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

2Toni Barjas Blanco - 26th Benelux Meeting on Systems and Control - March 15th, 2007

Problem Description

Principles of MPC

Model of the Demer

Uncontrollability

Results

Conclusion and Future Works

Outline

3Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th-8th, 2008

Introduction


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)


Model Predictive control: Principles

Real-life analogy:


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


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


Model Predictive control

Advantages:

Disadvantages:

Constraints

Predictive Rainfall due to horizon

Multiple Objectives

Priorities

Computational complexity


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


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


Resultaten Schulensmeer

Demer

SchulenslakeGate K7Gate A


Resultaten Schulensmeer

Hopw

qK7Hs

qAHafw


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


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


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


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


Fuzzy model for derivatives

model

estimatorMPC

Fuzzy model

y

x

u

x̂

^A,B

(Linearized system matrices)


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


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


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

Evaluation of River Flood Regulation using Model Predictive Control

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