midterm - Department of Mechanical Engineering...

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Department of Mechanical Engineering Massachusetts Institute of Technology 2.160 Identification, Estimation, and Learning Mid-Term Examination April 3, 2006 1:00 – 3:00 pm Close book. Two sheets of notes are allowed. Show how you arrived at your answer. Problem 1 (30 points) Consider a linear stable system, as shown below. Variable is input, is output, and is uncorrelated white noise with zero mean values. Answer the following questions. ) ( t u ) ( t y ) ( t e a). Obtain the one-step-ahead predictor of the output: ) 1 | ( ˆ t t y . b). Prove that the prediction error ) 1 | ( ˆ ) ( t t y t y is equivalent to the uncorrelated noise , if the parameters involved in the system are exactly known. ) ( t e Problem 2 (40 points) Consider a second order system with the following transfer function having a pair of complex conjugate poles: 22 1 () 2 2 sb s b c = Gs + ++ c >> where both parameters are positive real numbers, b . In an attempt to represent this system with a reduced-order Finite Impulse Response model, the continuous Laguerre series expansion method is used. Answer the following questions.
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.160 taught by Professor Harryasada during the Spring '06 term at MIT.

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midterm - Department of Mechanical Engineering...

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