hw3 - J.M. Gonalves c Fall 2003 CDS 212 - Introduction to...

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J.M. Gon¸ calves Fall 2003 CDS 212 - Introduction to Modern Control Homework # 3 Date Given: October 16th, 2003 Date Due: October 23th, 2003, in class P1. DFT: Chapter 4, Exercise 9. P2. DFT: Chapter 4, Exercise 10. P3. DFT: Chapter 4, Exercise 7. P4. [ Zhou 8.1 ] This problem shows that the stability margin is critically de- pendent on the type of perturbation, The setup is a unity-feedback loop with controller K ( s ) = 1 and plant ˜ P = P + Δ, where P ( s ) = 10 s 2 + 0 . 2 s + 1 Compute the largest β such that the feedback system is internally stable for all k Δ k β for the cases when (a) Δ ∈ S . (b) Δ IR. P5. [ Zhou 8.12 ] One of the main tools in this chapter was the small-gain theorem. One way to state it is as follows: de±ne a transfer function F ∈ S to be contractive if k F k 1 and strictly contractive if k F k < 1. Then for the unity feedback system the small gain theorem is this: if K is contractive and G is strictly contractive then the feedback system is stable. This problem concerns passivity and the passivity theorem. This is an
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This note was uploaded on 01/04/2012 for the course CDS 212 taught by Professor Tarraf,d during the Fall '08 term at Caltech.

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hw3 - J.M. Gonalves c Fall 2003 CDS 212 - Introduction to...

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