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NAMIBIA UNIVERSITY OF SCIENCE AND TECHNOLOGY

Department of Mechanical & Marine Engineering

Systems Modelling (SYM710S)

Project Proposal

Magnetic Levitation

Due: 16 April 2018

Prepared By:

Surname Name Student No: CHAKWESHA RODNEY TAKUDZWA 216098882 Mwatelulo Thomas 215057252 KALIHONDA -1123950-1333500ED-MARTIN 215059735 NAKANYALA JAMES SHALLOW 214015084 SHAANIKA MUPENIWO SELMA 216055997 MINGINGA JOSEPH MUKWALA 214020312 Prepared For:

Mr. T, Kaputu

30480031877031877030480030480097402657454265304800Table of Contents

Contents

Table of Contents …………………………………………………………………………………………………………………………21.Introduction ………………………………………………………………………………………………………………………….32.Literature reviews …………………………………………………………………………………………………………………33.Objectives ……………………………………………………………………………………………………………………………44.Motivation ……………………………………………………………………………………………………………………………45.Work plan…………………………………………………………………………………………………………………………….56.Current Progress ………………………………………………………………………………………………………………..66.1.The Block Model ……………………………………………………………………………………………………….66.2.The Mathematical Model …………………………………………………………………………………………….67.List of components ………………………………………………………………………………………………………………..68.Budget…………………………………………………………………………………………………………………………………79.Bibliography ………………………………………………………………………………………………………………………..8304800318770318770304800304800974026574542653048001. Introduction

In 1831 and 1832 Michael Faraday and Heinrich Lenz independently discovered electromagnetic induction as we know it today. Faraday created the Faraday’s law which states that if there is a change in the magnetic field of a coil of wire, there is a change is a change in the voltage and vice-versa. Lenz theory states that the direction of the magnetic field is always perpendicular to the direction of the current in the coil. These two theories are the basis upon which magnetic levitation is formed on. Faraday’s law allows for the achievement of ideal magnetic fields by varying the current. Lenz’ theory on the other hand makes it possible to predict the direction of the force and make it easy to set up for maximum force. Magnetic levitation/suspension is a method of suspending ferrous objects in the air with support of nothing but an electromagnet. The electromagnet is supplied with a voltage which induces a current in it. The levitation is made possible by the electromagnetic force from the magnet that acts opposite the gravitational pull on the object and lifts it. This system on its own is not stable and so a controller is needed to linearize and stabilise the system. Magnetic levitation has a lot of applications, the most recognisable being the Maglev trains magnetic bearings. This is a form of transport where a vehicle is moved without contacting the track. Here magnets are used to levitate and propel the vehicle.

2. Literature reviews

Review 1

Modeling and control for a magnetic levitation system based on SIMLAB platform in real time by Mundher H.A, Yaseen and Haider J. Abd.

The journal is a report on the design and implementation of maglev system using two methods of control namely, the PID and LQR controller. The authors lay out clear specifications and parameters of their levitation system from the beginning of the experiment. This made it easier and to understand their work. They have also taken care to not skip any step as is evident from the free body diagrams and mathematical models. This journal became the first choice because they use our preferred method of controller (PID controller). The block diagram is clear and they also go on to simulate the system on software that is accessible and user friendly as it gives real time feedback on the behavior of the system. The presentation of the results is also chronological and discussed fully to enhance understanding.

Review 2

Control of Magnetic Levitation System Using PD and PID controller by Pawan Kumar and Shashi Minz.

The journal focuses on two types of controllers that are applicable to maglev systems. The free body diagram in the document provides a simplistic overview of the ball and magnet. We chose

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this journal because it has parameters like the first one and yet it has a different implantation. The authors employed two designs of PID controllers. They use the PID controller which combines all controls into one controller and the DOF PID controller which uses two controllers. These authors used MATLAB to simulate their system and seeing that we are accustomed to MATLAB, it makes it easier to follow their steps.

Review 3

Mechatronics Magnetic Levitation System Dynamic System Investigation by Kevin Craig.

This author analysis the dynamics of the maglev system as a function of position and current. The document focuses on the design, modelling and control of a maglev system using a microcontroller for digital control. The method of control looks far simpler and relatively easier to implement and modify compared to the others. The author provides full specifications to his system and lays out all the steps from the mathematical model to the software. The digital components include, an electromagnet actuator, a current amplifier and a ball position sensor and a voltage sensor just to name a few.

Review 4

Modeling and Simulation of Magnetic Levitation System by Valer Doga and Lia Doga.

This journal has the clearest MATLAB simulation of the system.

3. Objectives

To design a magnetic levitation system.

To come up with a controller to levitate the object in a controlled way.

To simulate a working system in software.

To build an operational system.

4. Motivation

We as a group have been introduced to the concept of electromagnetism in earlier courses. We have done calculations on them and their small-scale applications but we never quite saw the broad applications of magnetic levitation and the endless possible applications.

30480031877031877030480030480097402657454265304800Why Magnetic Levitation?

There is a need for quiet machinery in this changing world that the usual solutions do not take care of. Researchers have often focused on the electrical part of electromagnets in motors, generators, loudspeakers etc. Lifting magnets and Maglev trains are about the only mechanical applications of electromagnets we know. If we could successfully levitate an object then it will pave the way for more applications. Maglev systems are make no noise and have far less friction since there is no contact with other surfaces. Little friction means less heat losses and more efficient mechanisms and that could be exploited for use in mechanical applications. The concept is appealing to us due to its diverse applications which we can consider after gaining sufficient knowledge from this project.

5. Work plan

Project Outline: Magnetic Levitation

Planned Duration

PERCENTAGE PERIODS ACTIVITY COMPLETE MARCH APRIL MAY JUNE 12 to 16 19 to 23 26 to 30 2 to 6 9 to 13 16 to 20 23 to 27 30 to 4 7 to 11 14 to 18 21 to 25 28 to 1 4 to 8 Project Selection 100% Research 70% Select Control Method 60% Break Model The System 70% 2045970-7448552045970-4984752045970-2520952045970-5715

First Draft ; Presentation 50% Code Model In Software 0% Simulate The Model 0% Final Report 0% Final Presentation 0% Figure 1. Gantt Chart

Figure 1 shows the Gantt chart. It is an outline of all the activities that we as a group will complete from the selection to the final presentation of the project.

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6. Current Progress 6.1.The Block Model v X0 PWM i Ref PID COIL Electromagn Hall-effect X DRIVER et Sensor Controller Linearization Amplification Linearized signal Figure 2. Block Model 6.2. The Mathematical Model

Mechanical Model

The magnetic force is given by Fm = C (tx)2 where i is the current and x is the distance of the levitated object from the reference position and C is the magnetic force constant given by:

C = Loxo 2where L0 is the inductance of the coil and x0 is the reference position of the levitated object.

Therefore: ??? = ?? ? C (ix) 2

Electrical Model

For a coil with internal resistance Ri and an inductance of L and connected to a resistor of RL ohms,

The voltage applied to the coil is given by the following equation: ? = (?? + ??) + ? didt Inductance changes with the position of the ball and is given by: L= Lo + 2Cx7. List of components

Arduino

Electromagnet

Resistors

Hall Effect Sensor

Voltage Regulator

Coil Driver/MOSFET

Potentiometer

Diode

Capacitor

30480031877031877030480030480097402657454265304800Op Amp

8. Budget

These are the prices as of 13 April 2017. Prices are subject to change and the total excludes additional costs such as the base of the electromagnet and transport costs.

Component Units Price/unit N$ Electromagnet 1 42.00 Resistors 1 7.00 Hall Effect Sensor 1 19.00 Voltage Regulator 1 8.00 Coil Driver/MOSFET 1 34.00 Potentiometer 1 20.00 Diode 1 7.00 Capacitor 1 7.00 Op Amp 1 25.00 Total 169.00 304800318770318770304800304800974026574542653048009. Bibliography

Mundher, H.A., ; Haider J. (2017). Modelling and control for a magnetic levitation system based on

SIMLABplatforminrealtime.RetrievedApril13,2018,from

https://www.sciencedirect.com/science/article/pii/S2211379717320065?via%3DihubKumar, P., ; Minz, S. (2016). Control of Magnetic Levitation System Using PD and PID controller. Retrieved April 13, 2018, from http://ijsae.in/ijsaeems/index.php/ijsae/article/view/1313Kraig, K. (2016). Magnetic Levitation System, Dynamic System Investigation. Retrieved April 13, 2018, from https://www.scribd.com/document/348133664/Magnetic-Levitation-System-pdfMaggiore, M., ; Becerril, R. (2006). Modelling and control design for a magnetic levitation system. Retrieved April 13, 2018, from

https://www.researchgate.net/publication/265821696_MODELLING_AND_SIMULATION_OF _A_MAGNETIC_LEVITATION_SYSTEM