Fundamental Design Of Model Predictive Controller, Performance Studies And Analysis.

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FUNDAMENTAL DESIGN OF MODEL PREDICTIVE

CONTROLLER, PERFORMANCE STUDIES AND

ANALYSIS

Wan Hazwani Binti Wan Hassan

B010810308

Bachelor of Electrical Engineering

(Control, Instrumentation and Automation)

Supervisor: Datuk Professor Dr. Mohd Ruddin

Bin Ab. Ghani

25 _{June 2012}

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PERFORMANCE STUDIES AND ANALYSIS

WAN HAZWANI BINTI WAN HASSAN

A report submitted in partial fulfilment of the requirement for the Degree of

Electrical Engineering (Control, Instrumentation and Automation)

Faculty of Electrical Engineering

UNIVERSITI TEKNIKAL MALAYSIA MELAKA

(3)

“I hereby declare that I have read through this report entitle “ Fundamental Design

of Model Predictive Controller, Performance Comparisons and Analysis” and found that it

has comply the partial fulfilment for awarding the degree of Bachelor of Electrical

Engineering (Control, Instrumentation and Automation)”

Signature

:

Supervisor‟s Name :

Datuk Professor Dr. Mohd Ruddin Bin Ab. Ghani

(4)

DECLARATION

“I declare that this report entitle “Fundamental Design of Model Predictive

Controller, Performance Comparisons and Analysis” is the result of my own research

except as cited in the references. The report has not been accepted for any degree and is not

concurrently submitted in candidature of any other degree”

Signature

:

Name

:

Wan Hazwani Binti Wan Hassan

(5)

To my beloved father and mother

(6)

ACKNOWLEDGEMENT

First and foremost, i would especially like to devote a great appreciation to my

supervisor, Datuk Professor Dr. Mohd Ruddin Bin Ab. Ghani for his help, advice and

motivation. Not forgetting my former supervisor Mdm. Sazuan Nazrah Binti Mohd Azam

for the ideas, guidance, suggestions and knowledge of controller design and performance

studies, and contributions in completion of this final year project.

I also would like to take this opportunity to express my gratitude to my university,

Universiti Teknikal Malaysia Melaka (UTeM) for giving me the opportunity in my studies.

Thank you to panels, Mr. Hyreil Anuar and Mdm. Ezreen Farina for kindly evaluates my

presentation and demonstration. I would also like to thank my academic advisor and all

lecturers in Faculty of Electrical Engineering for the help, guidance and support. Not

forgetting the lab technician for their help.

My deepest thanks go to my father, Wan Hassan and my mother, Maimunah for

their endless prayer, morally support and patience. To my family and friends for their

endless prayers, encouragement and understanding. To Noraini, Jazli, Hisham and Oon,

thank you for the support and opinions. Special thanks to my beloved friend Faizal for the

support, time and knowledge.

Nevertheless, thank you to everybody who helped me in completing the project and

report writing, directly or indirectly, may Allah S.W.T blessed you all.

(7)

ABSTRACT

This project is about the design of an advanced controller that is Model Predictive

Controller (MPC) for commercial use to control temperature in the Heat Exchanger Pilot

Plant. The design of MPC is to overcome the disadvantages of conventional controller. The

transfer functions of the plant was obtained by using MATLAB System Identification

Toolbox . After that, the First Order Plus Dead Time (FOPDT) model was selected as the

best model to use with the MPC. It is because consists of three parameters that are the gain,

time delay and time constant. By using SIMULINK, simulation and design controller were

tested by following the right tuning method and procedures. Then, the analysis and study

of performance in order to achieve the desire set point which is the temperature in the Heat

Exchanger about 50˚C. At the end, this advance controller was obtain the stable results and

safe operation. It can be concluded that MPC has the fastest response compare to PID

controller. Besides that, it can improve the detection for temperature changes of the plant

and quality of desired temperature set point.

(8)

ABSTRAK

Projek ini bertujuan merekabentuk sebuah pengawal yang maju yang mana

dikenali sebagai “Model Predictive Controller(MPC)” digunakan secara komersial untuk

mengawal suhu didalam penukar haba loji pandu. Pengawal MPC direka untuk mengatasi

keburukan-keburukan yang wujud didalam pengawal konvensional. Fungsi pindah telah

diperolehi dengan menggunakan “System Identification Toolbox” dari MATLAB. Selepas

itu, model “First Order Plus Dead Time(FOPDT)” dipilih sebagai yang terbaik untuk

digunakan bersama pengawal MPC. Ini kerana funsi pindah tersebut terdiri daripada tiga

parameter iaitu pemalar, masa tunda dan masa pemalar. Dengan menggunakan

SIMULINK, simulasi dan reka bentuk pengawal diuji dengan mengikuti kaedah dan

prosedur-prosedur menala yang betul. Kemudian, analisis dan kajian prestasi dilakukan

supaya mencapai titik set suhu Penukar Haba yang diinginkan sebanyak 50˚ Celcius.

Akhirnya, pengawal maju ini telah mencapai keputusan-keputusan yang stabil dan

beroperasi dengan selamat. Ia dapat disimpulkan bahawa MPC mempunyai tindakbalas

yang lebih pantas berbanding dengan pengawal PID. Selain itu, ia boleh meningkatkan

pengesanan perubahan pada suhu loji dan kualiti titik set yang diinginkan.

(9)

CHAPTER TITLE

ACKNOWLEDGEMENT

i

ABSTRACT

ii

ABSTRAK

iii

iv

LIST OF TABLES

vi

LIST OF FIGURES

vii

LIST OF APPENDICES

ix

1 INTRODUCTION

1

1.1 PROBLEM STATEMENT

1

1.2 OBJECTIVES

1

1.3 PROJECT SCOPE

1

2 LITERATURE REVIEW AND THEORY

3

2.1 INTRODUCTION

3

2.2 TEMPERATURE CONTROL

3

2.3 MODELING AND SYSTEM IDENTIFICATION

3 2.3.1 Transfer Function

4

2.4 MODEL PREDICTIVE CONTROLLER

7

2.5 ANALYSIS

9 2.5.1 Transient Response

9 2.5.2 Performance Evaluation

10 2.5.3 Robustness Tests and tuning validation

10

3 METHODOLOGY

12

3.1 INTRODUCTION

12

(10)

3.2.1 System Identification

15

3.3 PHASE 2 – CONTROLLER DESIGN

19

3.4 PHASE 3 – ANALYSIS

22 3.4.1 Performance Comparisons

22

3.4.1.1 Step Response 23 3.4.1.2 Set Point Changes 24

3.4.2 Robustness Tests

25

3.4.2.1 Disturbance Rejection 25 3.4.2.2 Random Set Point Tracking 26 3.4.2.3 White Noise Input Disturbances 27 3.4.2.4 White Noise Output Disturbances 27

4 RESULT AND DISCUSSION

29

4.1 INTRODUCTION

29

4.2 PHASE 1 – MODELING

29 4.2.1 System Identification

30

4.3 PHASE 2 – CONTROLLER DESIGN

31

4.4 PHASE 3 – ANALYSIS

36 4.4.1 Performance Comparisons

36

4.4.1.1 Step Response 38 4.4.1.2 Set Point Changes 39

4.4.2 Robustness tests

41

4.4.2.1 Disturbance Rejection 41 4.4.2.2 Random Set Point Tracking 43 4.4.2.3 White Noise Input Disturbances 45 4.4.2.4 White Noise Output Disturbances 50

5 CONCLUSION AND RECOMENDATION

55

5.1 CONCLUSION

55

5.2 RECOMMENDATION

56 REFERENCES

57

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LIST OF TABLES

TABLE

TITLE

3.1 Set Point Changes

4.1 Tuning for Control Horizon (M)

4.2 Tuning for Prediction Horizon (P)

4.3 Tuning of PID Controller

4.4 Graph for PID Controller Tuning

4.5 Performance Comparison between MPC and PID

4.6 Statistic Data 1% White Noise

4.7 Statistic Data 3% White Noise

4.8 Statistic Data 5% White Noise

4.9 Statistic Data 1% White Noise

4.10 Statistic Data 3% White Noise

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LIST OF FIGURES

FIGURE

TITLE

2.1 Block Diagram of Model Identification Method[2]

2.2 Block diagram of the transfer function

2.3 Basic Structure of MPC[6]

2.4 Basic Concept of Model Predictive Controller[8]

3.1 Overall Project Flowcart

3.2 GUI Import Data

3.3 GUI Time Plot

3.4 GUI System Identification Tool

3.5 GUI Process Models

3.6 MPC SIMULINK Model

3.7 Plant Subsystem Model

3.8 GUI Block Parameter for MPC Controller

3.9 GUI for Manipulated Variable

3.10 SIMULINK Diagram of PID Controller

3.11 SIMULINK Diagram of MPC Controller with set point changes

3.12 SIMULINK Diagram of PID Controller with set point changes

3.13 MPC controller design with disturbance

3.14 SIMULINK Diagram of MPC Controller with White Noise Input

3.15 SIMULINK Diagram of MPC Controller with White Noise

Disturbance

4.1 GUI Model Output

4.2 GUI Model Info

4.3 MPC Reaction Curve

4.4 Step Response of model

4.5 Reaction Curves of MPC and PID

4.6 Set Point changes input

(13)

4.10 Disturbance of MPC Controller

4.11 Random Set Point Tracking Reaction Curves

4.12 1% White Noise Input Disturbance

4.13 Output of MPC Controller with White Noise Input disturbance

for 1%

4.14 3% White Noise Input Disturbance

4.15 Output of MPC Controller with White Noise Input disturbance

for 3%

4.16 5% White Noise Input Disturbance

4.17 5% Variance of White Noise Input Disturbance Reaction Curves

4.18 1% White Noise Output Disturbance

4.19 1% variance of White Noise Output Disturbance Reaction Curve

on MPC Controller

4.20 3% White Noise Output Disturbance

4.21 3% variance of White Noise Output Disturbance Reaction Curve

on MPC Controller

4.22 5% White Noise Output Disturbance

4.23 5% variance of White Noise Output Disturbance Reaction Curve

on MPC Controller

(14)

LIST OF APPENDICES

APPENDIX

TITLE

A

Input and Output Data from Heat Exchanger

58

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CHAPTER 1. INTRODUCTION

1.1 PROBLEM STATEMENT

Most of industry still using the conventional controller and the problem with

conventional controller is low performance and stability. In order to overcome this

problem is by using Model Predictive Controller (MPC). It is to show that advance

controller is better than conventional controller. So, this project is proposed to obtain the

best model so that the dynamic behaviour of plant can be identified and MPC controller

can be designed. Experiment with system identification method and SIMULINK diagram

will be used to solve this issue.

1.2 OBJECTIVES

For this project there are three main objectives that need to be achieved:

1. To obtain the best model of transfer function for modeling MPC controller.

2. To design MPC controller for temperature control with the selected tuning

parameters.

3. To study the performance and comparison with conventional controllers.

1.3 PROJECT SCOPE

The scope of work for this project includes modelling MPC controller using

MATLAB System Identification Toolbox. Then, identify the behaviour of plant by

applying process model of System Identification Toolbox. Furthermore, design a Single

Input Single Output (SISO) MPC by using SIMULINK with basic tuning parameters

(16)

adjustment. Then, performance analysis based on comparison of transient response which

is rise time, percent overshoot, settling time, standard deviation and accuracy. These values

are evaluated to determine the performance, robustness and accuracy. Finally, the

performance of MPC was compared with PID controller via Step Response reaction curves

and Set Point Changes reaction. To show the controller had the stability, the robustness test

such as Disturbance Rejection, Set Point Tracking and White Noise Disturbances were

done.

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CHAPTER 2. LITERATURE REVIEW AND THEORY

2.1 INTRODUCTION

In this chapter, briefly explain about the literature conducted for this project. The

literature will cover temperature control and process control technique for advance control

in the industries. This literature will cover the basic structure, use and applications also the

important parameters to consider in the design process and tuning the controller

2.2 TEMPERATURE CONTROL

Processes which measured and change the temperature of a space to a specified

desired set point is called temperature control. In this process, the heat energy is

adjusted to achieve the desired temperature. It is normally in closed loop system. A

model based predictive algorithm is used for controlling a temperature of a fluid stream

using the shell and tube heat exchanger and analyzed the tuning [1].

2.3 MODELING AND SYSTEM IDENTIFICATION

A system used to get a model in order by doing a manual calculation and some

other step. System Identification Toolbox software estimate linear and nonlinear

Mathematical models of dynamic systems from measured data [2]. In this toolbox, there

are can be two type of model: black – box models and grey – box models. Such

black-box models

can simplify detailed first-principle models, such as Finite-element models

of structures and flight dynamics models, by fitting simpler models to their simulated

(18)

responses [2]. For the grey – box models is to compute the coefficients of ordinary

differential and difference equations for systems modelled from first principles.

Figure 2.1 : Block Diagram of Model Identification Method[2]

2.3.1 Transfer Function

The definition of transfer function is multiplying the factor in the

equation for transform of output to the transform of the input [3]. There are two

types of transfer function which are continuous system transfer function and

discrete-time system transfer function. The difference of both transfer function

is the domain use which is s-domain for continuous and z-domain for

time. There are listed a few properties of both continuous system and

discrete-time transfer function.

There are six properties of continuous system transfer function stated

in [3] which are:

1. The Laplace transform of its impulse response is Уδ(t), t ≥ 0. So that, the

transform of the output P(s) if the system input with transfer function is an

impulse and all initial values of zero.

(19)

system differential equation. The transfer function is

( )

Y s

P s

U s



(2.1)

3. By replacing the s-variable with the differential operator D which is D ≡

d/dt, the differential equation of the system can be obtained from the

transfer function.

4. Characteristic equation can be used in determining the stability of a

time-invariant linear system. The denominator of the transfer function is the

characteristic polynomial. So, in continuous systems, it is stable if all roots

of the denominator have negative real parts.

5. The denominator root gives the poles of the system while the numerator

roots give the zeros of the system. By specifying the poles and zero, the

transfer function can be specified to within a constant, K (gain factor). A

pole-zero maps in the s-plane can represent the poles and zero system.

6. The system is considered minimum phase if the transfer functions has no

poles or zero with positive real parts.

There are also six properties of discrete-time system transfer function as

listed below[3]:

1. P(z) is the z-transform of its Kronecker delta response Уδ(k), k = 0,1, …

2. P(z) can be used in obtaining the difference equation of the system by

replacing the z variable with the shift operator Z defined for any integers k

and n by

[ ( ) ( )]

Z y k y k n

(2.2)

3. The P(z) denominator is the characteristic polynomial of the system. So, the

system is stable if all the denominator roots located in the z-plane unit

circle.

(20)

4. The denominator indicates the poles and the numerator indicate the zeros of

the system. The pole-zero map in the z-plane can be used to represent the

system poles and zeros. The poles-zero map of P(z) used to construct the

output response by including the poles and zeros of the input U(z). in

specifying the P(z), the system poles and zeros and the gain factor K are

specified. The P(z) equation is as shows below:

1 2 1 2

(

)(

)...(

)

( )

(

)(

)...(

)

n n

K z z z z

z z

P z

z p z p



z p





_

(2.3)

5. The order of the denominator polynomial must be greater or equal to the

order of the numerator polynomial of the transfer function of a causal

(physically realizable) discrete-time system.

6. The steady state response of a discrete-time system to a unit step input is

called the d.c gain

The block diagram below shows the transfer function with the left is the

input, the right is the output and inside the block is the system transfer

function. The denominator of the transfer function is identifical to the

characteristic polynomial of the differential equation.

Figure 2.2 : Block diagram of the transfer function

1 1 0 1 1 0

(

...

)

(

...

)

m m m m n n n n

b s

b

a s

a

   



 



 

2.1

(21)

Model Predictive Control (MPC) is an advanced method of process control.

MPC is a form of control in which the current control action is obtained by solving

on-line

, at each sampling instant, a finite horizon open-loop optimal control problem, using

the current state of the plant as the initial state; the optimization yields an optimal

control sequence and the first control in this sequence is applied to the plant[4].

Nowadays, it is being popular among in the industry. MPC has become the primary

form of advanced multivariable control in the process industry and a number of

companies have developed and offered MPC products[5]

Figure 2.3 : Basic Structure of MPC[6]

MPC is more complex than the conventional Proportional Integral Derivative

(PID) controller as shown in Figure 2.3 is the basic structure of MPC. The controller

output of MPC is based on the prediction of process output generated by the internal

model, which commonly a kind of linear time-invariant (LTI) models. Most of the

systems are nonlinear, time-varying, may contain delays, and some variables or signals

of central importance may not able to be measured directly [7].

(22)

Figure 2.4 : Basic Concept of Model Predictive Controller[8]

MPC is a controller that uses an identifiable model of a certain process to

predict its future behaviour over an extended prediction horizon and the aim is to minimize

the cost function. The manipulated variable moves is implemented at a sampling instants

over the control horizon is evaluated. The feedback is achieved by implementing the first

move only and then the sequence will be repeated again and this is known as moving

horizon concept [8] Most of the research work done is the application of MPC controller in

specific processes such as gas recovery unit [9], gaseous pilot plant [7], shell and tube heat

exchanger [10] and pasta drying process[11] Large prediction horizon improves nominal

stability of the closed loop but too large of prediction horizon will take long computational

time [7] Advance control strategy such as MPC can lead to energy efficiency. This can

implement by combining the control structures with online process measurements which

can reduce the energy consumption [11].

Nowadays, many researchers come out with their tuning strategy for MPC

controller. One of the tuning methods that is widely used is heuristic approach [7] also

known as trial and error procedure. Almost of all the tuning strategies go for stability,

robustness and performance but requires complicated analysis. An easy-to-use tuning

(23)

the performance of the controllers and tuning strategy [8] by comparing the rise time,

percent overshoot and settling time. Moreover, the set point tracking and disturbance

rejection that causes the process to deviate from the desired operating condition can be the

evaluator of the controller performance [8].

2.5 ANALYSIS

In this phase, the performance of the controller can be measured at some criteria

to obtain the optimum control of the process by performance evaluation. To validate the

tuning strategies and further performance assessment, the set point tracking and

disturbance rejection tests will be run [8].

2.5.1 Transient Response

The transient response is defines as the part of total response which

approaches zero as time approaches infinity [3]. Transient response of the

system can be pictured clearly from the step response [12]. For first order

system, it has one pole on the real axis and time constant is the specification of

the transient response that being derived. The time response is the time for the

step response to reach 63% of its final value. It is the reciprocal of the real-axis

pole location and gives an indication of the transient response speed.

While for second order system which is more complex, by depending

on the values of the components (poles), its can reveal four kind of behaviour,

overdamped, underdamped, undamped, and critically damped. The system is

considered as overdamped if the system poles are real. If the system poles are

complex, the response is underdamped. Undamped is yield from purely

imaginary poles and critically damped response occur when there are two real

poles at the same point[12].

(24)

2.5.2 Performance Evaluation

The step response performances for MPC controller are evaluated by

observing the rise time, settling time and percentage of overshoot criteria.

Rise time (Tr) is the time taken from the initial set point raise until the

new set point. Long rise time will result in slow response to the controller thus

short rise time is usually required.

Settling time (Ts) is defined as the time for the response to reach the

value of within 98% to 95% from the final value [12]. As for this work, 95%

settling time will be use. Settling time can be related to rise time and decay

ratio.

Overshoot is the maximum amount in which the process variable

exceeds the set point change.

2.5.3 Robustness Tests and tuning validation

It is important to tune the controllers to be robust. The control system is

considered robust if with a certain amount of changes in the process

parameters, the controller can tolerate the changes with stable feedback system

[13]. In this thesis, the robustness test was completed by running a few tests

including Disturbance Rejection, Random Set Point Tracking, White Noise

Input Disturbances and White Noise Plant Disturbances.

For set point changes and set point tracking is to show that the

controller should be able to track the system to operate to any set point

changes. Time taken for the controller to trail the new set point will be

observed.

Disturbance Rejection test was to show that the controller should be

able to reject the unexpected disturbances that cause the process to deviate

(1)

2. By taking the Laplace transform and ignoring all terms come up from initial

values, the transfer function of the system can be determined from the

system differential equation. The transfer function is

( )

Y s

P s

U s



(2.1)

3. By replacing the s-variable with the differential operator D which is D ≡

d/dt, the differential equation of the system can be obtained from the

transfer function.

4. Characteristic equation can be used in determining the stability of a

time-invariant linear system. The denominator of the transfer function is the

characteristic polynomial. So, in continuous systems, it is stable if all roots

of the denominator have negative real parts.

5. The denominator root gives the poles of the system while the numerator

roots give the zeros of the system. By specifying the poles and zero, the

transfer function can be specified to within a constant, K (gain factor). A

pole-zero maps in the s-plane can represent the poles and zero system.

6. The system is considered minimum phase if the transfer functions has no

poles or zero with positive real parts.

There are also six properties of discrete-time system transfer function as

listed below[3]:

1. P(z) is the z-transform of its Kronecker delta response Уδ(k), k = 0,1, …

2. P(z) can be used in obtaining the difference equation of the system by

replacing the z variable with the shift operator Z defined for any integers k

and n by

[ ( ) ( )]

Z y k y k n

(2.2)

3. The P(z) denominator is the characteristic polynomial of the system. So, the

system is stable if all the denominator roots located in the z-plane unit

circle.

(2)

4. The denominator indicates the poles and the numerator indicate the zeros of

the system. The pole-zero map in the z-plane can be used to represent the

system poles and zeros. The poles-zero map of P(z) used to construct the

output response by including the poles and zeros of the input U(z). in

specifying the P(z), the system poles and zeros and the gain factor K are

specified. The P(z) equation is as shows below:

1 2 1 2

(

)(

)...(

)

( )

(

)(

)...(

)

n n

K z z z z

z z

P z

z p z p



z p





_

(2.3)

5. The order of the denominator polynomial must be greater or equal to the

order of the numerator polynomial of the transfer function of a causal

(physically realizable) discrete-time system.

6. The steady state response of a discrete-time system to a unit step input is

called the d.c gain

The block diagram below shows the transfer function with the left is the

input, the right is the output and inside the block is the system transfer

function. The denominator of the transfer function is identifical to the

characteristic polynomial of the differential equation.

Figure 2.2 : Block diagram of the transfer function

1 1 0 1 1 0

(

...

)

(

...

)

m m m m n n n n

b s

b

a s

a

   



 



 

2.1

(3)

2.4 MODEL PREDICTIVE CONTROLLER

Model Predictive Control (MPC) is an advanced method of process control.

MPC is a form of control in which the current control action is obtained by solving

on-line, at each sampling instant, a finite horizon open-loop optimal control problem, using

the current state of the plant as the initial state; the optimization yields an optimal

control sequence and the first control in this sequence is applied to the plant[4].

Nowadays, it is being popular among in the industry. MPC has become the primary

form of advanced multivariable control in the process industry and a number of

companies have developed and offered MPC products[5]

Figure 2.3 : Basic Structure of MPC[6]

MPC is more complex than the conventional Proportional Integral Derivative

(PID) controller as shown in Figure 2.3 is the basic structure of MPC. The controller

output of MPC is based on the prediction of process output generated by the internal

model, which commonly a kind of linear time-invariant (LTI) models. Most of the

systems are nonlinear, time-varying, may contain delays, and some variables or signals

of central importance may not able to be measured directly [7].

(4)

Figure 2.4 : Basic Concept of Model Predictive Controller[8]

MPC is a controller that uses an identifiable model of a certain process to

predict its future behaviour over an extended prediction horizon and the aim is to minimize

the cost function. The manipulated variable moves is implemented at a sampling instants

over the control horizon is evaluated. The feedback is achieved by implementing the first

move only and then the sequence will be repeated again and this is known as moving

horizon concept [8] Most of the research work done is the application of MPC controller in

specific processes such as gas recovery unit [9], gaseous pilot plant [7], shell and tube heat

exchanger [10] and pasta drying process[11] Large prediction horizon improves nominal

stability of the closed loop but too large of prediction horizon will take long computational

time [7] Advance control strategy such as MPC can lead to energy efficiency. This can

implement by combining the control structures with online process measurements which

can reduce the energy consumption [11].

Nowadays, many researchers come out with their tuning strategy for MPC

controller. One of the tuning methods that is widely used is heuristic approach [7] also

known as trial and error procedure. Almost of all the tuning strategies go for stability,

robustness and performance but requires complicated analysis. An easy-to-use tuning

(5)

strategy was proposed for Dynamic Matrix Control [8]. The performance of the controller

can be analyzed in variety of methods. The step response is one of the methods to compare

the performance of the controllers and tuning strategy [8] by comparing the rise time,

percent overshoot and settling time. Moreover, the set point tracking and disturbance

rejection that causes the process to deviate from the desired operating condition can be the

evaluator of the controller performance [8].

2.5 ANALYSIS

In this phase, the performance of the controller can be measured at some criteria

to obtain the optimum control of the process by performance evaluation. To validate the

tuning strategies and further performance assessment, the set point tracking and

disturbance rejection tests will be run [8].

2.5.1 Transient Response

The transient response is defines as the part of total response which

approaches zero as time approaches infinity [3]. Transient response of the

system can be pictured clearly from the step response [12]. For first order

system, it has one pole on the real axis and time constant is the specification of

the transient response that being derived. The time response is the time for the

step response to reach 63% of its final value. It is the reciprocal of the real-axis

pole location and gives an indication of the transient response speed.

While for second order system which is more complex, by depending

on the values of the components (poles), its can reveal four kind of behaviour,

overdamped, underdamped, undamped, and critically damped. The system is

considered as overdamped if the system poles are real. If the system poles are

complex, the response is underdamped. Undamped is yield from purely

imaginary poles and critically damped response occur when there are two real

poles at the same point[12].

(6)

2.5.2 Performance Evaluation

The step response performances for MPC controller are evaluated by

observing the rise time, settling time and percentage of overshoot criteria.

Rise time (Tr) is the time taken from the initial set point raise until the

new set point. Long rise time will result in slow response to the controller thus

short rise time is usually required.

Settling time (Ts) is defined as the time for the response to reach the

value of within 98% to 95% from the final value [12]. As for this work, 95%

settling time will be use. Settling time can be related to rise time and decay

ratio.

Overshoot is the maximum amount in which the process variable

exceeds the set point change.

2.5.3 Robustness Tests and tuning validation

It is important to tune the controllers to be robust. The control system is

considered robust if with a certain amount of changes in the process

parameters, the controller can tolerate the changes with stable feedback system

[13]. In this thesis, the robustness test was completed by running a few tests

including Disturbance Rejection, Random Set Point Tracking, White Noise

Input Disturbances and White Noise Plant Disturbances.

For set point changes and set point tracking is to show that the

controller should be able to track the system to operate to any set point

changes. Time taken for the controller to trail the new set point will be

observed.

Disturbance Rejection test was to show that the controller should be

able to reject the unexpected disturbances that cause the process to deviate