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An overview of centralized model predictive control (mpc), its structure, principles, advantages, and applications. Centralized mpc uses all measurements to calculate all manipulated variables simultaneously, leading to better control performance but increased controller complexity and real-time computations. The history, design methods, guidelines, and commercial products of centralized mpc.
Typology: Slides
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When I complete this chapter, I want to be
able to do the following.
Outline of the lesson.
L
F
T
A
CentralizedController
-^
-^
L
F
T
A
CentralizedController
-^
-^
-^
(s)d G
(s)P
(s)v
MPC
(s)
D(s)
CV(s)
SP(s)
MV(s)
m
(s)
m
(s)
(s)p
Centralized controller
The variables are vectors
The transfer functions are matrices
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1 2
s
CV
s
CV
s
CV
s
CV
N^
ù ú ú ú ú ú úû
1 21
1
12
11
s
s
s
s G s G s G s G
NM
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M
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[^
]^
m
MPC
[^
-1] )
m
MPC
input variable
output variable
0
time
5
− e s
s G
s
0
0
1
0
2
0
3
4
5
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10
11
Empirical identification
ContinuousModel usingprocess reactioncurve or statistics
Sampled output modelfor unit step with
∆∆∆∆
t =
2.5 minutes
Could we use the data from the experiment as the model?
Stephere
Samplenumber
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0
50
100
150
200
250
1.5^1 0.5^0
S-LOOP plots deviation variables (IAE = 20.0383)
Time
Controlled Variable
0
50
100
150
200
250
504030 2010 0
Time
Manipulated Variable
(s)P
(s)v
MPC
(s)
CV(s)
SP(s)
MV(s)
(s)p
Time
future
→→→→
←←←←
past
Controlled variable calculated using modeland past values of manipulated variable
Controlled variable calculated using modeland past values of manipulated variable
Set point
Past values of themanipulated variable
Calculated by MPC Controller Future values of the manipulatedvariable determined by the controller
Error at each time step that is reduced by the future values of the manipulatedvariable adjustments determined by the controller
Only the current result isimplemented
CV
MV
A
to
subject
CV
E
c
=
∆
−
)
(
min
Quadraticobjective withlinear equations;can be solved
Solution is leastsquares equations,involving solutionto linear equationsoffline and simplematrix-vectorproduct online.
Means minimizeby adjustingvalues of
∆∆∆∆
MV
c
Model relates ∆∆∆∆
MV
c^
to CV
c
0
20
40
60
80
100
1
2
3 concentration
0
50
100
150
55 50 45
Time
valve opening
Why didn’t the CV
track the setpoint exactly? We calculatedfour steps, but only two changed;
why?
Time
future
→→→→
←←←←
past
Controlled variable calculated using modeland past values of manipulated variable Current measured value of the controlled variable
Controlled variable calculated using modeland past values of manipulated variable, without feedback
Set point
Past values of themanipulated variable
Future values of themanipulated variabledetermined by the controller
Error
(corrected by feedback)
at each time step that is reduced by the future
values of the manipulated variable adjustments determined by the controller
Model mismatch, E
mm
What do weassume about the model error?
0
20
40
60
80
100
1
2
3 concentration
0
50
100
150
55 50 45
Time
valve opening
Returned to set
point; why? Diagnose thisperformance?
