CDS 110b, Winter 2006
See current course homepage to find most recent page available.
|Course Home||L7-2: Sensitivity||L8-1: Robust Stability||L9-1: Robust Perf||Schedule|
This is the homepage for CDS 110b, Introduction to Control Theory for Winter 2006.
Course Desciption and Goals: CDS 110b focuses on intermediate topics in control theory, including H_\infty control theory for robust performance, optimal control methods, and state estimation using Kalman filters. Upon completion of the course, students will be able to design and analyze control systems of moderate complexity. Students may optionally participate in a course project in lieu of selected homework problems. Students participating in the course project will learn how to implement and test control systems on a modern experimental system.
The final grade will be based on homework sets, a midterm exam and a final exam:
- Homework: 50%
Homework sets will be handed out weekly and will generally be due one week later at 5 pm to the box outside of 109 Steele. Late homework will not be accepted without prior permission from the instructor.
- Midterm: 20%
A midterm exam will be handed out at the beginning of midterms week and due at the end of the midterm examination period. The midterm exam will be open book.
- Final: 30%
The final exam will be handed out on the last day of class due at the end of finals week. It will be an open book exam.
Note: students working on the course project will not be required to take the midterm or final. Instead, two project reports will be due documenting the experimental work performed as part of the class.
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writing. MATLAB scripts and plots are considered part of your writeup and should be done individually.
No collaboration is allowed on the midterm of final exams.
Course Text and References
The recommended course texts are:
- B. Friedland, Control System Design: An Introduction to State-Space Methods, Dover, 2004. Available in the Caltech bookstore.
- K. J. Åström and R. M. Murray, Design and Analysis of Feedback Systems, Preprint, 2006. Available online.
- J. Doyle, B. Francis, A. Tannenbaum, Feedback Control Theory, Macmillan, 1992. Available online.
You may find the following texts useful as well:
- G. F. Franklin, J. D. Powell, and A. Emami-Naeni, Feedback Control of Dynamic Systems, Addison-Wesley, 2002.
- N. E. Leonard and W. S. Levine, Using Matlab to Analyze and Design Control Systems, Benjamin/Cummings, 1992.
- A. D. Lewis, A Mathematical Approach to Classical Control, 2003.
The course is currently scheduled for MW 1:30-3:00 pm in 104 Watson (course scheduling page).
|4 Jan (W)||Course Overview + Optimal Control||Handout||HW1|
|6 Jan (F)||Course Project overview (optional)|
|9 Jan (M)*||No class|
|11 Jan (W)||Linear Quadratic Regulators||Friedland, Ch 9||HW 2|
|13 Jan (F)||Control Implementation (optional)||AM05 Ch 12|
|16 Jan (M)||No class (Institute holiday)|
|18 Jan (W)||Receding Horizon Control||Handout||HW 3|
|20 Jan (F)||Control Implementation (optional)|
|23 Jan (M)||Observability and Estimators||AM05 Ch 6|
|25 Jan (W)||Introduction to Random Processes||Friedland, Ch 10||HW 4|
|30 Jan (M)||Linear Quadratic Estimators (LQE)||Friedland, Ch 11|
|1 Feb (W)||Kalman Filtering||Midterm (due 6 Feb)|
|2 Feb (F)||Midterm review (optional)|
|6 Feb (M)||Intro to Robust Control||DFT Ch 1-3, AM05 Sec 11.1||HW 5|
|8 Feb (W)||Norms of Signals and Systems|
|13 Feb (M)||Uncertainty Modeling||DFT 4.1, AM05 Sec 11.2||HW 6|
|15 Feb (W)||Robust Stability||DFT 4.2, AM05 Sec 11.2|
|20 Feb (M)||No class (Institute holiday)||HW 7|
|22 Feb (W)||Robust Performance||DFT 4.3, AM05 Sec 11.3|
|27 Feb (M)||Design Constraints||DFT, Ch 6 AM05 Sec 11.4||HW 8|
|1 Mar (W)|
|6 Mar (M)||Design Example||AM05 Sec 11.5||Final (due 17 Mar)|
|8 Mar (W)|
|10 Mar||Final review (optional)|
Students interested in the implementation of control systems may opt to do a course project in lieu of the midterm and final exams. The course project will involve implementing control algorithms on a working application. For 2006, the experiment will be control of an autonomous road vehicle, Alice.
The following work must be performed as part of the class project:
- Midterm report: 20%
By midterm, all students should implement and test an LQR controller on the experimental system. A report describing the control design and experimental results is due no later than 5 pm on the last day of the midterm examination period. The report should include a derivation of a nonlinear model for the system, an analysis and design of a control law based on the linearization of that model, and a comparison between simulation and experimental results on the system. For 2005-06, students will implement a lateral control law that controls the position of the vehicle and tracks a reference trajectory on flat pavement.
- Final report: 30%
By the end of the course, students should implement a state estimator and controller on the experimental system. A presentation and report descriging the control design and experimental results will be given in lieu of the final. The final presentation will be made after the end of classes and the report is due no later than 5 pm on the last day of finals. The report should build on the report submitted at midterms and should include a model-based design and experimentation of a controller using a state estimator. The controller may be implemented either in state space or in frequency domain, but should be analyzed for robustness using the techniques demonstrated in Weeks 6-9.