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
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Lecture Materials
Reading
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Notes
Lecture 2: Control of bifurcations
Outline
- Bifurcation control through nonlinear feedback
- Effects of actuation limits
- Example: compression system instabilities
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Lecture Materials
Reading
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Notes
Lecture 3: Control of limit cycles
Outline
- Motivating examples: combustion and cavity instabilities
- Control oriented modeling techniques
- Describing function analysis
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Lecture Materials
Reading
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Notes
Lecture 4: Additional topics
Outline
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Lecture Materials
Reading
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Notes
Homework and Project Ideas
