Intelligent Control of Mechatronic Systemsuav.ece.nus.edu.sg/~isic2003/Doc/ISIC03-plenary_04.pdf ·...

1

Intelligent Control of MechatronicSystems

T. H. Lee

(in collaboration with colleagues & students)

Centre for Intelligent Control

Department of Electrical & Computer Engineering National University of Singapore

eleleeth@nus.edu.sg

2

• Student projects in Mechatronics…

• Design - complexity of structure and control

• Simple “intelligence”

3

Mechatronics R& D projects: prototypesbeing refined in different stages

Fukuda & co-workers (Nagoya)Lewis & co-workers (Arlington)Moore & co-workers (Utah)Grimble & co-workers (Strathclyde)Tso & co-workers (Hong Kong)C.W. de Silva & co-workers (UBC)

4

Ship welding robotic system

5

Robotic Telepresence System

Fukuda & co-workers (Nagoya)Ang & co-workers (NUS)Daniel & co-workers (Oxford)J.H.Kim & co-workers (KAIST)

6

Other Systems (at CIC, NUS)

Gladiator Robots

Pole-balancing RobotSome of the other fun things our students work on…

7

8

Contents

1. Introduction

2. Preliminary

3. Intelligent Control of Servo Mechanisms

4. Intelligent Control of Robotic Systems

5. Conclusions and Further Research

9

MECHATRONICS

2. The combination of mechanical engineering and electronics, as used in the design and development of new manufacturing techniques. [From mecha(nics) + (elec)tronics]

http://www.wordreference.com/english/definition.asp?en=mechatronics

1. The synergistic combination of precision mechanical engineering, electronic control and systems thinking in the design of products and processes.

Bradley, Dawson et. Al, Mechatronics, Electronics in products & processes, Chapman and Hall Verlag, London 1991.

10

MECHATRONICS

The question of exactly what is "mechatronics" has been discussed for several years now and a reasonably consistent view has resulted.

There was a valuable workshop on Mechatronics, held at Stanford University in 1994, which brought together people who were actively involved in a range of courses, labs and programs in mechatronics.

11

MECHATRONICS

Several quotes from presenters at the workshop on the definition of mechatronics are given below.

1. “Although there is not a universal accepted definition of Mechatronics, most definitions refer in some way to the integration of electronics and software into mechanical systems. Many also refer to the integration of these disciplines through out the design process.” (Edward Carryer, Stanford University)

2. “It (mechatronics) integrates the classical fields of mechanical engineering, electronic engineering and computer science/information technology at the design stage of a product or system.” (Memis, Loughborough, UK)

12

MECHATRONICS

3. “Mechatronics is an application of the concept of concurrent engineering to the design of electromechanical systems. This design philosophy is exemplified by an interdisciplinary and integrated design approach where electrical, electronic, computer, and mechanical subsystems are simultaneously designed to function as an integrated single system.” (Charles Ume, Georgia Tech)

4. “Mechatronics, …, is the synergistic combination of mechanical engineering, electronics, control engineering and computer science. The key element in mechatronics is the integration of these areas through the design process.” (Kevin Craig, RPI)

13

INTELLIGENT CONTROL

1. “Intelligent controls respond to uncertainty and act to determine the best solutions.”

2. “Intelligent Control is a new cross scientific & technical field based on Artificial Intelligence & Automation Control etc.”

3. Intelligent controllers are envisioned emulating human mental faculties such as adaptation and learning, planning under large uncertainty, coping with large amounts of data etc in order to effectively control complex processes; ...

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INTELLIGENT CONTROL

4. “Intelligent Control is a fusion of a number of research areas in Systems and Control, Computer Science, and Operations Research among others, coming together, merging and expanding in new directions and opening new horizons to address the problems of this challenging and promising area.”

http://robotics.ee.nus.edu.sg/tcic

15

INTELLIGENT CONTROL

5. “Intelligent control systems are typically able to perform one or more of the following functions to achieve autonomous behavior: planning actions at different levels of detail, emulation of human expert behavior, learning from past experiences, integrating sensor information, identifying changes that threaten the system behavior, such as failures, and reacting appropriately.”

http://robotics.ee.nus.edu.sg/tcic

16

INTELLIGENT CONTROL

A CONTROLLER IS SAID INTELLIGENT

IF ITS

GAINS AND/OR STRUCTURES

ARE NOT FIXED!

17

Two Classes of Mechatronic Systems

Servo-Mechanisms• Friction Compensation• Precision Motion Control

Robotic Systems• Rigid Body Robots• Flexible Joint Robots• Flexible Link Robots• Smart Materials Robots

MECHATRONIC SYSTEMS

Fukuda & co-workers (Nagoya)Lewis & co-workers (Arlington)Moore & co-workers (Utah)Grimble & co-workers (Strathclyde)Tso & co-workers (Hong Kong)C.W. de Silva & co-workers (UBC)

18

MORE SYSTEMS (at CIC, NUS)

Ge & students

Tan & studentsPrahlad & students (just won 1st Prize at FIRA Competition, Austria; 7 Oct 2003)

19

MORE SYSTEMS (where funding is…)

20

Preliminary and

Methodology

21

STABILITY

Stability – Basic requirement of control design

Curve 1: asymptotically

stable

Curve 2: stable

Curve 3: unstable

Narendra & co-workers (Yale)Landau & co-workers (Grenoble)

22

LYAPUNOV BASED CONTROL DESIGN

Consider the nonlinear system( , )

Choosing ( ) as a Lyapunov function candidate, its time derivative is

( ) (

) ( , ( )

)

x f x uV x

V xV x f x u xx

=

∂=

∂

&

&

Choose ( )?Design ( )?

V xu u x=

( )( ) ( , ( )) ( )

( ) is positive definite.

V xV x f x u x W xx

W x

∂= ≤ −

∂&

The closed-loop system is stable.

23

LYAPUNOV BASED CONTROL DESIGN

For affine nonlinear system( ) ( )

The inequality becomes( ) ( )( ) ( ) ( ) ( ) ( )

x f x g x u

V x V xV x f x g x u x W xx x

= +

∂ ∂= + ≤ −

∂ ∂

&

&

The closed-loop system is stable.

For the case where ( ) is only negative semi-definiteV x&

LaSalle’s Invariant Principle ⇒ Asymptotic stability

24

DYNAMIC COMPENSATOR

1

2 2 2

Let ( ) ( ) ( ), where (s) is strictly proper & exponentially stable.

If then , , is continuous and 0 as . If, r 0 as , then 0.

r r

n n n n

r t G p e t G

r L e L L e Le e t

t e

−

∞

=

• ∈ ∈ ∩ ∈→ →∞

• → →∞ →

&

&

Lemma

21

2 31 2

( )

( )

( )

r

r

r

G s sIKG s sI Ks

K KG s sI Ks s

= + Λ

= + +

= + + +

Common choices :

Desoer and Vidyasagar, FB Systems: Input-Output Stability, circa 1975

25

FEEDBACK LINERIZATION

Nonlinear system

Linear system

State transformation

Nonlinear feedback

Has the advantage of being a nice systematic approach.

However, usually lacks freedom in selectively cancellingthe undesirable terms and retaining the nice well-behaved parts.

26

SINGULAR PERTURBATION

Multiple time-scale structures inherent in many practical systems

Discontinuous dependence of system properties on the perturbation parameter

),,,(),,,(

εεε

zxtgzzxtfx

==

&

&Kokotovic & co-workers (UIUC)Spong & co-workers (UIUC)

Tikhonov’s Theorem

The discontinuity of solutions caused by singular perturbations can be avoided if analyzed in separate time scales.

27

Intelligent Control

of

Servo Systems

28

4. Friction Compensation

Friction exists in any relative motion

29

Friction Compensation

Friction exists almost everywhere

30

Friction Model

smallmotion

Static friction (Stiction)

, ( )

( ) sgn( ),

Coulomb friction (Dry friction) sgn( ),

sm m t

s s

m c c n

u u ff f f x x

f x u u f

f f x f f

δδ

µ

⎧ <⎪= ⎯⎯⎯→ =⎨ ≥⎪⎩

= =

&&

&

Friction compensation is achievable with a reasonable accurate model!

Canudas de Wit & co-workers (Grenoble)Ge, Chen, Tan, Lee & co-workers (NUS)

31

Friction Model

Viscous friction Drag friction

Exponential model

( ) sgn( ) ( ) exp( )

L

m v

m d

m c s c vs

f f x

f f x x

xf x f x f f f xx

δ

=

=

= + − − +

&

& &

&& & &

&

2

orentzian model1 ( ) sgn( ) ( )

1 ( / )m c s c vs

f x f x f f f xx x

= + − ++

& & && &

32

Friction Model

A classical model including Stiction, Coulomb, viscous, drag friction and square root friction in LIP form

( , ) ( , )Tmf x x S x x P=& &

[ ]

12

where

( , ) ( ) sgn( ) sgn( )

Tt c v d r

S x x x x x x x x x x

P f f f f f

δ⎡ ⎤= ⎢ ⎥⎣ ⎦

=

& & & & & & & &

[29] Ge, Lee & Ren, “Adaptive friction compensation…”IJSS, Vol. 32, No. 4, 2001.

33

Friction ModelFriction is continuous though may be extremely highly nonlinear.

Neural network model

( , ) ( , ) ( , )Tf x x S x x P x xε= +& & &

[ ]1 2

where

( , ) , , , , basis function , corresponding weight vector ( , ), reconstruction error.

TlS x x s s s

Px xε

=& L

&

34

NN ApproximationLinearly parameterized neural networks (LPNNs)

( )Ty W S x=

• Gaussian RBF neural networks

• High order neural networks

Multilayer neural networks (MNNs)

[29] Ge, Lee & Ren, “Adaptive friction compensation…”IJSS, Vol. 32, No. 4, 2001.

35

Dynamic Friction ModelEnable position dependenceDesign dual observer for unknown (more later…)

LuGre model (.,.)α

0 1 2 0 1 2 ( ) ( , )

F z z x F z z xz x x x z z x x x x zσ σ σ σ σ σ

α α= + + = + += − = −

& && &

& & & & & && &

0 1 2

where , unmeasured average deflection of the bristles , and , friction paramters ( ), a finite positive function.

z

xσ σ σα &

[37] Ge, Lee & Wang, “Adaptive NN control… with unknown dynamic friction,” Proc of IEEE CDC 2000; pp 1760-1765.

36

Adaptive Friction Compensation

Servo mechanism+ =&&mx F u

Uncertain F

Model and Approximation based control

37

Model Based Control

A unified adaptive controllerτ

εε

= + + + + >

⎛ ⎞= = >⎜ ⎟

⎝ ⎠

∫))

&&

) )

1 10

2

, 0

where , tanh , 0

t

r m r i

Tm r r

r

u mx f k r u k rd k

rf S P u k

Parameter update law

= Γ Γ = Γ >)& , 0TP Sr

ε1 2

The tracking error converges to a small neighbourhoodof zero whose size is adjustable by the design parameters

, and .rk k

38

Approximation Based Control

Approximation based control is entering its accepted paradigm though not mature as yet.

Approximation based control has been developed for complex systems whose accurate model is difficult to obtain.

Neural networks and fuzzy systems are used as the main parameterization tools for unknown nonlinear systems without requiring the systems parameterization form.

39

Approximation Based Control

α

α ε ε ε

δσ

σδ δσ

•

= + ≤

• = +

•

= − +

&

& &

) )& &

*

1

01 1

1

NN approximation of ( , ) ( , ) ( , ) ,

Define

Dual observer to estimate the internal friction state

Tb

x xx x W S x x

mz r

z

x σ ξσ

σ σδ δ ξ σσ σ

+ −

= − + + +) )& & &

021

0 02 2 12

1 1

m r r

mx r rx

[37] Ge, Lee & Wang, “Adaptive NN control… with unknown dynamic friction,” Proc of IEEE CDC 2000; pp 1760-1765.

40

Approximation Based Control

σ σσσ δ σ α δσ

σ σ α σ δσ

•= + + +

= − + − −

− −

•

= Γ

& &&

) ))& &

)&&

&

0 1

01 0 1 1 2

12 21 2

1 20

Control law ( )

where ( , )

sgn( )

Adaptation law

(

r ar

ar

m

u x mx umu c r x x x r

rx k x r

W S σ δ)

& &1 2, )x x x r

The tracking error converges to zero and all the signals in the closed-loop are bounded.

41

Precision Motion Control

= − + +&& & &1 2 2

Servo systems

( , )K K Kx x u f x xM M M

A 3-tier composite control structure

Feedforward control

Feedback control

Non-linear Radial Basis Function (RBF) based compensator.

42

Precision Motion Control

φ φ=

= + +

= + = − +

= − = = −∑

&& &

) ) ) )&& &

10

2 2

1 20

Overall control

where

,

(

1)

( , ) ( , ) ,

FF PID RBF

TFF d d PID

mT

RBF i i i i ii

u u u u

M Ku x x u r B PxK K

u f x x x x w w r x PB r w

The tracking error converges to zero and all the signals in the closed-loop are bounded.

43

Precision Motion Control

[39] Tan, Lee, Dou & Huang, “Precision motion control,”Springer, U.K., 2001.

44

Intelligent Control

of

Robotic Systems

45

Control of Rigid Robots

With the application of neural network, the exact model structure of robots need not to be known.

Nonlinear dynamics of rigid body robots

τ+ + =&& & &( ) ( , ) ( )D q q C q q q G q

= • Ξ

= • Ξ

= • Ξ

))

) )& &

) )

Using NN estimation, we have

( ) { } { ( )}

( , ) { } { ( , )}

( ) { } { ( )}

TNN D D

TNN C C

TNN G G

D q W q

C q q W q q

G q W q

46

GL Matrix and Operator

{ } { } { } { }

{ }{ }

{ }

{ } { }

1 1

1 11 1

1

11 11 1 1

1 1

GL row vector and its transpose

,

GL matrix

GL o

perat

or

T T Ti i ik i i ik

k

n n nk

T Tk k

T

T Tn n nk nk

W W W W W W

W W WW

W W W

W X W XW X

W X W X

= =

⎧ ⎫ ⎧ ⎫⎪ ⎪ ⎪ ⎪= =⎨ ⎬ ⎨ ⎬⎪ ⎪ ⎪ ⎪

⎩ ⎭⎩ ⎭

⎡⎢⎡ ⎤• =⎣ ⎦⎣

L L

L

M M O M

L

L

M O M

L

⎤⎥

⎢ ⎥⎢ ⎥⎦

47

Control of Rigid Robots

τ τ τ= + + + + +∫) ))

&& & &0

( ) ( , ) ( )t

NN r NN r NN P I rD q q C q q q G q K r K rd

ξ

ξ

ξ

= Γ •

= Γ •

= Γ

)& &&)& & &)&

{ ( )}

{ ( , )}

( )

Dk Dk Dk r k

Ck Ck Ck r k

Gk Gk Gk k

W q q r

W q q q r

W q r

A general controller

Parameter adaptation laws

Tracking error converges to zero by appropriate selecting the control parameters.

48

Control of Rigid Robots

The controller presented is just one of the many controllers available

Many different controllers can be obtained using different techniques including

passivity based control,

model reference based adaptive control,

feedback linearization control …

[1] Ge, Lee & Harris, “Adaptive NN Control of Robotic Manipulators,” World Scientific, U.K., 1998.

49

Control of Flexible Joint Robots

Many industrial manipulators, particularly those equipped with harmonic drives for speed reduction, exhibit joint flexibility.

The simplified dynamic of flexible joint robots

+ + = −+ − =

&& & &

&&

( ) ( , ) ( ) ( )( )

m

m m

D q q C q q q G q K q qJq K q q u

[40] Spong, Lewis & Abdallah, “Robot Control: Dynamics, Motion Planning and Analysis,” IEEE Press, 1993.

50

Control of Flexible Joint Robots

1. Oscillation suppression control

−

= − +

& &

& &

To introduce joint damping ( ) effectivelyinto the closed-loop system to damp out the jointoscillations.

A general form of the control law ( )

is the slow time c

m m

m m s

s

K q q

u K q q uu ontrol to be designed later.

51

Control of Flexible Joint Robots

ε εε

ε ε − − −

= − = =

⇒

+ + =

+ + = −

&& & &

&& & &&

1 22

2 1 1 12 1 1 1

Define ( ), , ,

a small parameter Singular perturbed model of FJRs ( ) ( , ) ( )

Slow subsy

m m v

s

K Kz K q q K K

D q q C q q q G q zz J K z J K z J K u K q

+ + + =&& & &

stem ( ( ) ) ( , ) ( )which is same as the dynamics of rigid robots.

sD q J q C q q q G q u

52

Control of Flexible Joint Robots

η τ ε

η η ητ

− −

= =

+ + + =&2

1 12 12

1 2

Define - , with being constant in / .

Fast subsystemd ( ) 0

which is uniformly exponentially stable in ( , ) if, and are positive definite diagon

t

t

z z z t

K K J Dd

t qK K J al matrics.

[40] Spong, Lewis & Abdallah, “Robot Control: Dynamics, Motion Planning and Analysis,” IEEE Press, 1993.

53

Control of Flexible Joint Robots

2. Motor tracking error suppression control/ hierarchical control model

=

= + + +) ) )&& &

The motor tracking errors - are modeledas the fast variables instead of the joint elastic forces.

The composite control law

( ) is the slow time con

m md m

s md V m p m

s

e q q

u u J q K e K eu trol to be designed later.

54

Control of Flexible Joint Robots

α

α

ε

εε

−

= + + + +

= − + +

= = − + =

=

&& & & L

% %& && & %L

(4)

(4)

1 11 0 2

2

The control law is rewritten as ( ) ( , , , )

where ( , , , ) ( ).

Define , ( ), ,

, a sm

TT Ts md V m p m d d d

TT Td d d md V md p md

m md P

V

u u J q K e K e q q q

q q q J q K q K qKz Ke z K q q K KJ

KK

ε ε ε α

⇒

+ + = −

+ + = − − −

&& & &

&& &

0 12 2

1 2 1 1 1 1 0

all parameter

Singular perturbed model of FJRs ( ) ( , ) ( ) ( )( )P s

D q q C q q q G q z zz K z K z K K z u

55

Control of Flexible Joint Robots

α

τ α

τ

+ + = +

= + + −

+ +

=

∫

&& & &

) )) )&& & & & L

)&

(4)

0

Slow subsystem ( ) ( , ) ( )Control law for slow subsystem

( ) ( , ) ( ) ( , , , )

+ sgn( )

with

s

TT TNN r NN r NN NN d d d

t

P I r

Dk

D q q C q q q G q u

D q q C q q q G q q q q

K r K rd K r

W

α α α

ξ

ξ

ξ

ξ

Γ •

= Γ •

= Γ

= Γ

&&)& & &)&

)& & L (4)

{ ( )}

{ ( , )}

( )

( , , ,

)

Dk Dk r k

Ck Ck Ck r k

Gk Gk Gk k

TT Tk k k d d d k

q q r

W q q q r

W q r

W q q q r

56

Control of Flexible Joint Robots

η τ ε

η η ητ τ

= =

+ + =

1 1 1

2

2 12

Define - , with being constant in / .

Fast subsystemd d 0

which is uniformly exponentially stable.

t

t t

z z z t

K Kd d

57

Control of Flexible Joint Robots

ε ε ε

∈

<

1

* *

If the slow subsystem has a unique solution definedon an interval [0, ] and if the boundary-layersystem is exponentially uniformly stable in ( , ), thenthere exists such that for all

t tt q

η τ ε ε= + + = +∈ 1

( ) ( ) ( ) ( ), ( ) ( ) ( )hold uniformly for [0, -Tikh]. onov's Theorem.

tz t z t O q t q t Ot t

The statement is valid for a finite time interval. The statement is valid for an infinite time interval if the slow subsystem is exponentially stable.

58

Some works are documented:

59

Energy-based Control of FLRs

Flexible link robots (FLRs) have many advantages than traditional rigid robots.

Difficulties to control flexible link robots

Distributed parameter system

Infinite dimension

Nonminimum phase property from

base input to tip position output

[56] Lee, Ge & Wang, “Adaptive robust controller design for multi-link flexible robots,” Mechatronics, Vol. 11, No. 8, 2001.

60

Energy-based Control of FLRs

61

Other Flexible Systems

62

Energy-based Control of FLRs

Payload

NX

NY

Nx

Ny

NO

2Y

2y

2X

2x

1x

1y

2O

1O

2θ

1θ

Nθ

1X

1Y

Link N

Link 2

Link 1

Motor 2

Motor 1

Motor 3

Motor N

Geometry of a N-link FLR system

63

Energy-based Control of FLRs

Work done by external inputs

1 0 ( ) ( )N ti i iW t t d tτ θ== ∑ ∫ &

From the energy-work relationship, we have

1 0

[ ( ) ( )] [ (0 ) (0 )]

( ) ( )k p k p

N ti i i

E t E t E E

t t d tτ θ=

+ − +

= ∑ ∫ &

Thus we can obtain

1( ) ( ) ( ) ( )Nk p i i iE t E t t tτ θ=+ = ∑ && &

64

Energy-based Control of FLRs

Robust Control Law

''

''0

''

( ) ( , ) sgn( )

| | ( , ) 1, 2, ,

where , 0, ( , ) is the strain of each

link at location .

i pi i di di i si i s i

ti i s

pi di i s

s

k k k y t x

y s x ds i N

k k y t x

x

τ θ θ θ θ

θ

= − − − −

∫ =

>

& &

& L

[56] Lee, Ge & Wang, “Adaptive robust controller design for multi-link flexible robots,” Mechatronics, Vol. 11, No. 8, 2001.

65

Energy-based Control of FLRs

The energy-based robust control law can guarantee the stability of the closed-loop multi-link flexible robotic system.

The controller is constructed independent of system parameters.

The con

•

•

•

''

troller can be easily extended to general control where a general function is used

instead of . i

i s

f (x,t)

y (x ,t)

66

Energy-based Control of FLRs

Parameter tuning using genetic algorithm

Genetic algorithm is parameter search procedures based upon the mechanics of natural genetics. It combines the Darwinian’s principle of survival-of-the-fittest with a random, yet structured information exchange among population of artificial chromosomes.

Basic operation includes initial population, reproduction, crossover and mutation.

Ge, Lee & Zhu, “GA tuning of Lyapunov-based controllers…,” IEEE Trans on IE, Vol. 43, No. 5, 1996.

67

Energy-based Control of FLRs

The optimization of the fitness function is the basic goal of GA.

2

0

Modified function of integral of squared errors (MISE)

[ - ( , )]

Modified function of integral time-multplied absolute value of errors (MITAE)

T

fMISE K L p L t dtθ= ∫

0 | - ( , ) | ,

1.0, when | ( , ) | (no overshoot) where

10, when | ( , ) | (overshoot)

T

f

f

f

MITAE Kt L p L t dt

p L t LK

p L t L

θ

θ

θ

=

≤⎧⎪= ⎨ >⎪⎩

∫

68

Adaptive NN Control of SMRs

For conventional flexible robotsInfinite number of degrees of freedom

Finite number of actuators

Use of smart materials (e.g. piezo)Achieve the transformation between mechanical deformation and electrical fieldServe as actuators and sensorsApply additional control abilities to traditional flexible link robotControl loops increase

69

Adaptive NN Control of SMRs

2

D ynam ic m odel o f the sm art m ateria ls robo t

0

L et , , 1 /

S ingu lar pertu rbed m odel

rr rf r r

fr ff f f ff f f

ff f

r rr r rf f rf rr

M M q HM M q H K q F w

K kK kK q k

q D H D H D D

τ

ξ ε

ξ τ

•

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤+ + =⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎢ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣

= = =

•= − − − + +

&&

&&

% %

&&

2 rf f

fr r ff f ff fr ff f

D F w

D H D H D D D F wε ξ ξ τ= − − − + +&&

[59] Ge, Lee & Wang, “Adaptive NN control for smart materials robots…,” AsJC, Vol. 3, No. 2, 2001.

70

Adaptive NN Control of SMRs

1

S etting 0, w e ob tain ( )

S low subsystem w h ich co rresponds to the rig id body dynam ic m odel.

ff fr r fr f f

rr r rr r

D D H D H F w

M q C q

ε

ξ τ

τ

−

=

= − + − +

•

+ =&& &

71

Adaptive NN Control of SMRs

1 2

12

21

Define , , / ,

Fast subsystem

Since it is difficult to design , the fast subsystem

will be controlle

t f

t

ff fr f ff ft

f

z z t

dz zddz D z D D F wd

ξ ξ εξ τ ε τ τ τ

τ

ττ

τ

= − = = = −

•

=

= − + +

&

d using only.w

72

Adaptive NN Control of SMRs

Active Stabilization of fast subsystem

1 2 1

1 1

1 1 2 3

3

21

12

Fast subsystem becom es

C ontrol law

w here 0, [ , ], 0,

f

f f f f

f f f f

f

f

ff ff ft

d z D z D F wd

w U FF U F F F

F F F FF

F

τ

εκ ξκ

− −

+

+

+ =

= −

> = ≠

−⎡=⎣

&

.

T he fast subsystem is uniform exponential stable.

⎤⎢ ⎥

⎦

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Adaptive NN Control of SMRs

ε ε ε

∈

<

1

* *

If the slow subsystem has a unique solution defined on an interval [0, ] and if the boundary-layer system is exponentially uniformly stable in ( , ), then there exists such that for all

t tt q

ξ ξ τ ε ε= + + = +∈

1

1

( ) ( ) ( ) ( ), ( ) ( ) ( ) hold uniformly for [ -- Tikhonov'0, ]. s Theorem

t r rt t z O q t q t Ot t

[59] Ge, Lee & Wang, “Adaptive NN control for smart materials robots…,” AsJC, Vol. 3, No. 2, 2001.

74

Ship welding robotic system

75

MORE SYSTEMS (at CIC, NUS)

Ge & students

Tan & studentsPrahlad & students (just won 1st Prize at FIRA Competition, Austria; 7 Oct 2003)

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Conclusion

1. Intelligent control has been successfully applied to mechatronic systems using neural networks and approximation theory as the main tools.

2. A few selected techniques have been presented for a few typical systems, servo mechanisms and robotic systems.

3. Several manifestations of intelligent control have been proposed by various scientists. Different intelligent control methods should be employed as appropriate in the implementation of various functions at different levels of the intelligent systems.

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~ Thank You! ~