State-Space Design and Construction of A Magnetic Suspension System : Current School News

# State-Space Design and Construction of A Magnetic Suspension System

on January 26, 2022

Table of Contents

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– State-Space Design and Construction of A Magnetic Suspension System –

### ABSTRACT

The state space is applied in the design of a Magnetic Suspension System, where a controller is designed with the aim of making the system stable and providing the performance specifications of settling time less than or equal to 0.5 secs, Maximum overshot less than or equal to 5 percent and Steady-State errorless or equal to 1 percent.
A reference input was introduced which help to make steady-state error equal to zero from a value of about 100%. Also, an observer is designed which estimate the state variable that can not be measured.
The designed controller had a gain of 9.6, which was used to determine the gain of the power amplifier used in the system.
The designed controller caused the overshoot and settling time to reduce from undefined values to 4.1% and 0.22 seconds respectively which conformed with the performance specifications.
The observer also made it possible to observe the convergence of the actual and estimated values of the state variables in less than 0.5 sec. Prototype of magnetic suspension system was constructed and the system was able to suspend a ball of mass of 28g at a distance of 1.2cm below the coil.

### TABLE OF CONTENT

Title page                                      i
Declaration                                   ii
Certification                                 iii
Dedication                                    iv
Acknowledgements                     v
Table of Contents                        vi
List of Figures                              ix
List of Tables                                xi
Symbols and Abbreviation        xii
Abstract                                        xiii
CHAPTER ONE: General Introduction

• Introduction 1
• Background Information             1
• Motivation 2
• Statement of Problem 3
• Aim and Objectives 4
• Significance of the Studies 4
• Thesis Outline 4

CHAPTER TWO: Literature Review And Theoretical Background

• Introduction 6
• Review of Past Works in Area 6
• Theoretical Background 8
• State 8
• State Variables 8
• State Vector 8
• State Space 9
• State Space Equation 9
• The Mathematical Relationship between Magnetic Flux Density (B)and Temperature           9
• The Magnetic Flux Density on the Axis of a Circular Coil 10
• Determination of Step Response 12
• Maximum Overshot 13
• Settling Time 13

2.2.8.3   Steady State Error (SSE)                       13
CHAPTER THREE: Methodology

• Introduction 14
• Development of Mathematical Model 18
• State –Space Model 22
• Controllability and Observability 26

3,4,1   Controllability            26
3.4.2   Observability               26

• Controller Design using Pole Placement 27
• Performance Specification and System Response 28
• The Reference Input 35
• Observer Design 37
• System Block Diagram 39
• Design of Infrared Emitter 39
• Design of Signal Detector 40
• Design of Comparator 41
• Design of Compensator 42
• Design of Output Amplifier 43
• Design of Coil driver and Electromagnet 44
• Design of DC Power supply 45
• Design of Adjustable D.C Power Supply 46
• Implementation of Designed Controller 47
• Temporary Construction of the Circuit on breadboard 48
• Permanent Construction of the Circuit on Veroboard 49
• Design of the Casing 49

CHAPTER FOUR: Performance Evaluation, Results, And Analysis

• Introduction 50
• Performance Evaluation 50
• Analysis of Designed Controller and an Observer 50
• Complete Circuit Diagram 54

CHAPTER FIVE: Summary, Conclusion, And Recommendation

• Summary 58
• Limitation 58
• Conclusion 58
• Suggestion for Further Work 59

References                         60
Appendix                            62

### INTRODUCTION

Background of Study
Chapter one gives an overview of the magnetic suspension system, motivation, and statement of the problems, aim and objectives, and significance of the study.
1.1      Background Information
Magnetic suspension is a means by -which a metallic object is suspended with no support other than magnetic fields. The electromagnetic force is used to counteract the effects of the gravitational force (Dolga and Dolga, 2007).
There are several practical applications of the magnetic suspension system and this includes; the Magnetic Levitation (MagLev) train, which is a high-speed train that runs using the electromagnetic principle of levitation.
The train floats above the guide rail and the polarity of the magnet is used to move the train. Because the MagLev train is not in contact with the track, there is no friction and thus the MagLev train can travel faster than conventional trains.
Another application is frictionless bearing, in which the use of magnetic suspension reduces wear and tear on the bearing since there is no contact with other metallic parts (Glavin, 2005).
The magnetic suspension system is an unstable non-linear system. Therefore, it is always a challenging effort to design a feedback controller to control the position of the suspended object.
In recent years, many approaches have been reported. Hurley and Wolfe (1997) described the linearization of the plant by examining perturbation around the operating point. Compensation is achieved by implementing proportional plus derivative (PD) control.

### REFERENCES

Abbas, A. (2008). “State Space design of a controller for a dynamic System ( A case study of Armature Controller Dc motor)” M.Sc Thesis, Ahmadu Bello University, Zaria. (Unpublished)
Benjamin, C.K. and Farid, G. (2003). “Automatic Control Systems” John Wiley and Sons Inc. Eight Edition. Pp 113-114
Brain, D. H.,(2008). “Essential MatLab for scientists and Engineers” Second Edition.
Brian, R.H; Ronald, L.L. and Jonathan, M.R., (2006). “A Guide to MatLab for Beginners and Experienced User.
Carnegie,  M.(2009)  “Control Tutorials for Matlab” University of Michigan. http/www.engin.umich.edu/group/ctm/state/state.html
D.C. Kulshreshtha Electronics

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