CDS 101/110 - Loop Analysis
| CDS 101/110a | Schedule | Recitations | FAQ | AM08 (errata) |
Overview
The learning objectives for this week are:
- Students should be able to construct a transfer function from a state space system
- Students should be able to sketch the frequency response corresponding to a transfer function and label its key features
- Students should understand the concepts of poles and zeros, and their relationship with the eigenvalues of a state space system
Monday: Stability of Feedback Systems (Slides, MP3)
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.
- Lecture handout
- MATLAB handouts: L7_1_loopanal.m, amnyquist.m, arrow.m
Wednesday: Nyquist Analysis (Notes, MP3)
In this lecture we will derive the Nyquist criterion using the principle of the argument and show how to apply it to determine stability of a closed loop system. We will also see how to account for right half plane poles in the open loop transfer function. Finally, we will give a brief introduction to time delay and its effects on stability.
Friday: recitations
Reading
- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008. Chapter 9 - Loop Analysis.
Homework
- Homework #6 (due 17 Nov 08)
- Useful MATLAB commands
- tf - generate a transfer function from numerator/denominator coefficients
- nyquist - generate a Nyquist plot for an open loop system L(s)
- margin - generate a bode plot with gain and phase margin
FAQ
Monday <ncl>CDS 101/110 FAQ - Lecture 7-1, Fall 2008</ncl> Wednesday <ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2008</ncl> Homework <ncl>CDS 101/110 FAQ - Homework 6, Fall 2008</ncl>
