Evaluation of River Flood Regulation using Model Predictive Control
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Transcript of Evaluation of River Flood Regulation using Model Predictive Control
Evaluation of River Flood Regulation using Model Predictive Control
K. U. LEUVEN
Patrick Willems
Toni Barjas Blanco
P.K. Chiang
Bart De Moor
Jean Berlamont
SCD Research DivisionESAT- K. U. Leuven May 6th-8th, 2008
4th International Symposium on Flood Defence
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Problem Description
Principles of MPC
Model of the Demer
Uncontrollability
Results
Conclusion and Future Works
Outline
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Introduction
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Introduction
Current control strategy (three-position controller):
If-then-else rules
Based on current state
Takes no rain predictions into account
Simulations far from optimal
Better Alternative:
Model Predictive Control (MPC)
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Model Predictive control: Principles
Real-life analogy:
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State Space Model
Linear State Space Model:
Nonlinear State Space Model:
1k k k k
k k
x Ax Bu Dd
y Cx
1 ( , , )
( )k k k k
k k
x f x u d
y g x
State: water levels, discharges, volumes
Input: gate positions
Disturbance input: rainfall
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Model Predictive Control: Principles
Mathematical formulation:
12 2
, 1,...,0
min ( )k i
N
i k i ru i N
i
a y y
s.t.
1
2
1
0
( )
( )
( , , )
( )
k i
k i
k i k i k i k i
k i k i
k
h y c
r u c
x f x u d
y g x
x x
Initial state
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Model Predictive control
Advantages:
Disadvantages:
Constraints
Predictive Rainfall due to horizon
Multiple Objectives
Priorities
Computational complexity
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Model of the Demer
Possible modelling strategies:
Black box: based on data
Physical : physical laws
Grey box : Combination of previous strategies
In this work Grey box modelling from historical data (1998 and
2002) Reservoir Type
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Schematical overview bassin
vgl, hgl
qbg
vopw, hopw
qman
qopw
K7 A
v1, h1
E
vs, hs
qK7
qA qE
vs2, hs2
qs
vs3, hs3
D
qs2 qs3
vvg, hvg
qhopw
vs4, hs4
qs4 qhs
vhopw, hhopw
qvs qD
q2
qzbopw qzb1
qgopw
qgafw
v3, h3
qvopw
hvopw
qK18
q3 q4
vw, hw
qK19 qK30
qbgopw
qK7lg
qgl
vbg, hbg
qK7bg
qzb3
q7 Demer
Zw
arte
wat
er
Zwartebeek
Vlootgracht
Schulensmeer
Webbekom
Her
k
Get
e
Beg
ijne
beek
Vel
pe
Leu
gebe
ek
Gro
te L
eigr
acht
Hou
wer
sbee
k
q6 q5
qK31
qzb2
v4, h4
vzb, hzb
qzw
q1
vlg, hlg
qK24B
hbgopw
qK24A
vzw, hzw
qzwopw
qhs2
v2, h2
qh
qsa
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Resultaten Schulensmeer
Demer
SchulenslakeGate K7Gate A
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Resultaten Schulensmeer
Hopw
qK7Hs
qAHafw
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Model Validation
20
20.5
21
21.5
22
22.5
23
23.5
0 200 400 600 800 1000 1200 1400
tijd [h]
h [
m T
AW
]
h-afw, IW
h-afw, conc.model
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Expert knowledge
Water administration:
Experience :
Debatable w.r.t. optimality
1. Can be usefull to take into account e.g. N
2. Drastical change can be frightening
Experience Guidelines about filling order reservoirs
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Expert knowledge in MPC
• Constraint priorization:
Ensures satisfaction high priority constraints
1. Divide the constraints in sets with different priority
2. Solve MPC control problem with all constraints
3. If infeasible remove lowest priority contraints and resolve MPC control problem, increasing weights of variables corresponding to removed constraint set
4. Until a feasible solution apply first calculated input
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Uncontrollability problem
Typical use of MPC control to a reference value
In flooding prevention:
1. Control to reference value less important
2. Avoid flooding Nonlineair behaviour is very important
21 m
wachtbekken ka kd hopw
Most difficult nonlinearity
example
No derivatives
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Fuzzy model for derivatives
model
estimatorMPC
Fuzzy model
y
x
u
x̂
^A,B
(Linearized system matrices)
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Results (Historical rainfall 1998)
20
20.5
21
21.5
22
22.5
23
23.5
0 100 200 300 400 500 600 700Tijd [h]
Waterh
oo
gte [m
T
AW
]
HopwHsHafw
Three-position controller (currently in use):
20
20.5
21
21.5
22
22.5
23
23.5
0 100 200 300 400 500 600 700Tijd [h]
Wa
te
rh
oo
gte
[m
T
AW
]
HopwHsHafw
MPC with priorities:
Control to 21.5 m
Hopw en Hs < 23m TAW
Hafw < 22.75m
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Results (Fictituous data based on data from 1998)
Three-position controller (currently in use):
MPC with priorities:
19.5
20
20.5
21
21.5
22
22.5
23
23.5
24
0 200 400 600 800 1000 1200 1400 1600 1800Tijd [h]
Waterh
oo
gte [m
T
AW
]
HopwHsHafw
19.5
20
20.5
21
21.5
22
22.5
23
23.5
24
0 200 400 600 800 1000 1200 1400 1600 1800Tijd [h]
Wa
terh
oo
gte
[m
T
AW
]
HopwHsHafw
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Conclusions and future works
Conclusion:
Model Predictive Control outperformed three-position controller
Future works:
Extend MPC to control the whole model
Estimate state with moving horizon estimator
Robust MPC wrt uncertainty rain prediction and modelling errors