Download - Lecture 11 - 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 time

discrete time

dzPC

PC −=+1

d

d

zzPC −

−

−=

1 dzC −−

=1

1 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



Dahlin’s Controller

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

• Dahlin’s controller, 1967

d

d

zz

zQ

zbz

bgzP

−−

−−

−−=

−−=

1

1

11)(

1)1()(

αα

dzzbgbzzC −−

−

−−−−⋅

−−=

)1(11

)1(1)( 1

1

ααα

• plant, generic first order response with deadtime • reference model: 1st order+deadtime

• Dahlin’s controller

• Single tuning parameter: α - tuned controller a.k.a. λ - tuned controller

)(1)(

)(1)(

zQzQ

zPzC

−⋅=



Dahlin’s Controller• Dahlin’s 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

=−−= )( 0

01 QPQC

−=

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 stable01 CP

CQ+

=

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 −≈⇒<< PQS • in band

Inversion

Loopshaping



Q-loopshaping

• Loopshaping

• For a minimum phase plant 0

01QPT

QPS=

−= ( )11

1

0

10

<<⇒<<≈⇒<< −

QPTPQS

( )nsF

λ+=

11

• in band• out of band

• F is called IMC filter, F≈ T, reference model for the output

• Lambda-tuned IMC

( ) ,10

†0

−== PFPQ

FQPS −=−= 11 0

FQPT == 0



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 (µ-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

Download - Lecture 11 - Processes with Deadtime, Internal Model Control

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