# CDS 101/110 - Loop Shaping

CDS 101/110a | ← Schedule → | Recitations | FAQ | () |

## Contents |

## Overview

The learning objectives for this week are:

- Students should be to design a simple compensator with given performance and robustness (phase margin) specifications
- Students should be analyze and understand the overall performance of the system using the Gang of Four
- Students should compute the limits on the performance that arise from right half plane poles and zeros

**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: L8_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: L8_2_maglev.m

**Friday:** Recitation sections

## Reading

- K. J. Åström and R. M. Murray,, Princeton University Press, 2008..
- CDS 101: Read sections 11.1, 11.3-11.4 [45 min]
- CDS 110: Read sections 11.1, 11.2-11.5 [60 min]
- CDS 210: Skim AM08 Ch 11.1-11.4, read AM08 11.5, DFT Ch 4 and 6 [90 min]

## Homework

- Homework #7 (due 24 Nov 08): CDS 101, CDS 110, CDS 210

## FAQ

**Monday**

**Wednesday**

**Homework**

- A typo in equation (6.24).
- How do I evaluate a certain transfer function at desired frequencies numerically?
- In MATLAB, use feedback() command to obtain the closed loop transfer function. Do not use L/(1 L).
- When evaluating the Bode integral, I am not getting even close to the ideal result (something negative)?