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Final Solns F2011 580

# Final Solns F2011 580 - Name Problem#1 2 3 4 5 ECE 580...

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Name ______________________________ Revised 12/16/2005 ECE 580 FEEDBACK SYSTEMS (I) Fall 2011 Final Exam Tuesday, December 12, 2011 Instructions The exam is open book and notes. No electronic devices of any kind (including calculators) can be used during the exam. Questions are to be answered on the exam. There are ten questions with the indicated values. Problem #1: _______ 2: _______ 3: _______ 4: _______ 5: _______ 6: _______ 7: _______ 8: _______ 9: _______ 10: _______ Total: _______ Consistent with the ECE Honor Code, you are asked to read the following voluntary statement carefully and sign it before beginning your work in each exam booklet: I have not given or received unauthorized aid on this exam. ____________________________________ __________________ Signature Date

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Figure 1 Questions 1 through 7 address the unity feedback system shown in Figure 1. The bode plot of the plant transfer function G s ( ) is shown in Figure 2. Figure 2
Problem 1: (15 points) Assume the compensator is D s ( ) = 1 . Find the position constant K p , the velocity constant K v , and the acceleration constant K a of the closed-loop system. The loop Bode magnitude plot Figure 2 has a low-frequency asymptotic slope of –20 db/dec which indicates 1 pole at the origin. Thus, the posotion constant is infinity and the acceleration constant is zero. The velocity constant is found from the low- frequency asymptote at 1 r/s: 0.6. Then K v = 1 0.6 = 2.5 K p = ! K v = 2.5 K a = 0

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Problem 2: (10 points) Assume the compensator consists of a single integrator element D s ( ) = K I s Can the system be Type 2 with respect to references? If not, why?
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