Homework 5, due March 26, 2014.
Posted: Wed Mar 19, 2014 3:17 pm
Reading: all of Chapter 7.
Exercises: B-7-30, 31, 32, 33 and 34.
Also, Problem 6 from Chapter 4 from Doyle, Francis and Tannenbaum, which is the following.
Consider a unity feedback system with C(s) = 10 and plant P(s) = 1/(s-a) where a is real. Find the range of a for the feedback system to be internally stable. For a = 0 the plant is P(s) = 1/s and we can regard a as a perturbation. Write the plant as P'(s) = P/(1 + Delta W_2 P) with W_2(s) = -a. For this type of uncertainty, robust stability is guaranteed when ||W_2 P S|| < 1. Apply this condition to find when P' is internally stable. You should get a smaller range for a.
Finally, you must make progress on the project before next Wednesday. Include on your homework what you have done up to that date.
Exercises: B-7-30, 31, 32, 33 and 34.
Also, Problem 6 from Chapter 4 from Doyle, Francis and Tannenbaum, which is the following.
Consider a unity feedback system with C(s) = 10 and plant P(s) = 1/(s-a) where a is real. Find the range of a for the feedback system to be internally stable. For a = 0 the plant is P(s) = 1/s and we can regard a as a perturbation. Write the plant as P'(s) = P/(1 + Delta W_2 P) with W_2(s) = -a. For this type of uncertainty, robust stability is guaranteed when ||W_2 P S|| < 1. Apply this condition to find when P' is internally stable. You should get a smaller range for a.
Finally, you must make progress on the project before next Wednesday. Include on your homework what you have done up to that date.