ps2 - EE 428 PROBLEM SET 2 DUE: 17 SEP 2007 Reading...

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EE 428 PROBLEM SET 2 DUE: 17 SEP 2007 Reading assignment: Ch 3 sections 3.3 and 3.5. Problems Set 2 provides further insight on the representation of dynamic systems using state-space models. Problem 5: (20 points) Consider a LTI SISO system with state-space representation ˙ x = ± 01 200 - 10 ² x + ± 0 1 ² u y = ( 1 - 10 ) x. 1. (7 points) Determine the eigenvalues of the system matrix using the method described in lecture. 2. (2 points) Using your result from part 1, Is the system BIBS stable? 3. (7 points) Determine the system transfer function Y ( s ) /U ( s ) using the matrices in the state-space representa- tion. 4. (2 points) What are the poles of the system transfer function? 5. (2 points) Using your result from part 4, is the system BIBO stable? Problem 6: (25 points) Consider a LTI SISO system with the ODE representation ¨ y +3˙ y +2 y = u (1) 1. (8 points) Using Laplace transform methods, calculate the zero-input response y zi ( t ) and the zero-state response y zs ( t ) for the initial conditions y (0) = 1 , ˙ y (0) = - 1 and the input u ( t )= e - 3 t u o ( t ), where u o ( t ) is the unit-step function. 2. (4 points) Find a state-space representation using the state-variable assignment x 1 y and x 2 = y .Wh a ti s the initial state vector x (0)?
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This note was uploaded on 07/23/2008 for the course EE 428 taught by Professor Schiano during the Fall '07 term at Penn State.

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ps2 - EE 428 PROBLEM SET 2 DUE: 17 SEP 2007 Reading...

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