# CDS 101/110 - Loop Shaping

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

## Overview

**Monday:** Loop Shaping (Slides, MP3)

This lecture describes how to design a control system by converting the performance specifications to constraints on the loop transfer function, and then shaping the loop transfer function to satisfy the constraints. Sensitivity functinos are defined and tradeoffs between different input/output transfer functions are discussed.

- Lecture handout
- MATLAB handouts: L9_1_dfan.m

**Wednesday:** Performance Limits (Slides, MP3)

This lecture investigates some of the limits of performance for feedback systems, including the effects of right half plane poles and zeros on the closed loop system performance. A magnetic levitation system and lateral control of the Caltech ducted fan are used to illustrate the basic concepts.

- Lecture handout
- MATLAB handouts: L9_2_maglev.m

**Friday:** Recitation sections

## Reading

- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Preprint, 2007. Chapter 11 - Loop Shaping.

## Homework

This homework set provides practice in specification, design and limits of control systems using loop shaping. The first problem explores the relationship between the loop transfer function and the closed loop response. The second problem explores some of the effects of right half plane zeros on control performance. The third and fourth problems (CDS 110) are simple design problems for an insect flight control system and a magnetic levitation system.

## FAQ

**Monday**
<ncl>CDS 101/110 FAQ - Lecture 9-1, Fall 2007</ncl>
**Wednesday**
<ncl>CDS 101/110 FAQ - Lecture 9-2, Fall 2007</ncl>
**Homework**
<ncl>CDS 101/110 FAQ - Homework 8, Fall 2007</ncl>