الفهرس 
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Abstract
This thesis introduces a brief study about control systems on Active Magnetic Bearing (AMB) systems. The advantage of using AMB is reducing the maintenance costs, lubrication and reducing the bearing losses. Recently using the AMBs had gathered a great attention especially for applications that require high speed rotation or applications that requires low bearing friction losses. AMBs gives the ability of controlling the bearings damping by controlling the electromagnetic current. Although AMBs requires a cost for its running operation, it has been preferred in many applications rather than shutting down the overall system for maintenance. Despite the AMBs benefits, it experiences some stability problems which are discussed in this thesis. AMB systems are inherently unstable and nonlinear systems. Moreover, usually under high speed rotations the system dynamic effects increase and the system is affected by gyroscopic effects. Therefore, using proper controller is crucial to ensure system stability. This thesis is divided into five chapters which are described as follow: Chapter One- Introduction: Includes a brief definition of AMB systems and the classifications of the magnetically levitation systems with its two main types which are the Passive Magnetic Bearing and Active Magnetic Bearing. The chapter introduces the main features and the advantages of using AMBs in industrial applications such as turbo machineries and high speed compressors. The thesis objective and outlines are introduced in this chapter as well. Chapter Two- Literature Review: This chapter includes a survey on the usage of AMBs in the industry and its different applications. It introduces a survey on the different control systems which are carried out on AMB systems. The usage of conventional PID controllers and other control strategies used in the literature. A survey on other types on controllers applied on AMBs in the literature such as Kalman filters, Fuzzy logic controllers and neural networks. The chapter also introduces a survey on the Fractional order PID (FOPID) controllers and Fractional Calculus systems in previous work. In addition to that a survey is carried out on the usage of optimization techniques especially the Particle Swarm Optimization (PSO) which was used specifically in the thesis. Chapter Three- Construction of Magnetic Bearings and the principle of magnetic suspension and system dynamics: This chapter introduces the main types of Magnetic Bearings, the construction of single axis AMB system and discusses its non-linearity and instability. The principles of electromagnetic suspension and the mathematical proof of the levitation force is carried out. The chapter illustrates the basic construction of 4DOF AMB systems and the differential mode of operation and mathematical modeling of the system. The work represents the state space representation of the MIMO system considering the effect of the rotational speed and all external forces. Chapter Four- Controller design strategies AMB systems using PID and FOPID controllers and simulation results: This chapter introduces the two controller strategies which are carried out in this thesis on 4DOF AMB system. An optimal control strategy using PID and FOPID controllers are carried out using optimization technique which is Particle Swarm optimization. The strategies are explained by state equations and closed loop block diagrams. A comparative study is implemented on a case study and monitoring the effect of high rotational speeds on system response and stability. The detailed mathematical approaches are used for FOPID controller using fractional calculus methods such as Mittag Leffler methods. Simulations are implemented using MATLAB program. Results are illustrated for responses under different speeds. Chapter Five: Conclusion: This chapter gathered the summary of the work and gives an overall conclusion illuminating the benefits of using FOPID system and introduces a future work view for this application.