Tutorial-2-Vancouver.pdf

I.D.Landau :Digital Control/System Identification1

Robust R-S-T Digital Controland

Open Loop System IdentificationA Brief Review

I.D. LandauLaboratoire dAutomatique de Grenoble(INPG/CNRS), France

([email protected])ADAPTECH, 4 Rue du Tour de lEau, St. Martin dHres(38), France

([email protected])

IEEE Advanced Process Control

Workshop, Vancouver, April 29-May 1, 2002


Applications of R-S-T Controllers

Peugeot (PSA)

Sollac (Florange)Hot Dip Galvanizing

Double Twist Machine(Pourtier)

360 Flexible Arm (LAG)


Implementation of R-S-T Digital Controllers

PLC Leroy implementsR-S-T digital controllers andData acquisition modules

ALSPA 320ALSPA 320 implements R-S-T digital controllers andData acquisition modules


u yRef.

++

DESIGNMETHOD

MODEL(S)

Performancespecs.

PLANT

IDENTIFICATION

Robustnessspecs.

CONTROLLER

1) Identification of the dynamic model2) Performance and robustness specifications3) Compatible controller design method4) Controller implementation5) Real-time controller validation

(and on site re-tuning)6) Controller maintenance (same as 5)

Controller Design and Validation


Outline

Robust digital control-The R-S-T digital controller-Basic design-Robustness issues-An example

Open loop system identification-Data acquisition-Model complexity-Parameter estimation-Validation


Robust Digital Control


Computer(controller)

D/A+

ZOHPLANT A/D

CLOCK

Discretized Plant

r(t) u(t)y(t)

The R-S-T Digital Controller

r(t)

m

m

AB

TS1

ABq d-

R

u(t) y(t)

Controller

PlantModel

+

-

)1()(1 -=- tytyq


r(t)

m

m

AB

TS1

ABq d-

R

u(t) y(t)

Controller

PlantModel

+

-

The R-S-T Digital Controller

Plant Model:)(

)(*)(

)()(1

11

1

11

-

---

-

--- ==

qAqBq

qAqBqqG

dd

A

A

nn qaqaqA

--- +++= ...1)( 111 )(*...)( 1111

1 ----- =++= qBqqbqbqB BB

nn

R-S-T Controller: )()()1(*)()()( 111 tyqRdtyqTtuqS --- -++=

Characteristic polynomial (closed loop poles):

)()()()()( 11111 ------ += qRqBqqSqAqP d


rABy mm )/(* =

+

-

R

1 q-d

B

AST

A

B m

m

r(t)

y (t+d+1)* u(t) y(t)

q

-(d+1)

P(q -1 )

q

-(d+1)

B*(q )-1

B*(q )

-1

B(1)

q

-(d+1) B m(q )

B*(q )

-1-1

A m(q ) B(1)-1

Pole Placement with R-S-T Controller

';' SHSRHR SR ==Controller : :, SR HH fixed parts

Regulation: R and S solutions of:

dominantpoles

auxiliarypolesTracking :

FDRd

S PPPRBHqSAH ==+- ''

)1(/ BPT =

Reference trajectory: y*computer file


Connections with other Control Strategies

- Digital PID : 11;2 --=== qHnn SSR

-Tracking and regulation with independent objectives(MRC):

FD PPBP *= (Hyp.: B* has stable damped zeros)

- Minimum variance tracking and regulation (MVC):

CBP *=noise model

(Hyp.: B* has stable damped zeros)

- Internal Model Control (IMC):

FAPP = (Hyp.: A has stable damped poles)


+

-

R

1 q-d

BAS

Tr(t) u(t) y(t)

PlantModel

p(t)

b(t)

+

+

+ +

(disturbance)

(measurement noise)

The Sensitivity Functions

Syp(q-1) = AS

AS + q-dBR= AS

P

Output sensitivity function (p -> y)

Sup(q-1) = - ARAS + q-dBR= - AR

P

Input sensitivity function (p -> u)

Syb(q-1) = -q-dBR

AS + q-dBR= - q

-dBRP

Noise sensitivity function (b -> y)

Syp - Syb = 1


-1

DF1

D1

DM

1

crossoverfrequency

Re H

Im H

G

|HOL|=1w CR1

w CR2

w CR3

Robustness Margins

z = ejw

> 29DM 0.5 DG 2 ; DF

DM 0.5 (-6dB), Dt > Ts

DM = 1+HOL(z-1) min = Syp(z-1) max-1 = Syp

-1( ) ( )

Dt = mini DFi

wCRi

Modulus Margin:

Delay Margin:

Typical values:

The inverse is not necessarily true!


Im G

Re Gw = p

G (e )-j w

uncertaintydisk

d W

w = 0

Robust Stability

Family of plant models:

),,(' xyWGFG d

G nominal model; 1)( 1

-zd

)( 1-zWxy - size of uncertainty

Robust stability condition:a related sensitivity

functiona type of uncertainty

1

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