Dahlin algorithm imc

conrolar design

1. EE392m - Winter 2003 Control Engineering 9-1
Lecture 9 - Processes with
Deadtime, IMC
• Processes with deadtime
• Model-reference control
• Deadtime compensation: Dahlin controller
•IMC
• Youla parametrization of all stabilizing controllers
• Nonlinear IMC
– Dynamic inversion - Lecture 13
– Receding Horizon - MPC - Lecture 12

2. EE392m - Winter 2003 Control Engineering 9-2
Processes with deadtime
• Examples: transport deadtime in mining, paper, oil, food

3. EE392m - Winter 2003 Control Engineering 9-3
Processes with deadtime
• Example: resource allocation in computing
Computing T
asks
Resource
Resource
Queues
Modeling
Difference
Equation
Feedback Control
Desired
Performance

4. EE392m - Winter 2003 Control Engineering 9-4Control of process with deadtime • PI control of a deadtime process
0
5
10
15
20
25
30
0
0.20.40.60.8
1
P LANT: P = z
-5
; PI CONTROLLER: k
P = 0.3, k
I
= 0.2
• Can we do better?
–Make
– Deadbeat controller
d
sT
z P
e P
D
−
−
=
=
continuous time
discrete time
d
z
PC
PC
−
=
+1
d
d
z
z
PC
−
−
−
=
1
d
z
C
−
−
=
1
1
0
5
10
15
20
25
30
0
0.20.40.60.8
1
DEADBEAT CONTRO L
)( ) ( )(te dtu tu+ − =

5. EE392m - Winter 2003 Control Engineering 9-5
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
)()(
zQ
zCzP
zCzP
=
+
)( 1
)(
)(
1
)(
zQ
zQ
zP
zC
−
⋅ =
• Works if
Q
(
z
) includes a deadtime, at least as large as in
P
(
z
)

6. EE392m - Winter 2003 Control Engineering 9-6
Dahlin’s controller
• Eric Dahlin worked for IBM in San Jose (?)
then for Measurex in Cupertino.
• Dahlin’s controller, 1968
d
d
z
z
zQ
z
bz
b g
zP
−
−
−
−
−
−
=
−
−
=
1
1
1
1
)(
1
) 1(
)(
α
α
d
z z b g
bz
zC
− −
−
− − −
−
⋅
−
−
=
) 1( 1
1
) 1(
1
)(
1
1
α α
α
• plant, generic first order
response with deadtime
• reference model
• Dahlin’s controller
• Single tuning parameter:
α
- tuned controller
)( 1
)(
)(
1
)(
zQ
zQ
zP
zC
−
⋅ =

7. EE392m - Winter 2003 Control Engineering 9-7
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
60
0
0.20.40.60.8
1
CLOSED-LOOP STEP RESPONSE WITH DAHLIN CONTROLLER
T
a
=2.5T
D
T
a
=1.5T
D
Open-loop
0
10
20
30
40
50
60
0
0.5
1
1.5
CONTROL STEP RESPONSE
• Industrial tuning
guidelines:
Closed loop time
constant = 1.5-2.5
deadtime.

8. EE392m - Winter 2003 Control Engineering 9-8
Internal Model Control - IMC • continuous time s
• discrete time z
P P
0
e
Qe u
Pu y re
=
− −=) (
0
1QP
Q
C
−
=

9. EE392m - Winter 2003 Control Engineering 9-9
IMC and Youla parametrization
Q S
QP T
QP S
u
=
=
−=
0
0
1
• Sensitivities
u d
y r
y d
→
→
→
•If Q is stable, then S, T, and the loop are stable
• If loop is stable, then Q is stable
0
1
CP
C
Q
+
=
0
1
QP
Q
C
−
=
• Choosing various stable Q parameterizes all stabilizing
controllers
• This is called Youla parameterization
• Youla parameterization is valid for unstable systems as well

10. EE392m - Winter 2003 Control Engineering 9-10
Q-loopshaping
• Systematic controller design: select Q to achieve the
tradeoff
• The approach used in modern advanced control design:
H
2
/H
∞
, LMI, H
∞
loopshaping
•Q-based loopshaping:
• Recall system inversion
0
1
QP S−=
()
1
0
1
−
≈ ⇒ <<P Q S• in band
Inversion

11. EE392m - Winter 2003 Control Engineering 9-11
Q-loopshaping
• Loopshaping
• Lambda-tuned IMC †
0
0
1 QP T
QP S
=
−=
()
1 1
1
0
1
0
<< ⇒ <<
≈ ⇒ <<
−
QP T
P Q S
()
n
s
F
F QP S FP Q
λ
+
=
−≈ −= =
1
1
1 1 ,
0
†
0
• in band
• out of band
• F is called IMC filter, F
≈
T, reference model for the output
• For minimum phase plant
Loopshaping
()
F T PF FP Q= = =
−
,
1
0
†
0

12. EE392m - Winter 2003 Control Engineering 9-12
IMC extensions
• Multivariable processes
• Nonlinear process IMC
• Dynamic inversion in flight control - Lecture 13 - ?
• Multivariable predictive control - Lecture 12

13. EE392m - Winter 2003 Control Engineering 9-13
Nonlinear process IMC
• Can be used for nonlinear processes
– linear Q
– nonlinear model P
0
– linearized model L
e

14. EE392m - Winter 2003 Control Engineering 9-14
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

15. EE392m - Winter 2003 Control Engineering 9-15
Dynamic inversion in flight control
• Honeywell
MACH
) (
),( ),(
1
F v G u
uvxG vxF v
des
− =
+ =
−
&
&










=
NCV
MCV
LCV
v
X-38 - Space Station
Lifeboat

16. EE392m - Winter 2003 Control Engineering 9-16
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)

17. EE392m - Winter 2003 Control Engineering 9-17
Summary
• Dahlin controller is used in practice
– easy to understand and apply
• IMC is not really used much
– maintenance and support issues
• 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