CDS 101/110 - State Feedback
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This lecture introduces the concept of reachability and explores the use of state space feedback for control of linear systems. Reachability is defined as the ability to move the system from one condition to another over finite time. The reachability matrix test is given to check if a linear system is reachable, and the test is applied to several examples. The concept of (linear) state space feedback is introduced and the ability to place eigenvalues of the closed loop system arbitrarily is related to reachability. A cart and pendulum system and the predator prey problem are used as examples.
Wednesday: State Feedback Design (Notes, MP3)
This lecture will describe how to design state feedback controllers via eigenvalue placement. The performance of the system as a function of the placement of the closed loop eigenvalues will be described. The use of integral action and a brief introduction to LQR control will also be given.
Friday: Midterm review
|Monday|| Wednesday (CDS 110)
- K. J. Åström and R. M. Murray,, Preprint, 2006..
The exam will consist of 3-5 problems, covering the material in the first five weeks of the course (including reachability and state feedback). The exam will be open book. You may use the course notes, any of the optional texts (Friedland, Franklin-Powell and Emami-Naeni, Leonard and Levin, Strogatz, or Kuo), course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. No other books are allowed.
You may use a computer or calculator for carrying out numerical computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam (except for accessing local computing resources, such as MATLAB/SIMULINK), but you may download or print out copies of presentations, notes, FAQs, or other material posted on the course web site (CDS 101 or 110). You are not allowed to print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).
The exam will be due by 5 p.m. Tuesday, 31 October, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.
- Can you recommend a good linear algebra resource?
- Could we move office hours?
- Do we always need to know everything about the states? The Segway example sort of suggests not.
- Does lim (t to infty) E(x-x hat) = 0 imply that there will be less disturbance over time?
- Is T completely arbitrary in the definition of reachability?
- What is matrix rank and how do i calculate it?