CDS 140b: Control of Bifurcations and Limit Cycles

This page contains my lecture outline and notes for a set of lectures that I will be giving in CDS 140b Introduction to Dynamics, in Winter 2008. This page is mainly intended as a place for me to keep my notes, but might be useful as a reference for the lecture (the final lecture notes will be posted on the CDS 140 web page).

Goals

• Describe how bifurcations and limit cycles arise in engineering applications
• Review some tools for characterizing bifurcations and limit cycles
• Show how feedback can be used for design of (nonlinear) dynamics

Lecture 1: Introduction and review

Outline Motivating applications: compression systems, combustion, cavity flows Project ideas Review of bifurcations and normal forms Review of Lyapunov-based stabilization

Lecture Materials Lecture presentation Reading Standard text on normal forms (tbd) Sontag paper on CLFs (tbd)

Notes

• This lecture is intended to serve as an introduction to the material that will be covered in the set of lectures, including motivating applications
• Need to figure out how to cover project ideas in this lecture, since students who want to work on the project would need to get started soon (so this can't wait until the last lecture)
• Not sure how much normal form material is going to be required. Look through Liaw/Abed + Wang/Murray to get a sense. I also need to find a good source for this
• The review of Lyapunov-based stabilization is intended to show simple techniques for control of bifurcations in a nonlinear setting. Plan to cover Sontag's formula, which students often don't see in other contexts.
• Can use UTRC presentations for the introductory material

Lecture 2: Control of bifurcations

Outline Bifurcation control through nonlinear feedback Effects of actuation limits Example: compression system instabilities

Lecture Materials Lecture presentation Reading Liaw and Abed Wang and Murray, Bifurcation with actuation limits

Notes

• This lecture will be based on the second VKI lecture, but need to add in more complete derivations of the results
• Work through Liaw and Abed paper in some detail (blackboard), then cover Yong Wang's results using powerpoint

Lecture 3: Control of limit cycles

Outline Motivating examples: combustion and cavity instabilities Control oriented modeling techniques Describing function analysis

Lecture Materials Reading

Lecture 4: Additional topics

Outline

Lecture Materials Reading