examI_s98 - EE 429 EXAM I 26 February 1998 Name ID DO NOT...

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EE 429 EXAM I 26 February 1998 Name: ID#: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO Problem Weight Score 1 25 2 25 3 25 4 25 Total 100 This test consists of four problems. Answer each problem on the exam itself; if you use additional paper, repeat the identifying information above, and staple it to the rest of your exam when you hand it in. The quality of your analysis and evaluation is as important as your answers. Your reasoning must be precise and clear; your complete English sentences should convey what you are doing. 1
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Problem 1: (25 points) A SISO LTI continuous-time system with output y ( t ) and input u ( t ) is described by the ODE ¨ y ( t ) + ˙ y ( t ) - 2 y ( t ) = ˙ u ( t ) - u ( t ) . 1. (5 points) Determine the system transfer function Y ( s ) /U ( s ) using the ordinary differential equation. Based on this transfer function, is the system bounded-input bounded-output (BIBO) stable ? 2. (5 points) Obtain an all-integrator block diagram representation that uses the smallest number of integrators and which encompasses all internal dynamics of the system. 3. (5 points) Using the block diagram obtained in part 2, find a state state representation ˙ x = Ax + Bu y = Cx. 4. (5 points) Calculate the transfer function using the A , B , and C matrices, and check your answer against the result obtained in part 1. 5. (5 points) Given y (0) = 9 and ˙ y (0) = - 18, determine the initial state vector x (0). Is your answer for x (0) unique ?
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