Difference between revisions of "CDS 101/110  Dynamic Behavior"
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== Overview ==  == Overview ==  
−  '''Monday:''' Qualitative Analysis and Stability ({{cds101 handoutsL31_stability.pdfSlides}}, MP3)  +  '''Monday:''' Qualitative Analysis and Stability ({{cds101 handoutsL31_stability.pdfSlides}}, [[Media:9Oct06.mp3MP3]]) 
This lecture provides an introduction to stability of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predatorprey problem as examples.  This lecture provides an introduction to stability of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predatorprey problem as examples. 
Revision as of 19:59, 10 October 2006
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CDS 101/110a  Schedule  Recitations  FAQ  () 
Contents 
Overview
Monday: Qualitative Analysis and Stability (Slides, MP3)
This lecture provides an introduction to stability of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predatorprey problem as examples.
Wednesday: Stability Analysis (Slides, MP3)
Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts; domain specific examples will be presented in individual recitation sections.
Friday: Lyapunov Stability (Slides, MP3)
Handouts
Monday

Wednesday (CDS 110)

Friday 
Reading
 K. J. Åström and R. M. Murray,, Preprint, 2006..
Homework
This homework set covers stability and performance through a series of application examples. The first problem provides a set of three realworld models in which the student must identify the equilibrium points and determine stability of the equilibrium points (through simulation). The second problem explores performance specification in the conext of the cruise control example, including step response and frequency response.
FAQ
Monday
 Are the dynamics on slide 10 correct?
 Has a stable system a stable eq. point? a limit cycle?
 How are the z variables defined on slide 10, Lecture 31?
 How do equations given for dynamics on slide 10 relate to the statespace setup we used before?
 How do we choose epsilon in the definition of stability?
 How was V(x) derived on slide 13 of Lecture 31?
 Is the overshoot definition on slide 12 correct?
 Is the system on slide 5 stable?
 What is "closed form"?
 What is a plant in the context of this class?
 What is a stable system?
 Who/What is Lyapunov?
Wednesday
 Could you please make it clear what is an 'A' and what is a 'Lambda' (matrix)?
 Do complex matrices also have a Jordan canonical form?
 How do you actually find the Jordan canonical form of a matrix?
 I keep getting mixed up on whether the diagonalized form of A is T^(1)AT or TAT^(1). Is there an easy way to remember the correct form?
 Was the equation for V(q) for the spring mass example missing a transpose?
 What does "up to permutations" mean?
 Where can I find the proof to the Lyapunov Theorem?
Friday
Homework