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1 Objectives To analyse and control position of a Magnetic Levitation (Maglev) system. 2 Tools Required 1. MATLAB 2. MATLAB Control Systems Toolbox 3. Simulink 3 Background Figure 1: A typical attractive Maglev experimental setup. source by http://zeltom.com/products/maglevplus Magnetic Levitation (or Maglev in short) technology has been applied in various engineering applications including Maglev train systems, magnetic bearings, active suspension system in au- tomobiles and so on. The Magley technology is applied in wide applications due to its ability in generating nearly frictionless motions for ferromagnetic materials or permanent magnets. There are two types of Maglev systems, namely attractive Maglev and repulsive Maglev. Figure 1 depicts typical experimental platform for attractive magnetic levitation and dise magnet is levitated in mid-air. By varying the current through the coil of the electromagnet and thus the generated magnetic field. the vertical displacement of levitating object is adjusted stably in a range of few centimetres. Position feedback is generated using linear Hall effect sensor 4 which measures change of magnetic field due to change of vertical of position of the levitating object. You can watch the operation of the system at this link. The lynamic model of the magnetic levitation system is nonlinear system, due to the nonlinear model of the generated magnetic force by the electromagnet. The model is linearised about the desired equilibrium point at which the distance de between the levitating mass and the electro magnet is around 2 cm. The transfer function G(s) of the magnetic levitation system is given as. AD(s) 2360.0 G(s) (1) /(s) (s + 160.0)(s²-1960.0) where AD(s) and /(s) are the Laplace Transforms of the displacement of the levitating object about the equilibrium position de which is and the (negative current perturbation inputted to the elect romagnet respectively. In other words. the output of the maglev system is the actual position of the levitating object is d(t) de- Ad(t) and the input is the current i(t) =ive Di(t) flow in the coil of the electromagnet. where in is the equilibrium current. Figure depicts the block diagram of the feedback control system for position control of the object by magnetic levitation. In this coursework. we will design compensator so that its output response satisfies the given specifications. Current to Compensator Plant Displacement Coil AI(s) C(s) G(s) AD(s) Figure 2: Feedback Control of the Maglev system. 4 Procedures 1. Is the open loop system G(s) stable? Justify your answer. Simulate. with MATLAB OI Simulink. the unit step response of the plant G(s) to support your claim. 10% 2. Plot the root locus of the system with C(s) = K. when 0 < K < too using MATLAB function clocus. Find the exact location of the breakaway point of the root locus. [Hint: use the MATLAB function roots to find the roots of polynomial.] 3. Find the value of K when the closed loop system has double poles. 4. Can the system be stablised by a simple proportional controller C(s) = K? Justify your answer. Pick two values of K, say 50 and 500, and simulate the closed loop responses to see if the system is stable. 20% 5. Suppose C(s) K(s 50). Find the range of K so that the closed loop system is stable using the Routh-Hurwitz Stability Criterion. 6. Verify your result in Step (5) using root locus 7. By imposing the second order system approximation to the system, estimate the settling time (=5% of the settling value of output, peak time and rise time (10%-90% of the final value of response) of the closed loop system with 25% of overshoot 20% 8. We design compensator C(s) in position control of the Maglev system under the following criteria: Settling time less than seconds Percentage of Overshoot (P. O.) less than 16% Sketch the feasible region of dominant closed loop poles that satisfies the above design criteria in the s-plane. Select pair of dominant closed loop poles from the feasible region Determine the type of the compensator you need. phase-lead or phase-lag compensator Perform the design using the graphical method discussed in lecture. Simulate the unit step response of the compensated system using MATLAB or Simulink. Check if the sys- tem response satisfies the design criteria. You may need to refine your design if is not Remember to include your calculation and sketches in coursework submission. 9. Generate the Bode plots of the compensated system in Step (8) and find its gain margin and phase margin. [Hint: Check the MATLAB functions bode and margin). 40% 10. Produce a concise report detailing all your analysis, designs, investigations and results. Where relevant provide Simulink models and MATLAB in files that have been used to support your work. 10%

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