multiple models adaptive decoupling controller using dimension-by-dimension technology
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Multiple Models Adaptive Decoupling Controller Using Dimension-By-Dimension Technology. Xin WANG [email protected] Center of Electrical & Electronic Technology Shanghai Jiao Tong University. Outline. 1. Introduction 2. Description of the system - PowerPoint PPT PresentationTRANSCRIPT
ICICIC 2006
Multiple Models Adaptive Decoupling Multiple Models Adaptive Decoupling Controller Using Dimension-By-Controller Using Dimension-By-
Dimension TechnologyDimension Technology
Xin WANGXin [email protected]@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
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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
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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
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ProblemsProblems
Single input single output system Indirect adaptive algorithm Too many models
– 4 parameters, 100models each parameter
– 1004 = 100,000,000 models
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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
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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.
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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
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ThanksThanks