# CDS 110b, Winter 2006

 WARNING: This page is for a previous year. See current course homepage to find most recent page available.
 Contents

This is the homepage for CDS 110b, Introduction to Control Theory for Winter 2006.

 Instructor Richard Murray, murray@cds.caltech.edu Lectures: Mon/Wed, 2-3 pm, 102 Steele Office hours: Fridays, 4-5 pm, 109 Steele Teaching Assistants (cds110-tas@cds) Jeremy Gillula, jeremy@caltech.edu James Martin, duck@caltech.edu Shaunak Sen, shaunak@cds.caltech.edu Office hours: Tue 4-6p in 110 STL Recitation: Fri 2-3 pm, 125 STL

## Announcements

 Archive
• 14 Mar: HW8 Solutions.
• 11 Mar: Solutions to problems 1 and 2 of HW8 are posted.
• 11 Mar: Solution to Problem 4 of HW 6 : correction.
• 9 Mar: HW 7 solutions are now available.
• 6 Mar: dfan_robperm.m is now available; this is the script used in class
• Note: the variation in l is 0.25 in the script instead of 0.025
• 3 Mar: HW #8 is now posted. Due 8 Mar (Wed)
• 1 Mar: HW 6 solutions are now posted.
• 22 Feb: HW #7 is now posted. Due 1 Mar (Wed)
• 22 Feb: HW #5 solutions are coming; Average = 22/30

## Course Syllabus

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 taking the midterm and final. 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. In addition, for HW sets 6-8, students working on the course project are only required to complete 2 problems on each HW set.

### Collaboration Policy

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:

• F. L. Lewis and V. L. Syrmos, "Optimal Control", Second Edition, Wiley-IEEE, 1995. (Google Books)
• 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.

### Course Schedule

The course is currently scheduled for MW 1:30-3:00 pm in 104 Watson (course scheduling page).

##### 1
4 Jan (W) Course Overview + Optimal Control LS95, 3.1-3.2 HW 1, Solns
6 Jan (F) Course Project overview (optional)
##### 2
9 Jan (M)* No class
11 Jan (W) Linear Quadratic Regulators Friedland, Ch 9 HW 2, Solns
13 Jan (F) Control Implementation (optional) AM05 Ch 12
##### 3
16 Jan (M) No class (Institute holiday)
18 Jan (W) Receding Horizon Control Murray et al, 2003 HW 3, Solns
20 Jan (F) Control Implementation (optional)
##### 4
23 Jan (M) Observability and Estimators AM05 Ch 6
25 Jan (W) Random Processes Friedland, Ch 10 HW 4, Solns
##### 5
30 Jan (M) Stochastic Systems
1 Feb (W) Kalman Filters Friedland, Ch 11 Midterm, Solns
2 Feb (F) Midterm review (optional)
##### 6
6 Feb (M) Sensor Fusion Friedland, Ch 11 + notes HW 5, Solns
8 Feb (W) Intro to Robust Control DFT Ch 1-3, AM05 Sec 11.1
##### 7
13 Feb (M) Norms of Signals and Systems HW 6, Solns
15 Feb (W) Weighted Sensitivity
##### 8
20 Feb (M) No class (Institute holiday)
22 Feb (W) Robust Stability DFT 4.1-4.2, AM05 Sec 11.2 HW #7 (due 1 Mar)
##### 9
27 Feb (M) Robust Performance DFT 4.3, AM05 Sec 11.3
1 Mar (W) Design Constraints DFT, Ch 6 AM05 Sec 11.4 HW 8
##### 10
6 Mar (M)
8 Mar (W) Design Example AM05 Sec 11.5
10 Mar Final review (optional) Final (due 17 Mar)

### Course Project

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 description of the (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 describing 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 design, analysis and demonstration of the full system. An estimator must be part of the design. 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.

A special set of lectures on control implementation will be given for students interested in purusing the course project.

Students who are interested in continuing their work on the course project may wish to apply for the Autonomous Vehicle SURF team. Expression of interest is required no later than 27 Jan 06 (see SURF page for details).

## Old Announcements

• 4 Jan 05: Courses project information session: 6 Jan (Fri), 2-3 pm, 125 Steele
• 4 Jan 05: Please turn in course scheduling form by 6 Jan (Fri), 5 pm
• 4 Jan 05: HW #1 is now available; due 11 Jan (Wed)
• 4 Jan 05: No class on Monday (9 Jan); the next regularly schedule class is Wed from 1:30-3:00 pm
• 7 Jan 05: Office hours will be on Sun from 4-5 pm and Tue from 4-6 pm in 125 110 Steele (details)
• 6 Jan 05: There will be a course project information session today (Fri) at 2 pm in 125 Steele
• 10 Jan 05: Office hours will now be in 110 Steele, same times as before (check 125 Steele if nobody is in 110 Steele)
• 11 Jan 05: HW #2 is now available; due 18 Jan (Wed)
• 12 Jan 05: Lectures are now available in MP3 format; see individual lecture pages for link
• 15 Jan 05: HW #2 has been updated with some improved notation (details)
• 15 Jan 05: A new mailing list, cds110-project, has been set up for students participating in the course project
• 18 Jan 05: HW #1 Solutions are now posted. Average = 27/30
• 18 Jan 05: Next week's lectures will be on Mon and Wed from 2-3 pm in 102 Steele
• 18 Jan 05: HW #3 has been posted
• 25 Jan 05: HW #2 Solutions are now posted. Average = 31/40
• 25 Jan 05: HW #4 is now posted. Due 1 Feb @ 5 pm
• 3 Feb: HW 4 solutions are now posted.
• 3 Feb: Please remember to turn in the midterm survey
• 6 Feb: HW #5 is now posted (datasheet here). Due 13 Feb (Mon)
• 13 Feb: Midterm solutions are now available.
• 13 Feb: HW #6 is now posted. Due 22 Feb (Wed)