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# final99 - ECE 147A FEEDBACK CONTROL SYSTEMS THEORY AND...

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ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY AND DESIGN F99 Final Exam Closed book and notes. No calculators. Show all work. Name: Problem 1: /20 Problem 2: /20 Problem 3: /20 Problem 4: /20 Problem 5: /20 Total: /100 All feedback loops should be assumed to be in the negative unity feedback configuration.

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Name: Problem 1 Suppose C ( s ) P ( s ) = kG ( s ) where G ( s ) contains two unstable poles and its Bode plot is shown on the next page. 1. For what range of k ’s (if any) is the closed-loop stable? (If a range exists, you should give an approximate range based on readings from the Bode plot.) Explain your answer. (Hint: Nyquist stability criterion.) 2. At high frequencies, the Bode magnitude plot of G ( s ) has a slope of -60 db/decade. Is it possible to find a proper transfer function D ( s ) and a value ¯ k so that if C ( s ) P ( s ) = kD ( s ) G ( s ) then the closed-loop is stable for all k in the range [ ¯ k, )? If so, construct such a C ( s ) and ¯ k . If not, explain why. (Hint: root locus.)
10 -1 10 0 10 1 10 2 -40 -20 0 20 Frequency (rad/sec) Gain dB 10 -1 10 0 10 1 10 2 0 90 180 Frequency (rad/sec) Phase deg

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final99 - ECE 147A FEEDBACK CONTROL SYSTEMS THEORY AND...

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