processes with deadtime, internal model control

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



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



Processes with Deadtime

Example: transport deadtime in food processing



Processes with Deadtime

Example: resource allocation in computing

ComputingTasks

Resource

ResourceQueues

Modeling

DifferenceEquation

Feedback Control

DesiredPerformance



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, k I= 0.2

Can we do better? Make

Deadbeat controller

d

sT

zPeP D

=

= continuous timediscrete time

dzPC

PC

=

+1

d

d

zzPC

=

1 dzC

=

11 0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

DEADBEAT CONTROL

)()()( tedtutu +=

C P- yyd



Model-reference Control

Deadbeat control has bad robustness, especially w.r.t. deadtime

More general model-reference control approach make the closed-loop transfer function as desired

)()()(1

)()( zQzCzP

zCzP=

+

)(1)(

)(1)(

zQzQ

zPzC

=

Works if Q(z) includes a deadtime, at least as large as in P(z). Then C(z) comes out causal.

)(zQ is the reference modelfor the closed loop

C P- yyd



Causal Transfer Function

Causal implementation requires that N M

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

110

)(

11 tezbzbzbtuzaza

zB

NN

NMNM

zA

NN 444444 3444444 214444 34444 21

+++=+++

NN

NN

NMNMN

NNN

MM

zazazbzbzb

azazbzbzb

zAzBzC

+++

+++=

+++

+++==

...1...

......

)()()(

11

110

11

110



Dahlins Controller

Eric Dahlin worked for IBM in San Jose (?) then for Measurexin Cupertino.

Dahlins controller, 1967

d

d

zz

zQ

zbz

bgzP

=

=

1

1

11)(

1)1()(

dzzbgbzzC

=

)1(11

)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

=



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=2.5TDTa=1.5TDOpen-loop

0 10 20 30 40 50 600

0.5

1

1.5

CONTROL STEP RESPONSE

Industrial tuning guidelines: Closed loop time constant = 1.5-2.5 deadtime.



Internal Model Control - IMC

continuous time s discrete time z

P

P0

e

QeuuPyre

=

= )( 001 QP

QC

=

General controller design approach; some use in process industry

0QPT =Reference model:Filter Q Internal model: 0P



IMC and Youla parametrization

QSQPT

QPS

u =

=

=

0

01 Sensitivities

udyy

yd

d

If Q is stable, then S, T, and the loop are stable If the loop is stable, then Q is stable0

1 CPCQ

+=

01 QPQC

=

Choosing various stable Q parameterizes all stabilizing controllers. This is called Youla parameterization

Youla parameterization is valid for unstable systems as well

C P-

eyyd

uddisturbance

reference output

controlerror



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 = ( ) 101



Q-loopshaping

Loopshaping

For a minimum phase plant 0

01QPT

QPS=

= ( )11

1

0

10



IMC extensions

Multivariable processes Nonlinear process IMC Multivariable predictive control - Lecture 14



Nonlinear process IMC

Can be used for nonlinear processes linear Q nonlinear model N linearized model L

e



Industrial applications of IMC

Multivariable processes with complex dynamics Demonstrated and implemented in process control by

academics 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



Dynamic inversion in flight control

)(),(),(

1 FvGuuvxGvxFv

des=

+= &

&

=

NCVMCVLCV

v

X-38 - Space Station Lifeboat

Honeywell MACH Dale Enns

Reference model: desv

sv &1=



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)



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 modern advanced 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

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processes with deadtime, internal model control

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