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hw8 - use as many poles and zeros as you wish The...

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ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY AND DESIGN F09 Homework 8 Due Friday, December 4, 2009 Explain all answers! Problem 1 Consider a plant modeled by P ( s ) = 10 s + 5 . Design a controller that makes the transfer function from reference to tracking error of Type 1, provides no worse that 25% over- shoot to step references, gives a factor of 20 improvement in plant input disturbance attenuation (compared to using no control at all) over the frequency range up to 1 rad/sec, and provides attenuation of measurement noise in the frequency range above 1000 rad/sec by a factor of at least 1000. Explain your design using Bode plots, phase margins, etc. You may use matlab to compute these. Test your controller using the simulink file given with this homework assignment at the course web page. In the file, enter the poles, zeros and gain of your controller into the “con- troller” block. (The template shows three poles and three zeros in the controller, but you can
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Unformatted text preview: use as many poles and zeros as you wish.) The simulation, which covers 100 seconds, turns the controller on at time t = 30, has a step up at t = 45, a step down at t = 55 and turns the controller back o± at t = 75. By plotting “ tim ” vs. “ clean_out ” in the workspace, determine the overshoot percentage for the step up and the step down. Also estimate the steady-state average output magnitude due to the input disturbances compared to the steady-state average output magnitude without control. Run at least three simulations using a di±erent “seed” in the “input disturbance generator” block. (Changing the seed changes the “random” input sequence generated by simulink.) Extra credit: See how small you can make the steady-state average magnitude of the output in the simulation when the control is active....
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