CDS 101: Principles of Feedback and Control Lecture 7.1: Loop Analysis of Feedback Systems 11 November 2002

Lecture

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 Presentation

Mud card responses [advanced search]:

• The PPH reading (CH30-31) for this week has several plots missing. Were they taken out on purpose or is there an error in the PDF file?
• Under what conditions is the bode plot misleading vs. the nyquist plot for stability?
• What happens when the Nyquist plot goes exactly through -1? Stable, but not asymptotically stable?
• What are the conditions for stability or instability based on the number of zeroes in the RHP?

Reading Material and Handouts

Handouts from lecture

• Lecture handout
• L7_1-cruise.m
  
• Homework #6

Required reading

• Astrom, Control Systems Design, Sections 3.5
  

Supplemental reading

• Packard, Poola and Horowitz, Dynamic Systems and Feedback, Section 30-31
• A. D. Lewis, A Mathematical Introduction to Feedback Control, Chapter 7[pdf]

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 the stability and control of a simple disk drive positioning system and the ducted fan.

• Homework Assignment [pdf]

Modifications to the homework (link above is always the latest version):

• 11 Nov 02: problem set release

Frequently asked questions on homework and TA hints: