PID CONTROLLER DESIGN WITH

DIFFERENT TUNING METHODS

MUHAMMAD JAZLI AIMAN BIN ABDUL RAHIM

Bachelor of Electrical Engineering

June 2012

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SUPERVISOR DECLARATION

“ I hereby declare that I have read through this report entitle “PID CONTROLLER

DESIGN WITH DIFFERENT TUNING METHODS” and found that it has comply the

partial fulfillment for awarding the degree of Bachelor of Electrical Engineering (Control,

Automation and Instrumentation)”

Signature : .....................................

Supervisor‟s Name : Dr. Hamzah Bin Sakidin

Date : .....................................

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PID CONTROLLER DESIGN WITH DIFFERENT TUNING METHODS

MUHAMMAD JAZLI AIMAN BIN ABDUL RAHIM

A report submitted in partial fulfillment of the requirements for the degree of

Bachelor of Electrical Engineering

Faculty of Electrical Engineering

UNIVERSITI TEKNIKAL MALAYSIA MELAKA

JUNE 2012

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STUDENT DECLARATION

I declare that this report entitle “PID CONTROLLER DESIGN WITH DIFFERENT

TUNING METHODS” 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 : MUHAMMAD JAZLI AIMAN BIN ABDUL RAHIM

Date : .............................................................................

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Dedicated to My Beloved Father, Mother, Brother, Sister and all my friends

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ACKNOWLEDGEMENT

First of all I would like to express my utmost gratitude to my supervisors, Puan

Sazuan Nazrah Binti Mohd Azam and Dr. Hamzah Bin Sakidin, for their valuable advice

and guidance. They had been very tolerant, contributive and helpful in guiding me

throughout the project. Thank you for spending time with me despite your busy schedule.

Then I would like to thanks to all my friends who have helped in some ways or

other by discussing and exchanging ideas and information besides giving me moral

support, especially Aminuddin, Abu Bakar, Ahmad Afiq, Ikram and Wan Nur Farhana and

as the list continues, finally a very special thanks to all who has contribute to the birth of

this project directly or indirectly, may Allah S.W.T blessed you all.

Last but not least, I would like to dedicate my sincere appreciation to my beloved

family for their love, patience and support. Without their support, I would not be able to go

through all the hard times.

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ABSTRACT

The purpose of this project is to design a PID controller for a heat exchange pilot plant and

to study the best tuning method for the controller system. The data from the pilot plant will

be used to model the system and to set the transfer function of the system by using

MATLAB system identification toolbox. Once the analysis is completed, data gained will

be used to tuning PID controller so that the system satisfies the required performance

specification. This project also will included the studies on methods of tuning the

controller such as Cohen-Coon method, Ziegler- Nichols method and other method that

have been used in control system. The study of tuning method will be considered for their

effectiveness and simplicity of implementation. In this tuning method studies, comparison

between each method of tuning will be done included with their parameter and suitable

application in control system that to be used in industrial application and to look for the

best tuning method for the system design.

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ABSTRAK

Tujuan projek ini adalah untuk mereka bentuk pengawal kebezaan-kamiran-kadaran (PID)

bagi sebuah sistem pertukaran haba dan kajian tentang kaedah penetapan yang sesuai untuk

digunakan di dalam sistem penukaran haba tersebut. Data yang diambil dari sistem perintis

akan digunakan untuk mereka sistem dan untuk menetapkan persamaan bagi sistem ini

dengan menggunakan program “System Identification Toolbox”. Setelah analisis

dilakukan, data yang diperolehi akan digunakan untuk penetapan nilai parameter PID

supaya system direka dapat memenuhi spesifikasi yang diperlukan. Projek ini juga akan

mengkaji mengenai kaedah-kaedah penetapan yang lain seperti kaedah Cohen-Coon,

kaedah Ziegler-Nichols dan kaedah-kaedah yang lain. Kaedah penetapan ini akan

dipertimbangkan berdasarkan keberkesanan dan perlaksanaan sistem. Perbandingan kaedah

penetapan juga akan dilaksanakan berserta parameter dan system kawalan yang sesuai

digunakan berdasarkan kaedah penetapan yang dikaji untuk digunapakai di dalam industri

dan untuk menentukan kaedah penetapan yang terbaik untuk sistem penukaran haba ini.

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TABLE OF CONTENT

CHAPTER TITLE PAGE

ACKNOWLEDGEMENT ii

ABSTRACT iii

ABSTRAK iv

TABLE OF CONTENT v

LIST OF TABLE ix

LIST OF FIGURE xi

LIST OF SYMBOL xiii

LIST OF APPENDICES iix

1 INTRODUCTION 1

1.0 The Project Overiew 1

1.1 Problem Statement 1

1.2 Objective of the Project 2

1.3 Scope of the Project 2

1.4 Project Outline 2

2 LITERATURE REVIEW 3

2.0 Introduction 3

2.1 The Heat Exchanger System 3

2.2 Modeling and System Identification Toolbox 5

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CHAPTER TITLE PAGE

2.3 PID Controller 6

2.4 PID Tuning 9

2.4.1 Ziegler-Nichols 9

2.4.1.1 Ziegler-Nichols First Method 10

2.4.1.2 Ziegler-Nichols Second Method 11

2.4.2. Cohen-Coon 12

2.4.3 Internal Model Control based PID 14

(IMC based PID)

2.4.4 Maclaurin-PID (Mac-PID) 15

2.4.5 Heuristic 17

2.5 Calculation for System Response Parameter 17

3 METHODOLOGY 19

3.0 Introduction 19

3.1 Phase 1: Modeling Controller 21

3.1.1 System Identification 21

3.2 Phase 2: Controller Design 25

3.2.1 PID Controller 25

3.2.1.1 Ziegler-Nichols Tuning 26

3.2.1.2 Cohen-Coon Tuning 26

3.2.1.3 Internal Model Control (IMC) Tuning 27

3.2.1.4 Mac-PID Tuning 28

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CHAPTER TITLE PAGE

3.2.1.5 Heuristic Tuning 29

3.3 Phase 3: Analysis 29

3.3.1 Performance Evaluation 30

3.3.1.1 Step Response Comparison 30

3.3.1.2 Set Point Changes 31

4 RESULT AND DISCUSSION 32

4.0 Introduction 32

4.1 Phase 1: Modeling Controller 32

4.1.1 System Identification 32

4.2 Phase 2: Controller Design 34

4.2.1 PID Controller 34

4.2.1.1 Ziegler-Nichols Tuning (Z-N) 35

4.2.1.1 Cohen-Coon Tuning (C-C) 36

4.2.1.1 Internal Model Control (IMC) 37

4.2.1.1 Maclaurin-PID (Mac-PID) 39

4.2.1.1 Heuristic Tuning 40

4.3 Phase 3: Analysis 41

4.3.1 Performance Evaluation 41

4.3.1.1 Step Response Comparison 41

4.3.1.2 Set Point Changes 43

5 CONCLUSION AND RECOMMENDATION 47

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CHAPTER TITLE PAGE

5.1 Conclusion 47

5.2 Recommendation 48

REFERENCE 50

APPENDIX 53

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LIST OF TABLE

TABLE TITLE PAGE

2.1 The first method of Ziegler-Nichols Calculation 11

2.2 The second method of Ziegler-Nichols calculation 12

2.3 Cohen and Coon proposed method Calculation 13

2.4 IMC-based PID tuning parameters of a FOPDT process 14

2.5 Mac-PID tuning parameters of a FOPDT process 16

3.1 Ziegler-Nichols Tuning Calculation 26

3.2 Cohen-Coon Tuning Calculation 27

3.3 Internal Model Control Tuning Calculation 28

3.4 Maclaurin-PID Tuning Calculation 29

3.5 Step Response Characteristic Term 31

4.1 Ziegler-Nichols Tuning Parameter 36

4.2 Cohen-Coon Tuning Parameter 36

4.3 Internal Model Control (IMC) Tuning Parameter 38

4.4 Mac-PID Tuning Parameter 39

4.5 Heuristic Parameter 41

4.6 Tuning Parameter of PID Controller 43

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LIST OF FIGURES

FIGURE TITLE PAGE

2.1 Heat Exchange Simulink diagram of PID Controller 4

2.2 System Identification toolbox 5

2.3 Control Systems with PID Controller 6

2.4 Series Form of PID Compensator 7

2.5 Parallel Form of PID Compensator 7

2.6 Ideal Form of PID Compensator 8

2.7 Reaction Curve Tests 13

3.1 Overall project Flowcharts 20

3.2 System Identification Flowcharts 21

3.3 Importing the Data 22

3.4 Estimation and Validation Data 23

3.5 Process Model Estimation 23

3.6 Process Model Transfer Function Estimation 24

3.7 Model Output 24

3.8 PID Simulink Diagram 25

3.9 Step Response Characteristic Evaluation 31

4.1 System Identification Toolbox 33

4.2 Best Fit Model and Transfer Function Estimation 34

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4.3 PID Block Diagram 35

4.4 Ziegler-Nichols Tuning Reaction Curve 35

4.5 Cohen-Coon Tuning Reaction Curve 37

4.6 Internal Model Control (IMC) Tuning Reaction Curve 38

4.7 Mac-PID Tuning Reaction Curve 39

4.8 Heuristic Reaction Curve 40

4.9 PID Tuning Reaction Curve 42

4.10 Set point changes of tuning method 44

4.11 Set point changes of tuning method 45

4.12 Set point changes of IMC and Heuristic 46

4.13 Set point changes of IMC and Heuristic 46

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LIST OF SYMBOL

HEX Heat Exchanger

FOPDT First Order Plus Dead Time

PID Proportional , Integral, Derivative

Z-N Ziegler-Nichols

C-C Cohen-Coon

IMC Internal Model Control

Mac-PID Maclaurin-PID

Kp Proportional gain

Ki Integral gain

Kd Derivative gain

%OS Percent overshoot

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LIST OF APPENDICES

APPENDIX TITLE PAGE

1 Ziegler-Nichols Tuning Command 53

2 Cohen-Coon Tuning Command 53

3 IMC Tuning Command 54

4 Mac-PID Tuning Command 54

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CHAPTER 1

INTRODUCTION

1.0 The Project Overview

Many control method from the technology advancement that have been applied in

the industry brings benefit to the mankind. To obtain higher efficiency productivity many

control process offers substantial improvement.

Nowadays, heat exchanger is widely used in industry for cooling and heating

industrial process. Principle of heat exchange is where two fluid with different temperature

are brought into close contact but are prevented mixing by physical barrier. Heat exchange

used to recover heat and put the heat for use by heating a different stream in the process.

There is only one variable can be controlled which the amount of heat exchange. The heat

is simply exchanged from one fluid to the other and vice versa.

By using SIMULINK as a programming tool, this project is going to develop a PID

controller design for heat exchange system and comparing the suitable tuning method for

the system. This project used data from pilot plant to model the system and to set the

transfer function for the system. This project includes with graph display, different

controller selection and calculation for the controller performance.

1.1 Problem Statement

Most of the PID controller is tuned with different method, so this project is to

determine the best and most suitable tuning method for the system. Develop the model for

the plant by employing system identification from MATLAB software where a lot of

improvement can be achieved for its control strategy and improve the performance of the

plant.

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1.2 Objective of the Project

The objective of this project is:

To design PID controller for heat exchange system to the set point using

SIMULINK software.

To get the model for the heat exchange system and design the PID

controller by using several tuning method of tuning strategies.

To compare transient response from different tuning method and select best

tuning for used in the system.

1.3 Scope of the Project

This project is going to model heat exchange system using MATLAB system

identification toolbox. In this project the FOPDT model from the heat exchanger pilot plant

is used for simulation purpose. In this case MATLAB version 2010b is chosen as the

development design controller and tuning method comparison. The performance of all

controllers are evaluated and compared by looking at the transient response.

1.4 Project Outline

This report is organized into five chapters devoted to a specific topic. Chapter 1

explains the introduction and the overview of the project. This chapter also includes

problem statement, objectives of the project and project scope. Description of the system

background for the heat exchange controller, modeling, system identification toolbox and

PID controller are explained in Chapter 2.

In Chapter 3 will give the details of the method use for control system design,

modeling and analysis by applying tuning methods. Besides, the procedure to obtain the

controller system is also introduced. Chapter 4 discuss about the controller system result

and the MATLAB result. Lastly, the conclusion and recommendation for further study will

be presented in Chapter 5.

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CHAPTER 2

LITERATURE RIVIEW

2.0 Introduction

This chapter will describe the system background for the heat exchange system.

Besides that, the description of the modeling, system identification toolbox, designing PID

controller, PID Tuning and parameter calculation also included.

2.1 The Heat Exchanger System

Process industry of plant now need accurate, efficient and flexible operation due to

increasing concern such in energy, cost efficiency and time. The new development of

technologies always required for process modeling, dynamic optimization and high

performance industrial process control.

Heat exchangers (HEX) are widely use in process industries such as chemical

process and petroleum process as stated by Huang and Riggs [1]. They also define heat

exchanger as a specialized device in the transfer of heat from one fluid to the other liquid

through a solid wall to a cooler fluid [1] and Barnett stated from his journal of „The

Fundamental of Heat Exchanger‟ that function of solid wall or physical barrier is to

prevent two fluid of different temperature from mixing [2]. Since the heat content from the

two fluids is not constant therefore the heat exchanger system has to be kept at the desired

set point from the outlet temperature according to the process requirement [1].

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Figure 2.1: Heat Exchange Simulink diagram of PID Controller

Compared to the composition dynamics, heat exchanger typically have fast

dynamic for distillation column. Normally the time constant is measured in second but

could be up to a few minutes for large exchangers has been mention by Huang and Riggs

[1]. It is recommended a simplified approach based on using a more effective method to

calculate the steady-state exchanger exit temperatures and the delay these temperature but a

first-order-lag to capture the dynamic [3,4].

Therefore, in this project heat exchanger is selected as a process that will be used

for modeling. In order to achieve the objective, first order plus dead time (FOPDT) process

controller is proposed and will be apply with several tuning method that suitable with the

process.

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2.2 Modeling and System Identification Toolbox

Modeling or System Identification is an interactive process. From Ljung article [5],

he state that modeling requires a model structure where mathematical model between input

and output variable that contain unknown parameter. System Identification obtains

Validation Data, Estimation Data, and others. This system build mathematical model of the

dynamic system by referring to measured data. System Identification measure input and

output system in time domain and frequency domain. The measured input and output then

use to estimate value of adjustable parameter in a model structure as stated in [5]. Then the

validation data will be used for model validates purpose then this process will simulate the

model and computing the residual from the model when applied to the validation data.

System Identification estimate unknown model parameter by minimizing the error between

the model output and measured response. From step response obtain the FOPDT model can

be calculated by calculating the gain, time constant and time delay by referring to its step

response curve as stated by Thyagarajan, Shanmugam and Ponnavaikko [6]. The FOPDT

model is commonly used in many dynamic processes.

Figure 2.2: System Identification toolbox

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2.3 PID controller

The PID control algorithm is the most popular approaches used in process

industries due to easy to understand by operator, technician and maintenance. One

algorithm of PID control can be successful in many applications such as petroleum

processing, steam generation, polymer processing and many more. Willis On the author of

[7] PID consists three basic mode which is Proportional mode, Integral Mode and

Derivative mode. Thomas [8] briefly explained in his „Process Control‟ book that PID

control algorithm can provide good control performance for many different processes since

the PID algorithm is simple and single equation. There are only 5% to 10% of industrial

system that cannot be controlled by a PID controller as stated by Koivo and Tanttu [9].

Many industry use PID as their controller because of PID controller is remarkable

effectiveness, simple to implant in industrial process and easy to re-tuning as concluded by

Saeed and Mahdi [10]. Below is a simple diagram of control process that uses PID as

controller:

input, e(t) output, u(t)

Figure 2.3: Control Systems with PID Controller

Zoran and Ognjen [12] stated Proportional, Integral and Derivative controller (PID)

have three major classifications of PID which is Ideal, Series and Parallel as shown in

Figure 2.4, Figure 2.5 and Figure 2.6. In ideal PID controller the algorithm is represent as

(2.1). One of disadvantages of these kind of PID type, if a sudden change in set point it will

cause a derivative kick to the controller since the derivate term become large as has been

describe by Willis [7]. As for series PID or also known as interacting controller has a

controller equation represent as (2.2). In series PID, proportional (P), Integral (I) and

derivative (D) act decently. Thus, implementation of series mode can include either

derivative on the error or derivative on the measurement. But for parallel mode, the

proportional, integral and derivative gain act on the error signal. Since parallel mode

Process PID Controller

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carries the advantages of all three control mode, the transfer function of parallel PID

controller can be expressed as (2.3) and (2.4).

Figure 2.4: Series Form of PID Compensator [12]\

Figure 2.5: Parallel Form of PID Compensator [12]