vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF ABBREVIATIONS
xiii
LIST OF SYMBOLS
xiv
LIST OF APPENDICES
xvi
INTRODUCTION
1
1.1
Background of project
1
1.2
Problem statement
2
1.3
Objectives of the project
2
1.4
Scope of the project
3
1.5
Methodology
3
1.6
Thesis outline
4
LITERATURE REVIEW
6
2.1
6
Brief on wastewater treatment plant
viii
2.2
2.1.1
Primary treatment
7
2.1.2
Secondary treatment
8
2.1.3
Tertiary treatment
9
Activated sludge process
2.2.1
Bioprocess modeling of activated
9
11
sludge
2.3
3
Input/output data-based predictive control
SUBSPACE SYSTEM IDENTIFICATION AND
13
16
DESIGN OF PREDICTIVE CONTROL BASED
ON INPUT/OUTPUT DATA
3.1
Introduction
16
3.2
Subspace identification method
18
3.2.1
Matrix input-output equations
18
3.2.2
State sequence and system related
19
matrices
3.2.3
The least square problem
20
3.2.4
Orthogonal projection
20
3.2.5
Oblique projection
21
3.2.6
Numerical implementation
22
3.2.7
SV decomposition
22
3.2.8
Estimate model
23
3.2.9
Block Hankel matrices and input/output
24
equations
3.2.10 Identification of prediction model
3.3
Understanding model predictive control
26
3.4
Fundamental of MPC
28
3.5
4
25
3.4.1
Predictive model
28
3.4.2
Objective function
29
3.4.3
MPC control law
30
Subspace predictive control algorithm
31
SIMULATION RESULTS AND DISCUSSION
33
4.1
33
Introduction
ix
4.2
Control objectives
33
4.3
Simulink block
34
4.3.1
Input excitation
35
4.3.2
Subspace predictive controller
36
4.3.3
Activated sludge process plant
37
4.4
4.5
5
Inputs and outputs response
38
4.4.1
Steady state condition
38
4.4.2
System excitation
41
Controller performance
43
4.5.1
Sudden changes in the feed concentration
43
4.5.2
Set-points changes
46
CONCLUSION
50
5.1
Conclusion
50
5.2
Future works
51
REFERENCES
Appendices A – C
52
54 - 65
x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
2.1
Process parameters
13
2.2
Kinetic parameters
13
2.3
Initial conditions
13
xi
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
Project flowchart
5
2.1
General wastewater treatment stages
7
2.2
Schematic diagram of an activated sludge process
10
2.3
Activated sludge process model
11
3.1
Comparison between classical approach and subspace
17
approach to obtain predictive controller
3.2
Oblique projection
21
3.3
Principle of MPC
28
4.1
General activated sludge process
34
4.2 (a)
Input excitation 1, D
35
4.2 (b)
6 bits PRBS
35
4.3 (a)
Input excitation 2,W
36
4.3 (b)
4 bits PRBS
36
4.4
Subspace predictive controller
37
4.5 (a)
The activated sludge process plant
37
4.5 (b)
The subsystem of activated sludge process plant
38
4.6 (a)
System input – dilution rate
39
4.6 (b)
System input – air flow rate
39
4.7 (a)
System response – biomass
39
4.7 (b)
System response – substrate
40
4.7 (c)
System response – dissolve oxygen
40
4.7 (d)
System response – recycled biomass
40
4.8 (a)
The 4-level pseudo random input – dilution rate
41
4.8 (b)
The 4-level pseudo random input – air flow rate
41
xii
4.9 (a)
The corresponding excited output – biomass
42
4.9 (b)
The corresponding excited output – substrate
42
4.9 (c)
The corresponding excited output – dissolve oxygen
42
4.9 (d)
The corresponding excited output – recycled biomass
43
4.10 (a)
Sudden changes in the feed concentration – substrate, Y1
44
4.10 (b)
Sudden changes in the feed concentration – dissolve
44
oxygen, Y2
4.11 (a)
Sudden changes in the feed concentration – substrate, Y1
45
4.11 (b)
Sudden changes in the feed concentration – dissolve
45
oxygen, Y2
4.12 (a)
Changes in the set-points – substrate, Y1
46
4.12 (b)
Changes in the set-points – dissolve oxygen, Y2
47
4.13 (a)
Changes in the set-points – substrate, Y1
47
4.13 (b)
Changes in the set-points – dissolve oxygen, Y2
48
xiii
LIST OF ABBREVIATIONS
BOD
-
Biochemical Oxygen Demand
CVA
-
Canocical Variate Analysis
DMC
-
Dynamic Matrix Control
LQG
-
Linear Quadratic Gaussian
MBPC
-
Model-Based Predictive Control
MIMO
-
Multi-Input Multi-Output
MPC
-
Model Predictive Control
N4SID
-
Numerical Algorithms for Subspace State Space
System Identification
PRBS
-
Pseudorandom Binary Sequence
QP
-
Quadratic Programming
SISO
-
Single-Input Single-Output
SPC
-
Subspace Predictive Control
SVD
-
Singular Value Decomposition
WWTP
-
Wastewater Treatment Plant
xiv
LIST OF SYMBOLS
-
The Moore-Penrose pseudo-inverse of B
-
The orthogonal complement of
-
Recycled biomass
-
Frobenius norm
-
The deterministic lower triangular block-Toeplitz
matrix
-
The stochastic lower triangular block-Toeplitz matrix
-
Quadratic cost function
Kc
-
Saturation constant
Ks
-
Growth rate
-
Controller parameters
-
Controller parameters
-
The reference outputs
-
Substrate
-
Block Hankel matrices consisting of the future input
-
Block Hankel matrices consisting of the past input
-
The future control input
-
Block Hankel matrices consist of measurement noises
-
Short-hand notation related to the past inputs and
outputs
-
The future state sequence
-
Biomass
-
Dissolved oxygen concentrations
-
Block Hankel matrices consisting of the future output
-
Block Hankel matrices consisting of the past output
xv
-
The linear predictor
-
k-step-ahead predicted output
-
Block Hankel matrices consist of process noises
-
Monod law
-
Extended observability matrix
xvi
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
Program for subspace identification process
55
B
Program to obtain an optimal future control sequence
58
C
Program for implementing subspace predictive control
61
D
Program for initialize the system
66