# CDS 101/110 - Loop Analysis

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CDS 101/110a | Schedule | Recitations | FAQ | AM08 (errata) |

## Overview

**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

**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, Preprint, 2007. Chapter 9 - Loop Analysis.

## 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.

- Homework #6
- 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 2007</ncl>
**Wednesday**
<ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2007</ncl>
**Homework**
<ncl>CDS 101/110 FAQ - Homework 6, Fall 2007</ncl>