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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online