lecture9 imc
TRANSCRIPT
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7/29/2019 Lecture9 IMC
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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
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EE392m - Winter 2003 Control Engineering 9-2
Processes with deadtime Examples: transport deadtime in mining, paper, oil, food
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EE392m - Winter 2003 Control Engineering 9-3
Processes with deadtime Example: resource allocation in computing
ComputingTasks
Resource
Resource
Queues
Modeling
DifferenceEquation
Feedback Control
Desired
Performance
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EE392m - Winter 2003 Control Engineering 9-4
Control of process with deadtime PI control of a deadtime process
0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
PLANT: P = z-5
; PI CONTROLLER: kP
= 0.3, kI= 0.2
Can we do better?
Make
Deadbeat controller
d
sT
zP
eP D
=
= continuous time
discrete time
dz
PC
PC =
+1
d
d
z
zPC
=
1 dzC
=1
1 0 5 10 15 20 25 300
0.2
0.4
0.6
0.8
1
DEADBEAT CONTROL
)()()( tedtutu +=
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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
zPzC
=
Works if Q(z) includes a deadtime, at least as large as in
P(z)
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EE392m - Winter 2003 Control Engineering 9-6
Dahlins controller Eric Dahlin worked for IBM in San Jose (?)
then for Measurex in Cupertino. Dahlins controller, 1968
d
d
zz
zQ
zbz
bgzP
=
=
1
1
1
1)(
1
)1()(
dzzbg
bz
zC
= )1(1
1
)1(
1
)( 1
1
plant, generic first order
response with deadtime
reference model
Dahlins controller
Single tuning parameter: - tuned controller
)(1
)(
)(
1)(
zQ
zQ
zP
zC
=
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7/29/2019 Lecture9 IMC
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EE392m - Winter 2003 Control Engineering 9-7
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
CLOS ED-LOOP STEP RES PONSE WITH DAHLIN CONTROLLER
Ta=2.5T
D
Ta=1.5TDOpen-loop
0 10 20 30 40 50 600
0.5
1
1.5
CONTROL STEP RESP ONSE
Industrial tuning
guidelines:
Closed loop timeconstant = 1.5-2.5
deadtime.
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Internal Model Control - IMC
continuous times
discrete timez
P
P0
e
Qeu
Puyre
=
= )(
01 QP
QC
=
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EE392m - Winter 2003 Control Engineering 9-9
IMC and Youla parametrization
QS
QPT
QPS
u =
=
=
0
01 Sensitivities
ud
yr
yd
IfQ is stable, then S, T, and the loop are stable If loop is stable, then Q is stable
01 CP
C
Q +=
01 QPQC
=
Choosing various stable Qparameterizes all stabilizing
controllers This is called Youla parameterization
Youla parameterization is valid for unstable systems as well
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7/29/2019 Lecture9 IMC
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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:
H2/H, LMI, H loopshaping
Q-based loopshaping:
Recall system inversion
01 QPS = ( )1
01
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EE392m - Winter 2003 Control Engineering 9-11
Q-loopshaping Loopshaping
Lambda-tuned IMC
0
01
QPT
QPS
=
= ( )11
1
0
10
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IMC extensions Multivariable processes
Nonlinear process IMC Dynamic inversion in flight control - Lecture 13 - ?
Multivariable predictive control - Lecture 12
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Nonlinear process IMC Can be used for nonlinear processes
linearQ
nonlinear modelP0
linearized modelL
e
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EE392m - Winter 2003 Control Engineering 9-14
Industrial applications of IMC Multivariable processes with complex dynamics
Demonstrated and implemented in process control byacademics 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
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EE392m - Winter 2003 Control Engineering 9-15
Dynamic inversion in flight control
Honeywell
MACH
)(
),(),(
1 FvGu
uvxGvxFv
des=
+=
&
&
=
NCV
MCV
LCV
v
X-38 - Space Station
Lifeboat
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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 (-analysis etc)
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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