Study on DC Motor Control System -...

UNIVERSITI TEKNIKAL MALAYSIA MELAKA

Study on DC Motor Control System

Thesis submitted in accordance with the requirement of the Technical University

Malaysia, Melaka for the Degree of Bachelor of Engineering (Honours)

Manufacturing (Robotic & Automation)

By

Moahamad Ariff bin Mohd Arshad

Faculty of Manufacturing Engineering

April 2007

DECLARATION

I hereby, declare this thesis entitled “Study on Dc Motor Control System” is the result of

my own research except as cited in the reference.

Signature : ……………………………

Author’s Name : Mohamad Ariff bin Mohd Arshad

Date : 14 April 2007

APPROVAL

This thesis submitted to the senate of KUTKM and has been accepted as fulfillment of

the requirement for the degree of Bachelor of Manufacturing Engineering (Honours)

(Robotic and Automation). The members of the supervisory committee are as follows:

…………………………………………..

(MR SHARIMAN BIN ABDULLAH)

Main supervisor

Faculty of Manufacturing Engineering

i

ABSTRACT

This case study describes the physics of a standard dc motor. From this general

understanding, differential equations are developed to describe the motor’s dynamic

behavior. State space equations and Laplace transforms are then developed for further

analysis. Typical data for a specific motor are included within a Matlab/Simulink

program to illustrate the basic time domain behavior of the system. System modeling

methods for analysis, design and regulation purposes have conventionally employed

lumped linear and non-linear methods to provide the dynamic and steady state

information required. Adequate though this may be when the components employed are

largely concentrated, physically, as system dispersion and slenderness ratios increase, the

dynamics arising from spatial distribution assume increasing relevance. Recognition of

this and attempted accommodation, via the promotion of approximation and empiricism,

has often resulted in a lack of confidence in the computed predictions obtained.

ii

ABSTRAK

Tesis ini adalah kajian mengenai instrumentasi dan kawalan motor arus terus. Motor arus

terus digunakan bersama dengan gear, alat penghubung, dan power screw untuk

membentuk satu elektro-mekanikal sistem. Seterusnya mencari transfer function utuk

sistem tersebut. Simulasi menggunakan perisian MATlab digunakan untuk menganalisis

sistem tersebut berdasarkan transfer function yang telah diperolehi. Keputusan yang

diperolehi dikaji untuk melihat sama ada apabila motor arus terus berkuasa 12 voltan

dibekalkan, apakah jumlah yang terhasil. Sistem dianalisis dan dipertingkatkan untuk

mendapatkan hasil yang terbaik dimana jumlah voltan yang dibekalkan sama dengan

jumlah yang terhasil.

iii

ACKNOWLEDGEMENTS

Appreciations are expressed to those who have given generous contributions within the

period of this thesis development to fulfill the requirement of the Degree of Bachelor of

Engineering (Honours) Manufacturing (Robotic and Automation) program.

Here I would like to express my deepest appreciation to my supervisor, Mr.

Shariman, also acts as chief of department robotic and automation of faculty of

manufacturing engineering in Universiti Teknikal Malaysia Melaka.

His constant guidance and support during my thesis writing is invaluable to me.

His continuous direction and opinion regarding the flow of the project has a mass

contribution to achieve the objective of the project. Furthermore, the guide and help of

him on how to make this thesis a more effective reference are followed with my sincere

gratitude.

Finally, I would like to thank to all lectures, technicians and colleagues who had

involved directly or indirectly in my thesis.

Mohamad Ariff Mohd Arshad

May 2007

iv

TABLE OF CONTENTS

Abstract i

Acknowledgement iii

Table of Contents iv

List of Figure viii

List of Table xi

Sign and Symbols xii

1 INTRODUCTION 1

1.1 Introduction to the project 1

1.2 Problem Statement 2

1.3 Objectives, Aims and Scopes of the Research 3

1.3.1 Objectives 3

1.3.2 Aims 4

Scopes of the Project 4

1.4 Gantt Chart 5

2 LITERATURE REVIEW 7

2.0 Introduction 7

2.1 Dc Motor 8

2.1.1 Wound field DC motor 10

2.1.2 Theory 11

2.1.3 Speed control 12

2.2 Introduction to Control System

14

2.2.1 History of Control System

14

2.2.2 Classical control theory: the closed-loop controller 15

2.2.3 Stability 17

2.2.4 Control and Absorbability 18

v

2.2.5 Derivation of a Schematic for a DC Motor 19

2.3 Mathematical Model 23

2.3.1 Electrical Characteristics 24

2.3.2 Mechanical Characteristics 25

2.3.3 Step Response of a DC Motor 30

2.3.4 Matlab Commands 31

2.4 Performance Characteristics 36

2.4.1 Block Diagram 40

2.4.2 Closed-Loop Control 43

2.5 Gear 44

2.5.1 Spur Gear 45

2.5.2 A Gear System 46

2.5.3 The Transfer Function 46

2.6 Coupling 47

2.7 Power Screw 47

3 METHODOLOGY 51

3.1 Flowchart 52

3.2 Details 53

3.3 Detailed design 54

3.3.1 DC Motor 54

3.3.2 Coupling Specification 55

3.3.3 Lead Screw Specification 55

3.4 The Design Process 56

3.4.1 Transform Requirement into a Physical System 56

3.4.2 Draw a Functional Block Diagram 56

3.4.3 Create a Schematic 57

3.4.4 Developed a Mathematical Model (Block Diagram) 57

3.4.5 Reduce the Block Diagram 58

3.4.6 Analyze and Design 59

vi

3.5 Simulink 59

3.5.1 Simulink Basics 60

3.5.2 Opening Models 61

3.5.3 Using the Simulink Toolbar to Enter Commands 61

3.5.4 Simulink Windows 62

3.5.5 Saving a Model 63

3.5.6 Running a Simulation Programmatically 63

3.5.7 Modeling Dynamic Systems 64

3.6 System Model 67

3.7 Calculation of the Parameter 67

4 RESULTS 71

4.1 System Model Schematic Diagram 71

4.2 Calculation of the Transfer Function 72

4.3 Descriptions of the Blocks 75

4.3.1 Step 75

4.3.2 Transfer Fcn 77

4.3.3 Scope 78

4.4 Modeling Equations 80

4.4.1 Running the Model 82

4.5 Modelling Simulink With Gain 83

4.5.1 Gain 83


4.6 Modelling Simulink with Gain and Feedback 87

4.6.1 Feedback 87

4.6.2 Sum 87


4.7 Designs via Root Locus 91

4.7.1 Improving Transient Response 91

4.7.2 Improving Steady-State Error 92

vii

4.7.3 Improving Steady-State Error via Cascade Compensation 93

4.7.3.1 Ideal Integral Compensation (PI) 93

4.7.4 Improving Transient Response via cascade Compensation

95

4.7.4.1 Ideal Derivative Compensation (PD) 96

4.7.5 Improving Steady-State and Transient Response 96

4.7.5.1 PID Controller Design 97

4.8 Creating the Simulation Model 98

4.8.1 Integrator 99

4.8..2 Derivative 103


5 DISCUSSION 107

6 CONCLUSION AND RECOMMENDATION 113

7 REFERENCE 114

8 APPENDIX 116

viii

LIST OF FIGURES

2.0 A simple DC electric motor. 9

2.1 The armature continues 9

2.2 When the armature becomes horizontally aligned, the commutator

reverses the direction of current through the coil, reversing the magnetic

field. The process then repeats.

10

2.3 A simple feedback control loop 16

2.4 Current-carrying wire in a magnetic field 19

2.5 a. Current-carrying wire on a rotor

b. current-carrying wire on a rotor with commutation and coils added to

the permanent magnets to increase magnetic field strength

20

2.6 Magnetic flux density passing through a loop of wire on an armature 22

2.7 DC motor circuit diagram 23

2.8 Electrical representation of a dc motor. 24

2.9 Block diagram representation of equations 28

2.10 Block diagram of the dc motor as modeled in this study 29

2.11 Overall transfer function for the dc motor 29

2.12 Block diagram produced within Simulink 30

2.13 Step response of a dc motor for the Case 1 and Case 2 simulations 31

2.14 Dc Motor Representation 36

2.15 Rated Values of Speed, Torque And Power 39

2.16 The block diagram of a dc drive 40

2.17 Spur gear 45

2.18 A gear system 46

2.19 a. angular displacement in lossless gears

b. torque in lossless gears

46

2.20 Coupling 47

2.21 Lead Screw System 49

ix

2.22 Type Of Power Screw 50

3.1 Sketching Of the Mechanical Design Diagram 54

3.2 Simulink library 60

3.3 Model Window 62

3.4 inputs and/or output 64

3.5 Diagram Illustrates Some of the Tools Provided By The Mathworks 66

3.6 Schematic diagram 67

4.0 System Model Schematic Diagram 71

4.1 Step 75

4.2 Block Parameter of the Step 76

4.3 Transfer Fcn 77

4.4 Block Parameter of the Transfer Fcn 78

4.5 The Scope Block 79

4.6 The Scope Window 79

4.7 The Blocks Gather Into Model Window 81

4.8 Complete and connected block circuit 82

4.9 The Step Response from the Scope 83

4.10 The Gain Block 84

4.11 Block Parameter of the Gain Block 84

4.12 Simulink Block With Gain 86

4.13 The Step Response With Gain 86

4.14 The Sum Block 88

4.15 Block parameter of sum 89

4.16 Workspace model of the simulation with Gain and Feedback 90

4.17 Step response of the output. 90

4.18 Pole at A is on the root locus without compensator 94

4.19 Pole at A is not on the root locus with compensator pole added 95

4.20 Approximately on the root locus with compensator pole and zero added. 95

4.21 PID Controller 97

x

4.22 Model workspace with added block, Gain, Integrator, Derivative, and

Sum.

99

4.23 Integrator Block 99

4.24 Block Parameter: Integrator 100

102

4.25 Derivative Block 103

4.26 Complete circuit of the simulation with PID controller. 104

4.27 Steady-state response output 104

4.28 Voltage reach 12V 105

4.29 cmax decrease to cfinal 106

5.0 The Step Response from the Scope for the linear system 108

5.1 The Step Response from the Scope for the linear system with gain. 109

5.2 The Step Response from the Scope for the closed-loop system with gain. 110

5.3 The Step Response from the Scope for the closed-loop system with PID

controller

111

xi

LIST OF TABLES

4.0 Maxon Dc Motor Data 72

4.1 Coupling specification 73

4.2 Lead Screw Specification 73

xii

LIST OF ABBREVIATIONS, SYMBOLS, SPECIALIZED NOMENCLATURE

DC - Direct Current

EMF - Electric Motive Force

PWM - Pulse Width Modulation

AC - Alternating Current

SISO - Single-Input-Single-Output

MIMO - Multi-Input-Multi-Output

BIBO - Bounded-Input-Bounded-Output

PDF - Pseudo-Derivative Feedback

PID - Proportional-Integral-Derivative

SCR - Silicon Controlled Rectifier

RPM - Revolution per Minute

SM - Single loop Margin

DM - Double loop Margin

MM - Multi loop Margin

y(t) - Output Of The System

r(t) - Reference Value Through The Measurement Performed By A

Sensor

C and P - Linear And Time-Invariant For A Simple Feedback Control Loop

C(s) and P(s) - Transfer Function For A Simple Feedback Control Loop

x[n] - Impulse Response

i - Electric Current

l - Flowing In A Wire Of Length

B - Magnetic Field Of Strength

F - Force

Kt - Equivalently

Ia - Current Flow

A - Area

vb(t) - Induced Voltage

xiii

ia(t) - Wire Carrying Current

Tm(t) - Torque for DC Motor

Ra - Resistance

La. - Inductance

θm(t) - output angular displacement for DC Motor

Va - Voltage Source In Electrical Characteristic

kv - Velocity Constant Determined By The Flux Density Of The

Permanent Magnet

ωa - Rotational Velocity of The Armature

Te - Electromagnetic Torque in Mechanical Characteristic

Tw - The Torque Due To Rotational Acceleration of The Rotor

in Mechanical Characteristic

Tw’ - Torque Produced From The Velocity Of The Rotor

in Mechanical Characteristic

TL - Torque Of The Mechanical Load in Mechanical Characteristic

Ωref - Speed In Closed-Loop

Ωf - Speed Feedback Signal

CS - Critical Speed

D - Root Diameter Of Screw (Inches) for Power Screw

L - Length Between Supports (Inches) for Power Screw

F - End Support Factor (See Diagram) for Power Screw

1

CHAPTER 1

INTRODUCTION

1.1 Introduction to The Project

A permanent magnet direct current (dc) motor is a very common component within many

dynamic systems. This case study describes the physics of a standard dc motor. From this

general understanding, differential equations are developed to describe the motor’s

dynamic behavior. State space equations and Laplace transforms are then developed for

further analysis and for application to a light tracking system. Typical data for a specific

motor are included within a Matlab/Simulink program to illustrate the basic time domain

behavior of the system. System modeling methods for analysis, design and regulation

purposes have conventionally employed lumped linear and non-linear methods to provide

the dynamic and steady state information required. This approach although simple and

appealing assumes that the system components have no spatial dimensions, each element,

for example, comprising stiffness, inertia and frictional dissipation characteristics, all of

which exist at some undefined point in space. Adequate though this may be when the

components employed are largely concentrated, physically, as system dispersion and

slenderness ratios increase, the dynamics arising from spatial distribution assume

increasing relevance. Recognition of this and attempted accommodation, via the

promotion of approximation and empiricism, has often resulted in a lack of confidence in

the computed predictions obtained. Finite element (fe) methods, for example, are often

incorporated in efforts aimed at replicating the effects of spatial dispersion. However, this

approach generates large matrix models, computational errors, and erroneous modes of

response and decay rates. To overcome these difficulties combined distributed lumped

2

modeling was investigated for mechanical, power transmission system modeling, were

also researched and accurate, compact, computationally efficient realizations, for

controller design and real-time diagnostics, were derived. At this time single loading

effects and the dynamics arising from flexible beams, shafts and rotor-bearing assemblies

were addressed. Whirling speed applications studies continued in parallel with this work

using frequency response and numerical minimization methods. In this contribution

previous work will be advanced with a novel combined torsion and tension loading,

machine tool modeling method. The technique involved will be to describe significantly

distributed elements of the machine, such as the lead screw, using distributed parameter

procedures. This approach to the mathematical construction process enables greater

reality, accuracy and integrity to be achieved. Essentially, the system dynamics arising

from the combined, distributed lumped description enable all of the incident, traveling

and reflected waveform effects to be replicated in the final realization. Effectively, the

response signatures generated by the model will be shown to correspond closely with

those from the actual system. In particular, the effects of spatial dispersion and combined,

lead screw, torsion and tension loading provide a broadband realization, capable of

generating the low and high frequency behavior of the system’s, x-axis dynamics. This is

enhanced by the incorporation of lumped nonlinear effects. Details of these

characteristics were obtained, in this study, from manufacturer’s data and from measured,

experimental results. Following, the detailed derivation for the x-axis traverse, motor

drive and the multivariable lead screw model, for combined torsion and tension loading

will be presented. Thereafter, an overall, interactive representation, for the complete

distributed–lumped system configuration, will be derived. Finally, the simulated response

transients for the system, following voltage step changes on the lead screw, motor drive,

will then be computed.

1.2 Problem Statement

Certain high-speed document handling machines manufactured exhibit the undesirable

phenomenon of high frequency ringing and vibrations. This is attributed to compliance in

3

the system. The objective of this project was to study and analyze a simple test that had

all the relevant attributes of the more complicated machines. The dynamics and control of

a load driven by a DC motor was to be investigated in the context of high-speed high

precision motion control. High performance was desired without risking close-loop

stability. One particular addition of interest is a Simulink graphical model which

automatically performs the appropriate block diagram arithmetic and generates a state

space model for use in a standard Matlab simulation. This model is used here to relate the

output angular velocity of the motor to the input applied voltage. It is also used as a

subsystem in a Simulink model of the complete the simple mechanical design.

1.3 Objectives, Aims and Scopes of the Project

1.3.1 Objectives

1. To demonstrate the use of electrical blocks, in combination with Simulink

blocks, in the simulation of an electromechanical system with a control

system. The electrical part of the DC motor drive, including the DC

source, and the DC motor, is built using blocks from the Elements,

Machines, and Electronics libraries in the Matlab Software. The DC

Machine block models both electrical and mechanical dynamics. The load

torque-speed characteristic and the control system are built using Simulink

blocks.

2. Describe various methods of controlling the speed and direction of a DC

motor.

3. Learn the operation and modeling of DC motor systems.

4. Learn the driver circuitry for DC motors.

5. Understand the types and specification of DC motor.

4

1.3.2 Aims

Analyze the output voltage of DC motor that produce for the simple mechanical design

that have power screw. Be able to using the Matlab software to simulate the design and

test to see that the requirements and specification are met.

1.3.3 Scope of the Project

This project is to study on ‘Dc Motor Control System’. The project scope is to ‘Study the

Control Element in Single Axis Positioning with Consist of Motor, Gearing, Coupling,

and Power Screw’. The software that recommended in this research is Matlab 6.5.1. The

main of this research is to explore and design the mechanical element. From the

mechanical equations, transfer to the control system equations. Then, find the

specification of the element at calculate the value of the dc motor output voltage.

Construct the block diagram using Matlab software and simulate the design.

5

1.6 Gantt Chart

Table 1 Gantt Chart PSM 1.

CONTENTS W

1

W

2

W

3

W

4

W

5

W

6

W

7

W

8

W

9

W

10

W

11

W

12

W

13

W

14

W

15

W

16

Project Selection

Information research

Write a literature review

Discuss on simple robot that using dc motor

Draft the objective and select the instrument that need to

be used in the project

Study on MATlab Software

Design and solve mechanical diagram

Draft report preparation

Final draft report preparation

Presentation and report submission

SEMESTER BREAK

6

Table 2 Gantt Chart PSM 2.

CONTENTS W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 W14 W15 W16

Find the specifications

Find the transfer function

Simulation using MAtlab software

Analysis the result

Make a discussion

Gathering all information and sources

Draft report preparation

Final draft report preparation

Presentation and report submission

SEMESTER BREAK

7

CHAPTER 2

LITERITURE REVIEW

2.0 Introduction

An electric motor converts electrical energy into kinetic energy. The reverse task, that of

converting kinetic energy into electrical energy is accomplished by a generator or

dynamo. In many cases the two devices differ only in their application and minor

construction details, and some applications use a single device to fill both roles. For

example, traction motors used on locomotives often perform both tasks if the locomotive

is equipped with dynamic brakes. Most electric motors work by electromagnetism, but

motors based on other electromechanical phenomena, such as electrostatic forces and the

piezoelectric effect, also exist. The fundamental principle upon which electromagnetic

motors are based is that there is a mechanical force on any current-carrying wire

contained within a magnetic field. The force is described by the Lorentz force law and is

perpendicular to both the wire and the magnetic field. Most magnetic motors are rotary,

but linear motors also exist. In a rotary motor, the rotating part (usually on the inside) is

called the rotor, and the stationary part is called the stator. The rotor rotates because the

wires and magnetic field are arranged so that a torque is developed about the rotor's axis.

The motor contains electromagnets that are wound on a frame. Though this frame is often

called the armature, that term is often erroneously applied. Correctly, the armature is that

part of the motor across which the input voltage is supplied. Depending upon the design

of the machine, either the rotor or the stator can serve as the armature.

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