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Unformatted text preview: ME 132, Spring 2003, Quiz # 2 # 1 15 # 2 12 # 3 12 # 4 6 # 5 15 TOTAL 60 1. Three systems are described below by their ODE (input u , output y ). All are started with zero initial conditions at t = 0 , namely y (0 ) = y (0 ) = y (0 ) = 0. A unitstep input is applied at t = 0. In each case, determine: the new initial conditions at t = 0 + , namely y (0 + ) , y (0 + ) and y (0 + ); the final value of y , ie., lim t y ( t ). (a) y [3] ( t ) + 2 y [2] ( t ) + y [1] ( t ) + y ( t ) = 6 u [2] ( t ) 3 u [1] ( t ) + 2 u ( t ) (b) y [3] ( t ) + 2 y [2] ( t ) + y [1] ( t ) + 3 y ( t ) = 3 u [1] ( t ) + 2 u ( t ) (c) y [3] ( t ) + 2 y [2] ( t ) + 4 y [1] ( t ) + 5 y ( t ) = 2 u ( t ) 2. Assume G 1 , G 2 and H are transfer functions of linear systems. Compute the transfer function from R to Y in the figure below. G 1 G 2 H fl ? fl 6 R Y + + 3. A closedloop feedback system consisting of plant P and controller C is shown below....
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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 University of California, Berkeley.
 Spring '08
 Tomizuka

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