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
IEEE Advanced Process Control
Workshop, Vancouver, April 29-May 1, 2002
I.D.Landau :Digital Control/System Identification2
Applications of R-S-T Controllers
Peugeot (PSA)
Sollac (Florange)Hot Dip Galvanizing
Double Twist Machine(Pourtier)
360 Flexible Arm (LAG)
I.D.Landau :Digital Control/System Identification3
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
I.D.Landau :Digital Control/System Identification4
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
I.D.Landau :Digital Control/System Identification5
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
I.D.Landau :Digital Control/System Identification6
Robust Digital Control
I.D.Landau :Digital Control/System Identification7
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
I.D.Landau :Digital Control/System Identification8
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
I.D.Landau :Digital Control/System Identification9
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
I.D.Landau :Digital Control/System Identification10
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)
I.D.Landau :Digital Control/System Identification11
+
-
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
I.D.Landau :Digital Control/System Identification12
-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!
I.D.Landau :Digital Control/System Identification13
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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