art_2_modern and intelligent controller for a magnetic bearing system

8/7/2019 art_2_Modern and Intelligent Controller For a Magnetic Bearing System

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MODERN AND INTELLIGENT CONTROLLER FOR

MAGNETIC BEARING SYSTEM

SHARATUL IZAH BINTI SAMSUDIN

A thesis submitted in fulfilment of therequirements for the award of the degree of

Master of Engineering (Electrical - Mechatronics & Au


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ABSTRACT

A magnetic bearing system is a device that uses electromagne

support a rotor without mechanical contact. The focus of this project will

stability and control of the MBC 50 0 system test bed cons

Moments Incorporated. The MBC 50 0 system contains a strotor, which can be levitated using eight horseshoe electromagnets, fo

of the rotor. A controller, which is able to stabilize the po

varying the electromagnet force, 4 produced by the electromagn

shaft, will be designed. For this purpose, the formulation of the m

dynamic model of magnetic bearing system is derived initially and i

by establishing the state space model of the system. Then, system

linearized at the equilibrium point using a Tdylor Series and the shaft is assum

rigid body. In addition, a state feedback controller using a pole placement t

and a fUzzy logic controller as an altetnative control strategy are de

project will be implemented using M A ~ A B 6.5.


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Sistem magnetik bering adalah satu perkakasan

elektromagnetik untuk menyokong rotor tanpa meme

Fokus utama projek ini adalah pada kestabilan dan pe

yang dibina oleh Magntic Moments Incorporated. Sistemtahan karat atau rotor, yang mana boleh diapungkan m

elektromagnet, di mana terdapat empat ladam elektrom

rotor. Satu pengawal direkabentuk untuk menstabilka

mengubah daya electromagnet,4 yang dihasilkan pada hu

model matematik dinarnik bagi sistem magnetik bering in

dan kemudian disusuli dengan model keadaan-mang b

model sistem ini dilinearkan pada titik keseimbangan

Taylor sementata aci dianggap sebagai badan tegar.

pengawal suapbklik keadaan yang menggunakan teknik

pengawal ''fbzzy logic" sebagai pengawal alternatif

dijalankan dengan menggunakan perisianMATLAB 6.5.


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CHAPTER 1

INTRODUCTION

1.1 Project O v e m e w

Magnetic bearing is a device that uses electromagnetic forces to

rotor without mechanical contact. Magnetic bearings ca n

categories which are passive and active magnetic bearing. Passive magnetic be

typically use permanent magnets in conjunction with electromapermanent magnets, the force exerted on the rotor can

repulsive. A repulsive force results in a system that is stable without a

However, the force exerted by the permanent magnets cannot be controlled a


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1 3 Scopes of Project

This project presents a study of designing a contr

system based on the following:

1. Formulation and proving the mathematical dy

bearing system.

2. Th e design of mode m controller which is able

the rotor during operation. For this task, the s

pole placement technique is applied.

3. Th e design o f intelligent controlleras to m ainta

of a m agnetic bearing system.

This project willbe focused on designing a control

bearing system.

1.4 Research M ethodology

The research work is undertaken in the following eigh


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7. Verify and analyse the controller design of a magnetic b

simulated on MATLAB-SIMULINK.

8. Evaluate the results as to compare the performa

stated.

1.5 Literature Research

The research on stabilizing and controlling a rotor of a mag

system has gained momentum over the last decade. This is due to the non

inherently unstable dynamics of the system. As the applications for active

bearing can be found widely, the importance for designing the appro

efficient controller to monitor the magnetic bearings becomes vital. The

paragraphs briefly discuss on several researches that have been done by rese

MBC 500 magnetic bearing system has been identified

classical controller and this was done by J. Shi and J. Revel

Analysis and Synthesis toolbox was applied in system ide

Packard 3562A Dynamic Signal Analyzer is used to collect the experimfiom the MBC 500 magnetic bearing system. Specifically, signal an

sine function is applied experimentally to determine the transfer function o

input single output (SISO) path through the magnetic bearing system.


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controller was implemented on an AMB system using a program

processor @SP). The LMS system model utilized the validated SIMULIN

as a basis with the addition of an imbalance forcing function and LMS feed

algorithm. Finally, the LMS controller was implemented on the

significantly improved the concentricity of the unbalanced shaft.

P. Rebecca and P. Gordon (2003) from Michigan Technological

did a research based on disturbance rejection control of an electromagnetic

spindle. Adaptive control algorithm is applied to MBC 500 magnet

system. Adaptive control is an appealing approach for the system be

controller can tune itself to account for an unknown periodic dist

cutting or grinding forces, injected into the system. An adap

Amplitude-Phase Adaptive Control Algorithm (APACA) was designed to

the lead-filter compensator. The purpose of APACA is to predict and co

for the external disturbance. This paper proved that an adaptive control

can be applied to an Active Magnetic Bearing (AMB)

disturbance applied to the rotor and resulting in minimal motion of the spin

then, the position of the rotor can be stabilized.

It was followed by the research of Y. H. John (1995).

logic approaches to improve on dual acting magnetic bearing. The idea is to a

linear controller signal in such a way that nonlinear effects are better com

relationships of attractive force to the electromagnet currents and air gap


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1.6 Layout Of Thesis

This section outlines the structure of the thesis.

Chapter 2 deals with the background of an active magnetic bea

which is the MBC 500. It includes the introduction, the

disadvantages besides the analysis and system modeling for the magnetic b

system. In addition, the mathematical modeling of the dynamic mo

magnetic bearing is presented in details.

Chapter 3 discusses the state feedback control design theory which

in the project such a s the introduction of a state feedback

controllability and the observability of the system besides the technique in desia pole placement controller.

Chapter 4 explains the introduction of fuzzy logic s

fuzrtification, knowledge base and defuzzification besides the

approach.


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CHAPTER 2

2.1 Introduction MBC 500 Magnetic Bearing System

The MBC 500 is a desktop test bed made

Incorporation and the system can be seen as shown as in Fig

horlzbntal stainless steel shaft or rotor which can be levitated

electromagnets, four at each end of the rotor [14].

There are two silver housings that hold the electromagnetic be

levitate the spindle, so, the shaft nevet even touches the bearings when it is opeidtin


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Figure 2.1 : MBC 500 Magnetic Bearing

Figure 2.2 shows the magnetic bearing. The copper-colored are th

that make up the electromagnet. Each magnet has two "spokesn

"U". There are four magnets in each bearing [14].


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. + a,r--,ivef o r c e s

I + spindle- --I -*, - O Y C

---- - _

Figure 2 3 : Attractive force exerted by electromagnet

One problem when using electromagnets is that they

attractive force. The force is stronger when the spindle is closer to the

which in turn brings the spindle more close and makes the force even stro

leads to an unstable system. As a result, the magnets must

around a spindle, so that a magnet on one side of the spindle can counteract the

exerted by a magnet on the other side of the spindle. Moreover, a control sy

required to make the spindle levitate. The force exerted by the magnet

controlled by changing the current flowing through the coils of wire.

i2f a -

g

where f = exerted force

i = current flowing through the coils of wire


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2.1.1 Advantages and Disadvantages of a Magnetic Bearin

Magnetic bearing offer significant advantages because they do not

contact with other parts during operation, which can reduce maintenance.

speeds, no friction, no lubrication, weight reduction, precise position con

active damping make them far superior to conventional contact bearings

However, there are rephrase that limit the application of the magnet

such as to balance the electromagnets forces which are exerted on th

bearing and to maintain the position of the rotor at the equilibrium pointmagnetic bearing need a controller which is able to stabilize the position of th

during operation before it works successfblly.

2.1.2 Analysis and System Modeling for Magnetic Bearing

The target system for this project to control is the Magnetic Mom

500 Magnetic Bearing System. A diagram of this system is sho

This system contains a stainless steel shaft or rotor which can

horseshoe electromagnets, four at each end of the rotor. Hall E f f i t Senso


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An analysis of the geometry of the rotor will yield the following relationship

X I = x o - (+-+in e

x , = x o + (+-/)sin e

X , = x o - (4-12)Sin e

X , = x o + ($ - 1,)sin B

Table 2-1 : System variables

Table 2 2 : System parameters

Symbol

x, and xz

X I and X2

6

FI and F2

Description

The displacement of center of mass of rotorThe displacement of rotor at left and right bearings

The displacement of rotor at Hall Effect sensor

The angle that the long axis of the rotor makes with the

The forces exerted on the rotor by left and right bearing


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In general, moments and forces are interrelated in the following way

M = ? X F

This relationship is shown pictorially in Figure 2.6(a).

is any vector pointing from the point to the line of application of the force

+

vector r is chosen to be perpendicular to the line of application of the f

shown in Figure 2.60>) then the above equation reduces to

1

Figure 2.6(a)

i

Figu

Eigure 2.6 : Force / moment relation


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and the output equations can be expressed as

y, = X I = x , - 0.1317 sin 8

y, = X , = x , + 0.1317 sin 8

Moreover, linear equation, which described the dynamic system, is used in de

a controller. The steps on linearizing the nonlinear equation

6 is assumed too small in order to linearize the equations of motion. Thus, th

motion equation of magnetic bearing system can be represented

where sin6 = Oand cos6 = 1 .

A state-space system can be described as;


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CHAPTER 3

POLE PLACEMENT CONTROLLER DESIGN APPROACH

3.1 Introduction of Designing a Control System

Control system design is a multistage process involving. Before a

can be designed, the designer must have sufficient knowledge of the system

controlled. The designer begins by collecting information about the system

available sources and then representing this information in the form of a

model. One source of information is the physics governing the system.

of these physical laws will yield differential or difference equations which d

the motion of the system in response to certain input signals. Experiment

butput data taken on the actual system is another commo


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Once a suitable system model is obtained, the controller design

Typically, the initial design will be evaluated in computer simulation

software package such as MATLAB or SIMULINK. The pe

of the controlled system are evaluated and design iterations of the contr

performed until a controller is established which meets the design requiremen

This chapter discusses state-space design method based on

placement method. The pole-placement method is somewhat similar to

locus method in that closed-loop poles are placed at desired locations. T

difference is that in root-locus design only the dominant closed-loop poles are

at the desired locations while in the pole-placement design, all closed loop p

placed at desired location [19].

3.2 State-space Repreedtation o f ~ulti-Input-Multi-O

For linear multi-input-multi-output systems of order

outputs these equations become;

~ ( t )= A x ( t ) + B u ( t ) with the initial condition x( t )


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art_2_modern and intelligent controller for a magnetic bearing system

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