HW13 - 30 . 25 meters 30 < t (a) ind the control...

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ME 132 Homework # 13 Issued: December 02, 2009 Due: December 09, 2009 1 Consider the magnetically-suspended ball treated in class. The diferential equation relating the control input u to the height oF the ball y is ¨ y = g - c m u 2 y 2 with the Following constants: m 0 . 15 Kg mass oF ball c 0 . 01 Kg-m 3 /Coul 2 magnetic coupling constant Suppose the ball is initially y = 0 . 25 meters below the base oF the magnet and at rest. We want to design a controller For the height oF the ball to Follow the reFerence trajectory r = 0 . 40 meters 0 < t 10 0 . 20 meters 10 < t 20 0 . 60 meters 20 < t
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Unformatted text preview: 30 . 25 meters 30 &lt; t (a) ind the control u required to maintain the height at y = . Linearize the system about this operating point. (b) Design a gain-scheduled controller based on the operating point oF the current height oF the ball, oF the Form u = L x + Fr . Place the poles oF the observer at-8 ,-8 and the poles oF the closed-loop ball dynamics at-2 ,-2. Choose F so the steady-state gain From r to y is 1. Simulate the system and plot the response. 1...
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