# hw3 - s 5 Use the Fnal value theorem i.e steady-state...

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ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY AND DESIGN F09 Homework 3 Due Friday, October 16, 2009 Explain all answers! Problem 1 Problem 9.3(a) from the text. In addition, Fnd the transfer function from u 1 - u 1 to x 3 - x 3 . Problem 2 Problem 3.26 from the text. Problem 3 Problem 3.27 from the text. Problem 4 Using elementary calculus, prove that the sensitivity transfer function S ( s ) := 1 1 + P ( s ) C ( s ) is equal to ∂T ( s ) ∂P P ( s ) T ( s ) where T ( s ) = P ( s ) C ( s ) 1 + P ( s ) C ( s ) . Show your work, since the derivation also appears, to some degree, in Section 4.1.2. Problem 5 Consider the unity negative feedback conFguration with C ( s ) = 5( s + 6) s + 2 , P ( s ) = 1 s (
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Unformatted text preview: s + 5) . Use the Fnal value theorem, i.e., steady-state response, to determine the asymptotic value of the output when the reference is zero and the disturbance is a unit step. In addition, plot the bode magnitude plot of the loop gain C ( s ) P ( s ) and comment on if/how it agrees with the general principles of “high gain at low frequency”, “low gain at high frequency”, and “gentle slope at crossover.” What is the value of S (0)? Reconcile this answer with your answer to the Frst part of this question....
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