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Unformatted text preview: ME 132 Homework # 9 Issued: October 23, 2009 Due: October 30, 2009 1 Step Responses For each of the following differential equations do the following: Find the transfer function, the poles and zeros, and draw a pole-zero diagram. Find the damping ratio , and natural frequency n for each pair (if there are any) of complex poles. Analytically determine the step response, i.e. the response with zero initial conditions and with the input being a unit-step function u ( t ) = braceleftBigg for t 1 for t > Plot (using matlab ) the step response. (a) y (3) ( t ) + ( 1 + 10 2 ) y ( t ) + ( 100 + 10 2 ) y ( t ) + 100 y ( t ) = 100 u ( t ) (b) y ( t ) + y ( t ) = u ( t ) (c) y (3) ( t ) + 10 . 6 y ( t ) + 7 y ( t ) + 10 y ( t ) = 10 u ( t ) (d) y ( t ) + 1 . 2 y ( t ) + y ( t ) = u ( t ) 2 PI control with Anti-windup Consider the position control problem for the DC motor with zero load torque. The motor model is d dt ( t ) = ( t ) d dt ( t ) = . 97 ( t ) + 1 . 9 u...
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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.
- Fall '08