# 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 draw a Nyquist curve and use the Nyquist criterion to determine stability
- Students should be able to compute the gain a phase margin for a system using Nyquist and Bode plots

**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, ambode.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 - Frequency Domain Analysis.
- CDS 101: Read sections 9.1-9.3, skipping advanced subsetions [45 min]
- CDS 110: Read sections 9.1-9.3 [60 min]
- CDS 210: Review AM08 Ch 9.1-9.3, read AM08 9.4-.5, DFT Ch 3 [90 min]

## 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)
- amnyquist - same as Nyquist, but sometimes does a better job with arrows
- 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>