Lab

Neural Networks based control of nonlinear systems

1

Identification of dynamic systems with Artificial Neural Networks

))(,),1(),(,),((

))

)(

)1()(

)(

((()( 211122

ntytymtutufnty

tymtu

tu

WFWFty

nn ---=

=Q+Q+

úúúúúúúú

û

ù

êêêêêêêê

ë

é

-

--

××××=

!!

"

"

Dynamic/ feedback network:

Feedforward Neural Network

Identification with Artificial Neural Networks

U

sY

mY

is theinput of the system and the model

is the output of the system

is the output of the model

ms YYE -=

0®ESystem

Model

Identification with Artificial Neural Networks

System

NN

Calculation of new parameters

Inverse model

Calculation of new parameters

NN

System

)1()(:1 -®- tUtYf

))(,),2(),(,),(()1( 1 rtUtUqtYtYftU ---=- - !!

Inverse model

Consider a system:

))2(),2(),1(),(()1( 1 ---=- - tutytytyftu

))2(),1(),2(),1(()( ----= tututytyfty

Inverse model based control

))2(),2(),1(),(()1( 1 ---=- - tutytytyftu

Here )()( twty =

Inverse model Plant

Inverse model based adaptive control

Plant Inverse model

Example: Jacketed CSTR (Continuous Stirred Tank Reactor)

Input-Output equation:

)1()(5611.0)1()1(592.0)1(3921.0)1()(014.1

)1(6407.0)1(4801.0)(231.0)1(7653.0)2(

2

2

+-+++++-++

++-++

+-+=+

tutytutytytyty

tytutytyty

9

Collecting input-output data

To Workspace 1

output

To Workspace

input

Scope

Jacketed CSTR

In1 Out1

Input : Uniform RandomNumber

10

td=1N=size(output,1)P=[output(3:N)';output(2:N-1)';output(1:N-2)']T=input(2:N-1)'global net_c

net_c=newff([0 1; 0 1; 0 1],[5 1],{'tansig','purelin'})net_c.trainParam.show=1;net_c.trainFcn='traingd';net_c.trainParam.epochs=3000;net_c=train(net_c,P,T)

Training of inverse model

11

function control=controller(u)global net_ccontrol=sim(net_c,u);

Implementation of the controller in MATLAB (m-file controller.m)

12

dynamic _controller

In1 Out1

Step

Scope

Jacket

In1 Out1

Constant

0.6

Control scheme

13

“dynamic_controller” block

Out 11

Unit Delay 3

z

1

Unit Delay 2

z

1

MATLAB Fcn

MATLABFunction

In11

14

adaptive _dynamic _controller

In1

In2Out1

Step

Scope

Jacket

In1 Out1Constant

0.6

Adaptive control scheme

15

Out 11

Unit Delay 3

z

1

Unit Delay 2

z

1

MATLAB Fcn

MATLABFunction

Clock

In22

In11

“adaptive_dynamic_controller” block

16

Adaptive controller = function “controller_adaptive” (m-file controller_adaptive.m)

function control=controller_adaptive(u)global net_cinp=u(1:3);error=u(4);time=u(5);control=sim(net_c,inp);if time>10net_c=adapt(net_c,inp,control+error);end

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