Solutions_hw8

Solutions_hw8 - ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY...

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ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY AND DESIGN F09 Homework 8 Solutions 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 Fle given with this homework assignment at the course web page. In the Fle, 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 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. As with any engineering design problem, this control design problem begins with identify- ing the spciFcations and developing a design methodolgy. ±irst, we interpret the speciFcations and then proceed to form a method for satisfying those speciFcations. We are given a transfer function of a plant: P ( s ) = 10 s + 5 and we are required to satify the following speciFcations: 1. Type I tracking error 2. Overshoot 25% 3. ±actor of 20 improvement in plant disturbance input attenuation up to 1 rad/sec 4. Attenuation of measurement noise above 1000 rad/sec by a factor of 1000 Now, because these speciFcations were given with respect to the frequency domain, Bode design would be the most helpful here. Intpreting our speciFcations in terms of the frequency domain, we can see what needs to be accomplished by the controller in this sense.
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1. Type I tracking error Controller must have 1 integrator. 2. Overshoot 25% Phase margin of approximately 45 .
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This note was uploaded on 08/03/2010 for the course ECE PROF. VOLK taught by Professor Volkanrodoplu during the Spring '10 term at UCSB.

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Solutions_hw8 - ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY...

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