reinitialized Adaptive ModelReinitialized Adaptive Model

j ≠ m+2– reinitialize the initial value to the adaptive model– .

j = m+2– reinitialized adaptive model is selected as the opti

mal model– Using the same recursive estimation algorithm as t

he free-running adaptive model

jmt

)(ˆ

2

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Controller DesignController Design

Performance index

Diophantine equation

Controller

)()()()( 1111 zzzzz kGAFP

21 1 1( ) ( ) ( ) ( ) ( ) ( )c z t k z t z t J P y R w Q u r

1 1 1( ) ( ) ( ) ( ) ( ) ( )z t z t z t G y H u r R w

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4 Global Convergence4 Global Convergence

Theorem Subject to the assumptions, if the

algorithm is applied to the system

– are bounded;

– .0)(lim

t

te

)(,)( tuty

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System

– t=50, B0 jumps

– t=150, w changes

5 Simulation5 Simulation

1 11 2 ( )z z t I A A y

10 1 ( 2)z t B B u d

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5 Simulation5 Simulation

2401 models MMADC

28 models DBD MMADC

2400 models DBD MMADC

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6 Conclusions6 Conclusions

Nonminimum Phase System

The number of fixed models Reduction

Switching disturbance

Nonlinear system

ICICIC 2006

ThanksThanks