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Exam1_Fall03

# Exam1_Fall03 - MEEN 364 Exam 1 Texas A&M University...

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MEEN 364 Exam 1 1/9 Texas A&M University Department of Mechanical Engineering MEEN 364 Dynamic Systems and Controls Exam 1 – October 9, 2003 7:00 – 9:00 PM; 124 HRBB Name: Please circle your section below: Section (Lab Time): 501(M 1:50-4:40 PM) 502 (T 8:00-10:50 AM) 503 (T 2:20-5:10 PM) 504 (W 1:50-4:40 PM) 506 (R 2:20-5:10 PM) NOTE: No calculators are allowed. No open books or open notes. Problem 1: You are given a system with input u ( t ) and output y ( t ) described by the following set of state-space equations: dx 1 / dt = 3 x 2 + u dx 2 / dt = – x 1 4 x 2 u y = x 1 We are interested in solving for the response of the system (its output) for t > 0 when the state at t = 0 is given. (a) [7 points] Write an expression for the Laplace transform of the output, Y ( s ), in terms of the Laplace transform of the input, U ( s ), and the initial conditions for the states, x 10 and x 20 . (b) [6 points] If x 10 = 1, x 20 = 0, and u ( t ) = 0, solve for the output as a function of time ( y ( t ) for t > 0) using Laplace transform methods. (c) [6 points] If x 10 = 0, x 20 = 0, and u ( t ) = 2 e – 2 t , solve for the output as a function of time using Laplace transform methods.

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Exam1_Fall03 - MEEN 364 Exam 1 Texas A&M University...

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