Keywords:- **Magnetic** **Levitation**, Controller, Optimization, Particle swarm optimization.
I. INTRODUCTION
In electromagnetic attraction type **magnetic** **levitation** **system**, the levitated object attains steady position when **magnetic** force and gravitational force are equal and opposite. Hence proper flow of current through the electromagnet coil is essential in suspending the object at the desired position. This is achieved by a controller. For applications like bearingless motors (Chiba 1995), maglev (Taniguchi 1992) etc where „Y‟, the distance between the coil and the suspended object has to remain constant, the nonlinear **system** can be linearized and represented by a transfer function as presented by Trumper 1997,Shiao 2001 etc. By using a proper controller, the current through the coil can be made a function of „Y‟ and the **system** can be stabilized.

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CHAPTER 1
INTRODUCTION
1.0 Background
**Magnetic** **levitation** **system** is a method to levitate object by using electromagnetic force only. The force from the **magnetic** field counteract with the gravitational force which make the object float. **Magnetic** **levitation** is not a new thing in engineering in fact Robert Goddard and Emile Bachelet in (1990’s) is the earliest people that seen the theory of **magnetic** **levitation**. They envision coming up with frictionless transportation **system** using repulsive forces generated by alternating current. But the **system** is put on hold because it uses too much power for conventional conductors.

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For **magnetic** **levitation** **system**, there are two way can be implemented to control the **system**. The ways are analogue mode control and digital mode control [3]. For analogue mode control, the **magnetic** **levitation** **system** can operate itself by using RC circuit. Therefore, it can work independently without using any computer software. On the other hand, digital mode control is based on computer software. For example, the **magnetic** **levitation** **system** can operate with Matlab and simulink software. The advantage of using digital mode control if compare with analogue mode control is digital mode control will be more users friendly and easier to analyze the performance of the **system**. Apart from that, digital mode control also can use to determine the parameters of the **system** and use it to model the **system**. Basically, Matlab and simulink are used for simulation and develop control algorithm based on the design requirement. Therefore, it will be easier to implement different control algorithm into the **system** and analyze the transient performance of the **system** with Matlab and simulink. Therefore, digital mode control will be implemented in this project rather than using the analogue mode to analyze the performance of the **magnetic** **levitation** **system**.

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Controller parameters are important components of the factors which affects the performance of controllers. It may not be possible to adjust these parameters with higher efficiency and performance using classical methods. Therefore, various optimization algorithms are used for optimizing the controller parameters.
Abstract: **Magnetic** **levitation** systems are one of the popular structures in control applications. These systems are non-linear and it is possible to observe the performance of various types of controllers on these systems. Nowadays there are application areas like maglev train technologies, vibration isolation systems etc. While designing a controller, determination of the controller coefficients is complex, and the classical methods require long time for tuning process. With the help of optimization algorithms, the parameter tuning process of the controllers can be done in short time and it is possible to take an optimum performance from the controller. In this study, a **magnetic** **levitation** **system** is modeled and linearized. PID controller is designed for position control of the linearized model. The PID controllers are widely used in the industry and have enough performance for many applications. Increasing the performance of a PID controller is possible with optimization techniques. The coefficients of the designed controller are tuned using the Genetic Algorithm and the optimum values are found. As a result, the system’s performance is developed sufficiently with short settling time and small overshoot.

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1 pnattest@gmail.com, 1 junaid.ee@suit.edu.pk, 2 sadaqat.ee@suit.edu.pk
ABSTRACT
This paper explains **Magnetic** **Levitation** **system** of a train which comprises of guidance track made with magnets. The main objective is to design a proper controller that can suspend and propelled the train on a guidance track made with magnets. To perform the desired task state space model of **Magnetic** **Levitation** **system** is derived. The response of the **system** is simulated in MATLAB. The open loop response showed that the derived model is unstable. Observer Based Controller (OBC) is designed to analyze the **system** in closed loop. The controller showed improved performance for different tracks. Different types of realization techniques (minimal realization, balanced realization, modal realization, observer canonical realization) are compared for minimum fragility in controller implementation.

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Attraction type **magnetic** **levitation** devices are nonlinear and unstable systems with fast dynamics. If a model of such a **system** can be produced, it could be used in the design process of a stabilizing controller. Internal Model Control (IMC) provides a strategy that explicitly uses an existing model of the controlled process for developing a suitable controller. In this paper, a linear model that represents the nonlinear dynamics of the **magnetic** **levitation** **system** is first derived. Then, this model is used in the design procedure of an IMC-based PID controller, which is used for achieving stable **levitation** of a ferromagnetic object at predetermined distances with the help of the **magnetic** field produced by a coil. The results are shown by means of digital simulation, based on Simulink.

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1,2 Department of Electronics Engineering
University College of Engineering, Rajasthan Technical University, Kota, Rajasthan
ABSTRACT
This paper presents the design of feedback linearization and neural network based feedback linearization (NARMA- L2) controller for a **magnetic** **levitation** **system**. The **magnetic** **levitation** **system** is one of the classical nonlinear systems. The paper provides simulation results to validate the theoretical design.

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3 STORM Lab, Mechanical Engineering Department, Vanderbilt University, Nashville, TN, USA Correspondence to: M. Simi (m.simi@sssup.it)
Received: 10 March 2011 – Revised: 6 July 2011 – Accepted: 15 December 2011 – Published: 18 January 2012 Abstract. A novel compliant **Magnetic** **Levitation** **System** (MLS) for a wired miniature surgical camera robot was designed, modeled and fabricated. The robot is composed of two main parts, head and tail, linked by a compliant beam. The tail module embeds two magnets for anchoring and manual rough translation. The head module incorporates two motorized donut-shaped magnets and a miniaturized vision **system** at the tip.

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1. INTRODUCTION
**Magnetic** **levitation** or maglev **system** is a technique to make objects can float in the air using **magnetic** fields. The force produced by the **magnetic** field counteracts the gravitational force in order to the object does not fall. The Maglev **system** has advantages such as no friction with other objects so that the efficiency of movement becomes faster and requires low energy consumption. For example, the maglev train **system** can run at a top speed of 603 kilometers per hour [1] . However, the maglev **system** has high nonlinear dynamics, where nonlinear systems are more challenging to control than linear systems.The research conducted was controlling an object that can float a stable at a certain height. Illustration of the maglev **system** shows in Fig. 1 . The **system** requires an electromagnetic coil, around iron object, a sensor (phototransistor and LED to detect the position of an object), a driver (to adjust the current and voltage needed by an electromagnetic coil), a microcontroller (as a controller). Several studies have used various methods to control object of a maglev **system**, including controlling maglev objects using sliding mode control [2] , but the maglev equation is changed from nonlinear to linear so that if implemented on the plant the controller will not be optimal. Then, control of a **magnetic** **levitation** **system** using PD (Proportional Derivative) and PID (Proportional Integral Derivative) controller [3] . The PID control **system** demonstrates better performance in steady-state error and settling time rather than PD control **system**. However, this paper did not consider disturbance in **magnetic** **levitation**. In addition, there are also other methods such as fuzzy logic controller [4] , feedback linearization

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4. RESULTS AND DISCUSSION
The results shows that the controlled electromagnetic current can stabilize the disturbance that otherwise would cause the metal sphere to fall or attach itself to the electromagnet. In case of PID controller the integral action in **magnetic** **levitation** **system** can improve the **system** performance in terms of error minimization. However because of the fact that the **system** is not self starting the integral action has to be turned on when the ball acquires the stabilized position by the PD controller.

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Abstract—In high accuracy applications such as designing autopilot **system** for aircrafts, missile guiding systems and in various fields for robotics and automation, one needs to design the control **system** with more powerful and advanced techniques so as to maintain the satisfactory performance of the overall **system**. The paper presents the comparative analysis of MIT rule based control with Differential Evolution (DE) algorithm based control by implementing them on **magnetic** **levitation** **system** in real time. It also shows the development of adjustment mechanism with necessary mathematics using gradient algorithm based MIT rule along with the mathematical modeling of **magnetic** **levitation** **system**. The simulations have been performed using MATLAB, and a comparative study among two strategies has been done based on these simulations. The performance of the developed controllers has been evaluated on **magnetic** **levitation** **system** in real time, which suggests that DE based offline tuned PID controller performs comparatively better than MIT rule based online tuned PID controller. Results also depict that MIT rule control is very sensitive to parameter variations, whereas DE based control shows robust performance.

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PID control and PID-GS-C structures are next designed to ensure zero steady-state control error and bumpless switching between PID controllers for the linearized mod- els. Real-time experimental results are presented for validation.
Keywords: gain-scheduling, **magnetic** **levitation** **system**, Proportional-Integral- Derivative control; real-time experiments.

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Copyright©2019 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License
Abstract This manuscript deals with the simulation and comparison of linear as well as non-linear results for **Magnetic** **Levitation** **System** ED-4810 for different parameters assigned to the model. At first, different results for the simulations are achieved, using Simulink R2017a as a tool. Different results achieved through simulations were than analyzed. **Magnetic** **Levitation** **System** considered in the manuscript, taken as a steel ball suspended in a voltage controlled **magnetic** field. Furthermore, state space controller is modeled in order to gain the linearity of the **system**. This study demonstrates the modeling, simulations and comparison of the model ED-4810 upon which, Routh Hurwitz Criterion is executed to accomplish the stability test of the **system**.

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IV. C ONCLUSION
Stabilization of a **magnetic** **levitation** **system** has been the focus of this paper. Although the **system** is an unstable nonlinear one, it is clear that a linear compensator can be designed to stabilize it if its operation is limited to a small range (although this greatly limits the robustness of the compensator). We develop a complete nonlinear model of the **system**, and then form an approximate linearized equivalent from it. Based on this linearized model, we consider two linear compensators—proportional-derivative and phase lead—and show that the **magnetic** **levitation** s ystem can be stabilized by an appropriate selection of the parameters of the compensators using a classical design approach aided by a computer software tool. We compute and present the closed -loop poles of each design and the corresponding step responses, and also show the **system** stability limits. This approach proves quite useful and effective, as several simulation runs can be performed quickly to expedite the design. However, for a large-range operation, a more robust controller will be required to effectively bring the **system** into a region of stability. And for this latter type of controllers, several strategies, such as sliding mode control, adaptive control, etc., have been employed and are available in the literature, while the maglev **system** continues to attract more research attention.

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The aim of this paper is to propose a robust controller to highly nonlinear **Magnetic** **Levitation** **system** using TSF model control in the discrete form. By using the PDC concept, a H 1 controller will be applied to Maglev exposed to external distur- bances. Thus, the proposed controller is TSF control **system** that the stability analysis is achieved and then LMI conditions are presented to calculate the gain of the controller. The nov- elties here is that a proposed controller will robustly stabilize the Maglev **system** for both current-controlled and voltage- controlled schemes exposed to external disturbances using straightforward algorithms. Finally, simulation results are given to prove that the proposed technique ensures the stabil- ity conditions and guarantees robustness against external dis- turbance for a complex nonlinear **system**. The paper is organized as follows. First, the related work is presented in Section 2 . Then some preliminaries and problem formulation are given in Section 3 . Section 4 shows the fuzzy controller design. In Section 5 , the simulations are given to emphasize the efficiency of the proposed method and compare it with other PDC schemes for voltage and current controlled Maglev **system**. Finally, the paper is concluded in Section 6 .

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Abstract
This paper addresses a digital controller for a real time **magnetic** **levitation** **system** using series expansion of pulse transfer function, which achieves desired closed loop response. The proposed digital controller designed, based on series expansion of pulse transfer function by solving a linear equation using the method of least squares, which improves the transient performance and step tracking capability of the com- pensated **system**. The designed algorithm used for the control input is not iterative, so the calculation is very fast. The proposed control scheme has successfully applied on maglev **system** and also validated through the simulation and hardware experi- mental results.

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Figure 13. The amplitude at 𝛤 𝑦 = 2, 𝛤 𝑢 = 10
6. CONCLUSION
The work applied in this paper was designed the dynamic **magnetic** **levitation** of nonlinear **system** that was investigated in terms of its modeling, simulation and linearization. Because of the non-linear and unstable and featur of **magnetic** **levitation** systems, in this paper, we tried to convert the nonlinear to the linearize model by analyzing with state-space and doing a simulation. Three controllers applied to the **system** to check what it is the best controller. The first and second classic control were PI controller and PID controller and these controllers were not satisfied for stability and steady state error. The third controller was MPC to predict the future response related to reference input and this controller was satisfied for stability, get zero steady state error and fast response with minimum settling time. Further, a new research uses linear quadratic form to control the **magnetic** **levitation** syatem to ensure the stability with changing the input.

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the MIMO **system**. An LQG/LTR controller is designed to reject vibration disturbance in a MIMO **system**.
To derive a more accurate model of the maglev **system**, a dynamic model of the optical table with a pneumatic passive vibration isolator is also considered. The stiffness and damping parameters of the optical table are obtained from an impulse response. The **magnetic** stiffness has been added by the linearization of the EOMs of the optical table and the platen in vertical motion. The enhanced model is validated by comparing between the simulations and the experiments. To test the performance in the vibration control, an unbalanced vibrating motor is designed for generating vibration disturbances. The dual-loop control **system** with velocity feedback makes it possible that the maglev **system** tracks positioning commands and rejects vibration disturbance simultaneously. The design procedures of the dual-loop control systems are introduced in vertical and horizontal motions. The inner-loop compensator regulating the velocity is developed for vibration rejection, and the outer-loop compensator is designed to position of the platen. The stabilizing regions of the gain values for vibration-rejecting compensators are analyzed. The capacitance probes as vertical motion sensors do not directly provide the velocity information. The velocity in vertical motion is obtained by differentiating the noisy position signals. A software low-pass filter is designed to prevent amplification of the high frequency noise of position signal by differentiation.

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also, to bound the rule adaptation it is used a small number
jpðkTÞj < ! pðkTÞ ¼ 0: ð35Þ
In this way, the output of the inverse model pðkTÞ displaces the center of the membership function fired dT sampling times before, due the change in the control signal takes dT seconds in modify the **system** behavior. For stability issues, the centers displacements are bounded with ½b min ; b max ¼ ½0; g v , some results are reported for stability in fuzzy systems, they are for Takagi–Sugeno fuzzy systems [30,31], where a fuzzy model is used to approach the real **system** with linear subsystems in the rules consequents, then by using Lyapunov’s theory, stabil- ity can be guaranteed; a similar procedure to the presented in this paper was shown by Passino and Yurkovich [3] and then compared with a Lyapunov-based model reference adaptive control, but this last method presents an important overshoot;

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With the ECP 730 **system** this typically small, but driving a train with 200 passengers and numerous amounts of cargo at 500 km/h this can no longer be ignored.
As technology has advanced, as wonderful as it is, a significant problem has arisen in the form of e-waste has arisen. According to CleanUpAustralia (2009), e-waste is one of the fastest growing contributors to Australia’s waste stream. This a problem because most (if not all) electronic equipment contains materials which are potentially dangerous to humans. Chemicals such as arsenic, lead and mercury are found in abundance in landfills across the country. In addition to this, many electronic components contain valuable resources that can be recycled and reused in the future. In regards to this project, it is imperative that when the development **system** comprising of the maglev plant and the host PC reach their useful end-of-life that they are disposed of correctly, to ensure environmentally sustainability in the long term.

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