ECE147B_HW4_Practice_Final_Exam_rev1

# ECE147B_HW4_Practice_Final_Exam_rev1 - ECE147B...

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ECE 147B HW4 : Practice Final – Rev. 1 Winter 2011 Prof. Katie Byl 1 / 11 UCSB Name ______________________________ ECE 147B Practice Final Exam Mar. 16, 2011 You are allowed two, single-side 8 ½ x 11 sheets of self-prepared notes. Use must submit these “Cheat Sheets” with your exam; they will later be returned, as is. No calculators, laptops, or other computing devices are allowed. /16 Problem 1: G(s) vs G(z) (via ZOH) Bode analysis. /16 Problem 2: C(z) controller design. /16 Problem 3: P(z) time response. /16 Problem 4: C(z) controller analysis . /20 Problem 5: State space control and estimation. /18 Problem 6: State space block diagram analysis. (102 total points possible.)

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ECE 147B HW4 : Practice Final – Rev. 1 Winter 2011 Prof. Katie Byl 2 / 11 UCSB 1) Given a plant with the continuous time (CT) transfer function (TF) below, ܩሺݏሻ ൌ 2000 ሺݏ൅20ሻሺݏ ൅ 20ሻ in the standard ZOH (zero-order hold) configuration, with T=.03 sec. a) Sketch a Bode plot for G(z). [You may plot magnitude either in dB or simply as a number, plotted in log scale. e.g., “10” could be either 20 dB or simply a magnitude of “10”. Just label which convention you are using!] b) What is the approximate phase of G(z) at 20 rad/sec? c) What is the approximate gain of G(z) at 20 rad/sec? d) What is the DC gain of G(z)? e) Assume we use a proportional controller, C(z) = 1, in the standard unity-feedback configuration. What would the steady state error be to a unit step input? (Note for study: always first check if the CLTF is stable…)
ECE 147B HW4 : Practice Final – Rev. 1 Winter 2011 Prof. Katie Byl 3 / 11 UCSB 2) Below is a Bode plot shown below for some discrete-time plant, P(z). (See next page for parts 2a through 2d.

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ECE 147B HW4 : Practice Final – Rev. 1 Winter 2011 Prof. Katie Byl 4 / 11 UCSB (Problem 2, continued…) a) Solve for values of a and b (but NOT for K ) for a DT controller of the form: ܥሺݖሻ ൌ ܭ ቀ ݖെܽ ݖെܾ to achieve a phase margin of approximately 30 degrees at 30 rad/sec. (Note, you will later solve for K in part c.)
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## This note was uploaded on 12/28/2011 for the course ECE 146b taught by Professor Staff during the Fall '08 term at UCSB.

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ECE147B_HW4_Practice_Final_Exam_rev1 - ECE147B...

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