LIQUID LEVEL CONTROL OF A COUPLE TANK SYSTEM BASED ON SMOOTH TRAJECTORY TRACKING USING PID CONTROLLER

SALMAN BIN RAZENI

This thesis is submitted as partial fulfillment of the requirements for the award of the

Bachelor of Electrical Engineering (Control & Instrumentations)

Faculty of Electrical & Electronic Engineering

Universiti Malaysia Pahang

24 NOVEMBER, 2009

i

“All the trademark and copyrights use herein are property of their respective owner.

References of information from other sources are quoted accordingly; otherwise the

information presented in this report is solely work of the author.”

Signature : ____________________________

Author : SALMAN BIN RAZENI

Date : 24 NOVEMBER 2008

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“I hereby acknowledge that the scope and quality of this thesis is qualified for the

award of the Bachelor Degree of Electrical Engineering

(Control & Instrumentations)”

Signature : _____________________________________

Name : MOHD SYAKIRIN BIN RAMLI

Date : 24 NOVEMBER 2008

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ACKNOWLEDGEMENT

Bismillahirrahmanirrahim

Alhamdullillah, Praise be Upon Him, The Most Compassionate and Gracious.

Throughout the period of accomplishing this project, I received ideas,

supports and assistance from few individuals. Firstly, I would like to express my

sincere appreciation to my project’s supervisor, Mr. Mohd Syakirin bin Ramli for his

guidance, patience and motivation.

I am also very thankful to all my lecturers, for their advices, guidance and

experience sharing. Without all of their continued support and interest, this project

would not have been not the same as presented here.

I am also indebted to all Associate and Librarians of Universiti Malaysia

Pahang (UMP) for their assistance in supplying the beneficial relevant literatures and

references. I would like also to convey my thanks to my fellow friends especially

BECian classmates that given me full of support until the end of the process.

Most importantly, I would like to convey my special thanks to my parents

who had persistently giving spiritual motivation and inspiration throughout the

course of the project. With their concern and support, I managed to motivate myself

to overcome problems occurred in this project.

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ABSTRACT

Industries such as petro-chemical industries, paper making industries, waste

management and others are the vital industries where liquid level and flow control

are essential. Liquids will be processed by chemical or mixing treatment in the tanks,

but always the level fluid in the tanks must be controlled, and the flow between tanks

must be regulated in the presence of nonlinearity and inexact model description of

the plant. This project investigates the usage of Proportional-Integral-Derivative

(PID) controller in controlling the liquid level in the second tank of Coupled-Tank

plant through variable manipulation of water pump in the first tank. This project

presents the ability of controlling the liquid level of a coupled tank system that used

Programmable Logic Controller (PLC) as a main controller hardware. A PID

controller has been developed and designed via ladder programme of CX-

programmer. A mathematical model of the couple tank system was derived by

refering to the experimental manual and verified by using MATLAB software. The

controller parameters derived from the simulation and design process using

MATLAB as well. The project is based on Single Input Single Output (SISO) system

which mean the liquid will entering the tank 1 (pump 1) in couple tank while the

level control is in tank 2 in the condition of pump 2 is set OFF. The aim of the

project is to design controller that can maintain the level and minimize the error (SP-

CV) value at any of given set point(SP). It is to show that PID controller could

produce appropriate control signal to the coupled-tank system and minimize the error

value for the system. A series of tracking performance tests conducted to evaluate the

controller performance in comparison to other controller such are fuzzy controller,

DMRAC controller or other controller that used by other reearcher before. . The

outcome of the project reveals that PID controller could carry a small error rate when

the appropriate value of Kp, Ki, and Kd are applied. The framework of this project is

generic enough to have an overview of the possible outcome before implementing

the PID controller in real-time system in the future.

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ABSTRAK

Industri seperti industri petro-kimia, industri pembuatan kertas, pengurusan sisa dan

lain adalah industri penting di mana kadar cecair dan kawalan aliran adalah penting.

Cecair akan diproses dengan mencampurkan bahan kimia atau perlakuan dalam

tank, tetapi tahap cecair di dalam tangki harus dikawal, dan aliran antara tank harus

diatur. Projek ini menyiasat penggunaan “ PID) controller “ dalam kawalan tahap

cecair di kedua tangki melalui manipulasi pembolehubah pam air pertama tangki.

Ini adalah untuk menunjukkan bahawa PID boleh menghasilkan isyarat kawalan

yang sesuai kepada sistem tangki dan meminimumkan nilai kesalahan sistem. Sebuah

model dinamik tanaman awalnya dikembangkan. Simulasi pengajian kemudian

dilakukan berdasarkan model yang dikembangkan dengan menggunakan Matlab dan

Simulink. Ujian yang dilakukan untuk menilai prestasi pengawal berbanding dengan

kaedah kawalan lain adalah seperti kaedah pengendali fuzzy, DMRAC atau

pengendali lain yang digunakan oleh penganalisa lain terdahulu. Keputusan daripada

projek menunjukkan bahawa PID boleh membawa tingkat kesalahan kecil ketika

nilai yang sesuai Kp, Ki, dan Kd diterapkan. Rangka projek ini adalah cukup umum

dan mempunyai keputusan yang mungkin berbeza sebelum pelaksanaan PID pada

masa yang akan datang.

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TABLE OF CONTENTS

CHAPTER TITLE PAGE DECLARATION i

DEDICATION iii

ACKNOWEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLES OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF SYMBOLS xiii

LIST OF ABBREVIATION xiv

LIST OF APPENDICES xv

1 INTRODUCTION

1.1 Research Overview 1

1.2 PID controller 3

1.2.1 PID Characteristics

1.3 Programmable Logic Control (PLC) 4

1.3.1 CX Programmer

1.4 Introduction to Coupled-Tank Control 5

Apparatus CT-100.

1.4.1 Fundamental Control Principle of Coupled-Tank System

1.4.2 Important parameters of the coupled-tank system

1.5 Problem Statement 9

1.6 Objective of the Project 11

1.7 Project Scope 11

1.8 Summary 12

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2 LITERATURE REVIEW

2.1 Background 14

2.2 Genetic Algorithm (GA) tuning of a neuro-fuzzy controller on a coupled- tank system. 14

2.3 Current research studies on the application of self-tuning controller on coupled-tank system. 15

2.4 Current research studies on the application of

PID controller on coupled-tank system. 16

2.5 Summary 17

3 RESEARCH METHODOLOGY

3.1 Introduction 18

3.2 Understanding the coupled-tank system. 19 3.3 PLC configuration. 20

3.3.1 Power consumption consideration

3.3.2 Circuit connection & Layout design

3.3.3 RS232 cable (Integration cable) and

setting part for PLC integration.

3.3.4 CX-Programmer software setup :

Analog Input and Analog Output Setting

3.3.5 Analog Input and Analog output Setting

3.3.5.1 Analog Output Card

3.3.5.2 Analog Input Card

3.4 Identifying dynamics of nonlinear plant 38

3.5 Controller Design 39

3.5.1 Simulation for controller performance

ix

3.5.2 Step for tuning PID controller using

MATLAB®

3.6 Summary 43

4 RESULTS AND ANALYSIS

4.1 Overview 44

4.2 Modeling of Couple Tank Parameter 44

4.2.1 Second Order Single-Input Single Output (SISO) Plant System

4.2.2 Calibration data result for couple tank

4.2.3 Couple tank parameter Identification

4.3 PID controller Design 51

4.4 (CX-Programmaer) Ladder Diagram for 52

PID controller design.

4.5 Discussions on result obtained 57

5 CONCLUSION

5.1 Conclusion 61

5.2 Future Recommendation 62

5.3 Costing & Commercialization 63

REFERENCES 64

APPENDIX A 65

APPENDIX B 76

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LIST OF TABLES

TABLE NO. TITLE PAGE

Table 1.1 Data collected from calibration process on couple tank 6

Table 1.2 Steady-state condition for the coupled-tank system 9

Table 1.3 Parameters of Coupled-Tank system. 9

Table 3.1 PLC components part 21

Table 3.2 Datasheet for power and current consumption of 23

CJ1M-CPU12 (CJI series)

Table 3.3 Ziegler-Nichols (method 1) Tuning Rule Table 41

Table 3.4 Ziegler-Nichols (method 2) Tuning Rule Table and 42

PID General Equations

Table 4.1 Data collected from calibration process on couple tank 45

Table 4.2 Parameter used for CX-Programmer PID controller design 52

Table 4.3 Result obtained without any controller 57

Table 4.4 Result obtained with applying P controller 58

Table 4.5 Error percentage comparison of the system 58

xi

LIST OF FIGURES

FIGURE NO. TITLE PAGE

Figure 1.1 Project overview (in term of diagram) 2

Figure 1.2 Proportional-Integral-Derivative (PID) Control Model 2

Figure 1.3 Coupled-Tank Control Apparatus CT-100 5

Figure 1.4 Schematic diagram of CTS-100 8

Figure 3.1 Overall Flow of Research methodology 18

Figure 3.2 Block Diagram for the system 19

Figure 3.3 Couple tank (system) used for the project 19

Figure 3.4 PLC hardware connection 24

Figure 3.5 PLC overall hardware connection with power supply 25

Figure 3.6 DC power supply used for SP input value 25

Figure 3.7 Power Circuit basic connections 26

Figure 3.8 Digital Input / Output Circuit ports/terminals. 27 Figure 3.9 Analog Input / output Circuit ports 28

Figure 3.10 Start the new file in CX Programmer 30

Figure 3.11 Basic construction of CJ1M PLC 30

Figure 3.12 The IO Table and Unit Setup 31

Figure 3.13 Select Slot Address Type 32

Figure 3.14 Output Table Edit Parameter 32

Figure 3.15 Input Table Edit Parameter 33

Figure 3.16 Analog output card 34

Figure 3.17 Analog input card 34

Figure 3.18 Analog Output Card 34

Figure 3.19 Operation mode switch and unit number switch 35

Figure 3.20 DM and CIO output card setting 36

Figure 3.21 Analog Input Card 37

Figure 3.22 DM and CIO analog input card 38

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Figure 3.23 General equation for PID controller 39

Figure 3.24 Block Diagram for Simulation in MATLAB Simulink 40

Figure 3.25 Detail Diagram for PID Controller 40

Figure 3.26 S-shaped curve respon due to step input 41

Figure 3.27 Curve reponse for Ultimate Sensitivity Method 41

Figure 4.1 The system transfer function response 50

(open loop system)

Figure 4.2 The system transfer function response 50

(root locus plotting method).

Figur 4.3 Model of the System (source MATLAB® ) 51

Figure 4.4 PID model for tuning controller 51

Figure 4.5 Ladder Diagram for PID controller 53

Figure 4.6 Graph of SP and CV performance without controller 59

Figure 4.7 Graph of SP and CV performance without controller 59

Figure 5.1 Control system with disturbance 62

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LIST OF SYMBOL

Kp - Proportional gain

Ki - Integral gain

Kd - Derivative

Kcr - The first value of Kp when the output exhibits sustained

oscillation

Pcr - A time for one cycle at the graph when Kp = Kcr

A - Ampere

V - Voltage

Ti - Integral Time

Td - Derivative Time

Ts - Sampling Time

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LIST OF ABBREVIATION

PID - Proportional Integral Derivative

PLC - Programmable Logic Controller

AI - Analog Input

AO - Analog Output

I/O - Input/Output

PV - Process Variable

SP - Set Point

CV - Controlled Variable

E - Error

xv

LIST OF APPENDICES

APPENDIX TITLE PAGE

1 CJ1M - AI CARD MANUAL SETTING 65

2 CJ1M - AO CARD MANUAL SETTING 76

1

CHAPTER 1

INTRODUCTION

1.1 Research Overview

Nowadays, the process industries such as petro-chemical industries, paper

making and water treatment industries require liquids to be pumped, stored in tanks, and

then pumped to another tank. The control of liquid in tanks and flow between tanks is a

basic problem in the process industries. The above mentioned industries are the vital

industries where liquid level and flow control are essential. Many times the liquids will

be processed by chemical or mixing treatment in the tanks, but always the level fluid in

the tanks must be controlled, and the flow between tanks must be regulated. Level and

flow control in tanks are the heart of all chemical engineering systems.

2

Figure 1.1 : Project overview (in term of diagram)

The aim of this project is to control the liquid level in tank 2 of the Coupled Tank

Liquid Level System based on a smooth trajectory tracking using the PID controller.

This project will implement Proportional-Integral-Derivative (PID) controller algorithm

(for controlling liquid level in couple tank system) perform by PLC. The controller

algorithm that has been chosen is Proportional-Integral-Derivative (PID) controller

while the plant or system used is the coupled tank system.

An algorithm will be programmed in PLC via CX-programer software where it

will generate a smooth trajectory signal send to the couple tank after execution process.

The system will also shows the relation between PLC, PC (software development,

interface) and couple tank liquid system itself in term of controlling the liquid level. PID

control mode is shown in figure 1.2 below.

Figure 1.2: Proportional-Integral-Derivative (PID) Control Model

-

Proportional-

Integral-Derivative (PID)

CONTROLLER

Coupled Tank System

PLANT

Sensor

FEEDBACK

Smooth trajectory tracking (output)

+

(set point/value)

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1.2 PID controller

Proportional-Integral-Derivative (PID) controllers are still widely used in

industrial systems, despite the significant developments of recent years in control theory

and technology. This is because they perform well for a wide class of processes. Also,

they give robust performance for a wide range of operating conditions. Furthermore,

they are easy to implement using analogue or digital hardware and familiar to engineers.

The proposed controller has three parameters to be adjusted. This can often be

done easiIy by trial and error or by using one of many tuning rules. In the conventional

PID control algorithm, the proportional, integral and derivative parts are placed in the

forward loop, thus acting on the error between the set point and closed loop response.

This PID controller implementation apart from the derivative kick, which occurs if a

step change takes place in the set point, is suitable for control of stable processes with

small time delays. However, it is well known that for processes with resonances,

integrators and unstable transfer functions, difficulties are encountered.

1.2.1 PID characteristics

Proportional action is the simplest form of continous control, producing a ontrol

output that is directly proportional (by an amplifying factor K) to the error input, for

example K=5 (five times greater).

Output = (K) X (error signal)

However, proportional action is rarely sufficient in itself because, as the system

output approaches the desired set point (SP) the error reduces proportionally, and so

reduces the control output. This results in a steady-state error or gap between the set

point and the controlled value (CV) at the output.This steady-state error can be reduced

by increasing controller gain, but this turn can lead to the system instability and

oscillation.

To overcome these problems it is common to use proportional action

combination with derivative and integral action.

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Derivative action provides an output signal proportional to the rate of change of

the error. Thus, if the rapidly increasing error occurs, then a large correcting output will

be produced. As the rate of error change slows, so the derivative output decreases. This

improves the system response to dynamic errors but does not improve steady-state error.

Integral action generates an output signal proportional to the mathematical

integral of the error, meaning the summed history of the error. This is used to overcome

steady-state error, since the integral term provides a matching error output value ; i.e. the

output of the integrator will varys as long as the error input is nonzero. When the

measured error reaches zero (steady-state error now occuring- achieved by proportional

action alone) then the integral output will equal the steady-state error, offsetting it and

driving the system into alignment.

1.3 Programmable Logic Control (PLC)

As already known, a programmable logic controller (PLC), or programmable

controller is a digital computer used for automation in industrial processes, such as

control of machinery on factory assembly lines. Unlike general-purpose computers, the

PLC was designed for multiple inputs and output arrangements, extended temperature

ranges, immunity to electrical noise, and resistance to vibration and impact. Programs to

control machine operation are typically stored in battery-backed or non-volatile memory.

A PLC is an example of a real time system since output results must be produced in

response to input conditions within a bounded time, otherwise unintended operation will

result. In order to function, PLC has to synchronize with CX-Programmer software that

allowing users to control PLC from computers. For this project, OMRON CJ1M model

of PLC will be used due to the wide range of function and applications.

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1.3.1 CX Programmer

The PLC packaged software, CX-Programmer is the programming software for

all Omron's PLC series, is fully integrated into the CX-One software suite. CX-

Programmer includes a wide variety of features to speed up the development of the PLC

program. New parameter-setting dialogues reduce setup time, and with standard function

blocks in IEC 61131-3 structured text or conventional ladder language, CX-Programmer

makes development of PLC programs a simple drag & drop configuration.

CX-Programmer now includes support for Sequential function charts (SFC)

1. Enables the flow of the program to be understood at a glance

2. Helps to achieve a structured program

3. Easy monitoring and debugging

4. Requires v4 CPU[12]

1.4 Introduction to Coupled-Tank Control Apparatus CT-100

Figure 1.3: Coupled-Tank Control Apparatus CT-100

For this project, we used the CT-100 model of coupled tank system (Figure 1.3).

The equipment consists of two small tower-type tanks mounted above a reservoir which

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functions as storage for the water as in Figure 1.4. Water is pumped into the top of each

tank by two independent pumps. The head of water in each tank is clearly visible on the

attached scale at the front of the tanks. Each tank is fitted with an outlet, at the side near

the base. The amount of water which returns to the reservoir is approximately

proportional to the head of water in the tank since the return tube is made of flexible

tubing which aids in varying the hydraulic resistance (by the use of a screw-type clamp).

The level of water in each tank is monitored by a capacitive-type probe or

transmitter. Signal conditioning circuits (at the rear of the unit) convert the measured

capacitance (a function of water level) to electrical signals in the range of 0 to +5 volt

DC that will be used for data signal in the project. The zero level has been calibrated to

represent the rest point of the water level, that is, when the tank is nearly empty

(approximately 20mm on the scale), while the full state (+ 5 volts) is calibrated at the

level of the opening to the rear overflow stand pipes with scale showing 300 mm

approximately. The calibrated value for the couple tank parameters are shows in table

1.1 below:

Table 1.1 : Data collected from calibration process on couple tank

An internal baffle controls leakage between the two tanks to simulate interacting

tank arrangements. The baffle is raised by a small amount by turning the wing-nut on the

WATER LEVEL (mm)

VOLTAGE (Volt)

(measured) (calculated)

300 5.20 5.00

250 4.40 4.17

200 3.60 3.33

150 2.70 2.50

100 1.70 1.67

50 0.90 0.83

0 0.00 0.00

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top of the tank assembly in order to provide a useful range of inter-tank resistance. A

spring returns the baffle to the closed position when the wing-nut is released.

The two pumps at the rear of the unit are controlled by PWM (pulse-width

modulation) circuits using power MOSFET devices. The input signal to each pump

circuit may be a PWM waveform generated by a microcontroller or other external

devices or an external DC voltage in the range 0 to +5 volts.

1.4.1 Fundamental Control Principle of Coupled-Tank System

Brief information on the hardware of the system had been discussed previously.

Now, a focus on the control principle of Coupled-Tank is brought forward. The basic

control principle of the coupled-tank system is to maintain the level of liquid in the tank

at a desired set point value when there is inflow of water into tank and outflow of water

out of the tank.

The terms that are normally used in process control industries will be used to

describe the variable involve in this coupled-tank system. Process variable or controlled

variable for this system; that is the variable which quantifies performance; is actually the

water level in the coupled-tank control system. To maintain and control the water level

at a specified desired value, the inlet flow rate is adjusted. The adjustment is made or

actuated by pump voltage. The input flow rate is known as manipulated variable, i.e. the

variable that is used to maintain the process variable at its set point.

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Figure 1.4: Schematic diagram of CTS-100

Figure 1.4 shows the schematic diagram of the coupled-tank system showing the

important characteristic of the system. The level will be maintained as long the inflow

rate, i.e. the pump flow rate and the outflow rate remained unchanged. However, if any

disturbances occur which result in the change in either the inflow rate or the outflow

rate, or the changes that may be necessary for the process, then the liquid level in the

tank would change and settle at different steady-state level.

If the outflow rate is greater than the inflow rate, the liquid level will settle at a

lower level than before, assuming that a steady state condition had already been

achieved before the tank is empty. Similarly, if the inflow rate is higher than the liquid

level will settle at a higher level assuming that a steady state conditions is achieved

before the tank overflows.

The control objective is that the input flow rate has to be adjusted in order to

maintain the level at the previous condition. In the case where the outflow rate is greater

than the inflow rate, the inflow rate has to be adjusted so that the liquid level in the tank

is increased and settled. Table 1.2 below summarizes the condition for the system to be

in a steady-state manner.

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Table 1.2: Steady-state condition for the coupled-tank system

1.4.2 Important parameters of the coupled-tank system Table 1.3 below shows the default value of the coupled-tank system’s parameters.

Table 1.3: Parameters of Coupled-Tank system.

Name Expression Value

Cross Sectional Area of the coupled tank reservoir

A1&A2 32 cm2

Proportionality α constant that depends on discharge coefficient, orifice cross sectional area and gravitational constant

αi

subscript i denotes which tank it refers

α1

α2

α3

14.30 cm3/2 / sec

14.30 cm3/2 / sec

20.00 cm3 /2 / sec

Sensor gain Ksensor 0.157 V/cm (0.179 V/cm for 2nd tank’s sensor)

Pump gain Kpump 13.571 cm3 / s / volt

Maximum allowable volumetric flowrate pumped by motor

Qimax 300 cm3 / s

Pump motor(valve) time constant

TC 1 sec (can be adjusted)

System Type Condition Alternative Condition

First Order

Tank 1 Water into the tank via the respective inlet equals to water out of tank via the respective outlet

Inflow rate at the inlet equals to outflow rate at the outlet

Tank 2

Second Order

Tank 1 Water into the tank via the respective inlet equals to water out of tank via the respective outlet and the baffle gap.

Inflow rate at the inlet equals to the outflow rate at the outlet plus the outflow rate at the baffle gap.

Tank 2 Water into the tank via the respective inlet and the baffle gap equals to water out of tank via the respective outlet.

Inflow rate at the inlet plus the inflow rate at the baffle gap equals to the outflow rate at the outlet.