HW2_08S - University of California at Berkeley Department...

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University of California at Berkeley Department of Mechanical Engineering ME132 Dynamic Systems and Feedback Spring 2008 Homework Set #2 Assigned: February 5 (Tu) Due: February 19 (Tu) [1] 2.1.1 [2] Mathematical representations of the controlled physical process are necessary for controller design and analysis. The accuracy of the mathematical representation (“model”) can have a significant impact on the performance of the controller; for example, if a motor moved to the right in response to a positive voltage, but the model predicted that it move to the left, the controller design based on the model would perform very poorly. This problem will provide an example of a process-model mismatch. Assume that the actual plant is governed by the following nonlinear differential equation: ) ( )) ( sin( ) ( ) ( ) ( 2 t u t x t x t x dt t dx + - + - = (1) It is known that the process will operate near the point 0 = eq x . Around this neighborhood, the
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This note was uploaded on 08/01/2008 for the course ME 132 taught by Professor Tomizuka during the Spring '08 term at Berkeley.

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HW2_08S - University of California at Berkeley Department...

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