Week 7: Loop Analysis
Overview
Monday: This lecture describes how to analyze the stability and performance of a feedback system by looking at the open loop transfer function. We introduce the Nyquist criteria for stability and talk about the gain and phase margin as measures of robustness. The cruise control system is used as an example throughout the lecture.
Wednesday: A more detailed description of the Nyquist criterion and its application to second order systems will be given.
Friday: Ali Hajimiri (EE) will discuss stability in feedback circuits.Handouts
Monday (CDS 101/110)
- Monday lecture handout
- MATLAB handout: L7_1_analysis.m
Wednesday (CDS 110 only)
Reading
-
K. J. Åström and R. M. Murray, Analysis and Design of Feedback Systems, Preprint, 2004. Chapter 7 . (Caltech access only).
Homework
This homework set covers stability and robustness using the Nyquist criterion. The first problem consists of two sample systems for which gain and phase margin should be computed using both Nyquist and Bode plots. The second problem investigates the stability and performance of the cruise control system under different PI controllers. The CDS 110 questions explore stability in the presence of delay and the stability and control of a simple disk drive positioning system.
- HW #6
- Useful MATLAB commands
- tf - generate a transfer function from numberator/denominator coefficients
- nyquist - generate a Nyquist plot for an open loop system L(s)
- margin - generate a bode plot with gain and phase margin
Additional Information