lecture11 imc

7/29/2019 Lecture11 IMC

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EE392m - Spring 2005Gorinevsky

Control Engineering 11-1

Lecture 11 - Processes with Deadtime,

Internal Model Control

Processes with deadtime

Model-reference control

Deadtime compensation: Dahlin controller

IMC

Youla parametrization of all stabilizing controllers

Nonlinear IMC

Receding Horizon - MPC - Lecture 14


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Processes with Deadtime Examples: transport deadtime in paper, mining, oil

Deadtime = transportation time


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Processes with Deadtime Example: transport deadtime in food processing


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Processes with Deadtime Example: resource allocation in computing

ComputingTasks

Resource

Resource

Queues

Modeling

DifferenceEquation

Feedback Control

Desired

Performance


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Control of process with deadtime PI control of a deadtime process

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

PLANT: P = z-5

; PI CONTROLLER: kP

= 0.3, kI= 0.2

Can we do better?

Make

Deadbeat controller

d

sT

zP

eP D

=

= continuous time

discrete time

dzPC

PC =

+1

d

d

z

zPC

=

1 dzC

=1

1 0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

DEADBEAT CONTROL

)()()( tedtutu +=

C P- yyd


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Causal Transfer Function

Causal implementation requires that N M

( ) ( ) )(...)(...1)(

1

10

)(

1

1 tezbzbzbtuzaza

zB

N

N

NMNM

zA

N

N 444444 3444444 214444 34444 21

+++=+++

N

N

N

N

NMNMN

NN

N

MM

zaza

zbzbzbazaz

bzbzb

zA

zBzC

+++

+++=

+++

+++==

...1

......

...

)(

)()(

1

1

1

10

1

1

1

10


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Dahlins Controller Eric Dahlin worked for IBM in San Jose (?) then for Measurex

in Cupertino.

Dahlins controller, 1967

d

d

zz

zQ

zbz

bgzP

=

=

1

1

1

1)(

1

)1()(

dzzbg

bz

zC

= )1(1

1

)1(

1

)( 1

1

plant, generic first order response

with deadtime reference model: 1st order+deadtime

Dahlins controller

Single tuning parameter: - tuned controller

a.k.a. - tuned controller

)(1)(

)(1)(

zQzQ

zPzC

=


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Dahlins Controller Dahlins controller is broadly used through paper industry

in supervisory control loops - Honeywell-Measurex, 60%.

Direct use of the identified model parameters.

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

CLOSED-LOOP STEP RESPONSE WITH DAHLIN CONTROLLER

Ta=2.5T

D

Ta=1.5T

DOpen-loop

0 10 20 30 40 50 600

0.5

1

1.5

CONTROL STEP RESPONSE

Industrial tuning

guidelines:

Closed loop timeconstant = 1.5-2.5

deadtime.


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Internal Model Control - IMC

continuous times

discrete timez

P

P0

e

Qeu

uPyre

=

= )( 0

01 QP

QC

=

General controller design approach; some use in process industry

0QPT=Reference model:

FilterQ Internal model: 0P


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IMC and Youla parametrization

QS

QPT

QPS

u =

=

=

0

01 Sensitivities

ud

yy

yd

d

IfQ is stable, then S, T, and the loop are stable

If the loop is stable, then Q is stable01 CP

CQ

+=

01 QP

QC

=

Choosing various stable Qparameterizes all stabilizing

controllers. This is called Youla parameterization

Youla parameterization is valid for unstable systems as well

C P-

e

yyd

u

ddisturbance

reference output

control

error


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Q-loopshaping Systematic controller design: select Q to achieve the

controller design tradeoffs

The approach used in modern advanced control design:

H2/H, LMI, H loopshaping

Q-based loopshaping:

Recall system inversion

01 QPS = ( )1

01


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Q-loopshaping Loopshaping

For a minimum phase plant

0

01QPT

QPS=

= ( )11

10

1

0


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IMC extensions Multivariable processes

Nonlinear process IMC Multivariable predictive control - Lecture 14


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Nonlinear process IMC Can be used for nonlinear processes

linearQ

nonlinear model N

linearized model L

e


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Industrial applications of IMC Multivariable processes with complex dynamics

Demonstrated and implemented in process control byacademics and research groups in very large corporations.

Not used commonly in process control (except Dahlin

controller)

detailed analytical models are difficult to obtain

field support and maintenance

process changes, need to change the model

actuators/sensors off

add-on equipment


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Dynamic inversion in flight control

)(

),(),(

1FvGu

uvxGvxFv

des=

+=

&

&

=

NCV

MCV

LCV

v

X-38 - Space Station

Lifeboat

Honeywell MACH

Dale Enns

Reference model:

desv

s

v &1

=


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Dynamic inversion in flight control NASA JSC study for X-38

Actuator allocation to get desired forces/moments

Reference model (filter): vehicle handling and pilot feel

Formal robust design/analysis (-analysis etc)


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Summary Dahlin controller is used in practice

easy to understand and apply

IMC is not really used much maintenance and support issues

is used in form of MPC Lecture 14

Youla parameterization is used as a basis of modernadvanced control design methods. Industrial use is very limited.

Dynamic inversion is used for high-performance control of

air and space vehicles this was presented for breadth, the basic concept is simple need to know more of advanced control theory to apply in practice

lecture11 imc

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