CDS 101: Principles of Feedback and Control Lecture 8.1: Frequency Domain Design 18 November 2002

Lecture

This lecture covers the basic tools in frequency domain control design through "loop shaping". After reviewing the role of the controller on the loop shape and the relationship between the gain and the phase, we consider several standard controller types (proportional, lead, PI) and apply them to design a high performance controller for the pitch axis of the Caltech ducted fan.

• Lecture Presentation

Mud card responses [advanced search]:

• Are there rigorous ways of determining if it's impossible to meet certain/multiple performance specifications?
• I recall someone telling me not to treat phase as the same as time delay. Is there any truth to that?
• Does a net encirclement of (-1,0) always imply instability on a Nyquist plot?
• On slide 4, what is the difference between the top graph in the Bode diagram and the bottom right graph? What are they graphing such that one is at 20dB and the other is at 0dB?
• What's wrong with -90deg phase lag?
• What is a negative phase margin; what does it mean?
• Could you post the midterm average on the solutions?
• Are there any MATLAB toos for simplifying transfer functions? e.g. factoring the numerator and denominator in order to cancel out terms common to both?
• What is the bandwidth?

Reading Material and Handouts

Handouts from lecture

• Lecture handout
• L8_1-dfan.m
  
• Homework #7

Required reading

• None
  

Supplemental reading

• A. D. Lewis, A Mathematical Introduction to Feedback Control, Chapter 12 [pdf]

Homework

This homework set provides practice in specification and design of control systems in the frequency domain. The first two problems work through examples that are very similar to the one used in lecture. The CDS 110 problems explore control of a more complicated system, the cart pendulum system (with the pendulum pointing down).

• Homework Assignment [pdf]

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

• 21 Nov 02: fixed minor bugs in problem 2 problem specification
• 19 Nov 02: updated wording on problem 3 to correspond to Wednesday lecture
• 18 Nov 02: problem set release

Frequently asked questions on homework and TA hints: