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7/29/2019 Lecture11 IMC
1/19
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
7/29/2019 Lecture11 IMC
2/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-2
Processes with Deadtime Examples: transport deadtime in paper, mining, oil
Deadtime = transportation time
7/29/2019 Lecture11 IMC
3/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-3
Processes with Deadtime Example: transport deadtime in food processing
7/29/2019 Lecture11 IMC
4/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-4
Processes with Deadtime Example: resource allocation in computing
ComputingTasks
Resource
Resource
Queues
Modeling
DifferenceEquation
Feedback Control
Desired
Performance
7/29/2019 Lecture11 IMC
5/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-5
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, kI= 0.2
Can we do better?
Make
Deadbeat controller
d
sT
zP
eP D
=
= continuous time
discrete time
dzPC
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 +=
C P- yyd
7/29/2019 Lecture11 IMC
6/19
7/29/2019 Lecture11 IMC
7/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-7
Causal Transfer Function
Causal implementation requires that N M
( ) ( ) )(...)(...1)(
1
10
)(
1
1 tezbzbzbtuzaza
zB
N
N
NMNM
zA
N
N 444444 3444444 214444 34444 21
+++=+++
N
N
N
N
NMNMN
NN
N
MM
zaza
zbzbzbazaz
bzbzb
zA
zBzC
+++
+++=
+++
+++==
...1
......
...
)(
)()(
1
1
1
10
1
1
1
10
7/29/2019 Lecture11 IMC
8/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-8
Dahlins Controller Eric Dahlin worked for IBM in San Jose (?) then for Measurex
in Cupertino.
Dahlins controller, 1967
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: 1st order+deadtime
Dahlins controller
Single tuning parameter: - tuned controller
a.k.a. - tuned controller
)(1)(
)(1)(
zQzQ
zPzC
=
7/29/2019 Lecture11 IMC
9/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-9
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
CLOSED-LOOP STEP RESPONSE WITH DAHLIN CONTROLLER
Ta=2.5T
D
Ta=1.5T
DOpen-loop
0 10 20 30 40 50 600
0.5
1
1.5
CONTROL STEP RESPONSE
Industrial tuning
guidelines:
Closed loop timeconstant = 1.5-2.5
deadtime.
7/29/2019 Lecture11 IMC
10/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-10
Internal Model Control - IMC
continuous times
discrete timez
P
P0
e
Qeu
uPyre
=
= )( 0
01 QP
QC
=
General controller design approach; some use in process industry
0QPT=Reference model:
FilterQ Internal model: 0P
7/29/2019 Lecture11 IMC
11/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-11
IMC and Youla parametrization
QS
QPT
QPS
u =
=
=
0
01 Sensitivities
ud
yy
yd
d
IfQ is stable, then S, T, and the loop are stable
If the loop is stable, then Q is stable01 CP
CQ
+=
01 QP
QC
=
Choosing various stable Qparameterizes all stabilizing
controllers. This is called Youla parameterization
Youla parameterization is valid for unstable systems as well
C P-
e
yyd
u
ddisturbance
reference output
control
error
7/29/2019 Lecture11 IMC
12/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-12
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 = ( )1
01
7/29/2019 Lecture11 IMC
13/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-13
Q-loopshaping Loopshaping
For a minimum phase plant
0
01QPT
QPS=
= ( )11
10
1
0
7/29/2019 Lecture11 IMC
14/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-14
IMC extensions Multivariable processes
Nonlinear process IMC Multivariable predictive control - Lecture 14
7/29/2019 Lecture11 IMC
15/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-15
Nonlinear process IMC Can be used for nonlinear processes
linearQ
nonlinear model N
linearized model L
e
7/29/2019 Lecture11 IMC
16/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-16
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
7/29/2019 Lecture11 IMC
17/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-17
Dynamic inversion in flight control
)(
),(),(
1FvGu
uvxGvxFv
des=
+=
&
&
=
NCV
MCV
LCV
v
X-38 - Space Station
Lifeboat
Honeywell MACH
Dale Enns
Reference model:
desv
s
v &1
=
7/29/2019 Lecture11 IMC
18/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-18
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)
7/29/2019 Lecture11 IMC
19/19
EE392m - Spring 2005Gorinevsky
Control Engineering 11-19
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 modernadvanced 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
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