HW12 - K and the state feedback gain L so that the observer...

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ME 132 Homework # 12 Issued: Monday, November 23, 2009 Due: Monday, November 30, 2009 1 Observers Consider the plant y = b 1 s 2 B u + n Here n represents measurement noise. (a) Design an observer to estimate the state of the plant using measurements of the output y and knowledge of the input u . Place the observer poles at - 2 , - 2. (b) Simulate the plant and observer for 0 t 30 seconds. Plot the state x and the estimates state ˆ x versus t . For your simulation, use the initial conditions y (0) = 3 , ˙ y (0) = - 2, and the input u ( t ) = 2 sin( t ) + cos(2 t ) Also, use the Band-Limited White Noise block for the sensor noise n , with noise power 0 . 2. (c) Repeat parts (a) and (b) above with the observer poles being placed at - 5 , - 5. (d) Repeat parts (a) and (b) above with the observer poles being placed at - 15 , - 15. 2 Output feedback Consider again the plant y = b 1 s 2 B u + n Here n represents measurement noise. (a) Find the observer gain
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Unformatted text preview: K and the state feedback gain L so that the observer poles are at-10 ,-10, and the controller poles are at-1 j 2. (b) Draw a block diagram of the closed-loop system including the reference command r . (c) Express the controller in state-space form. (d) Find the controller transfer function. (e) Simulate the closed-loop system for 0 t 30 seconds. Plot the output y and the command r versus t . For your simulation, use the initial conditions y (0) = 3 , y (0) =-2, and the command r ( t ) = t < 5 6 5 t < 15-2 15 t < 30 Also, use the Band-Limited White Noise block for the sensor noise n , with noise power 0 . 5. (f) Does it make sense to use integral control in this example? 1...
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This note was uploaded on 01/25/2010 for the course ME 132 taught by Professor Tomizuka during the Fall '08 term at University of California, Berkeley.

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