CDS 110/ChE 105, Spring 2024

Analysis and Design of Feedback Control Systems
Instructors Richard Murray (CDS/BE), murray@cds.caltech.edu Lectures: MWF, 2-3 pm, TBD Office hours: Wed, 3-4 pm, Annenberg Lounge	Teaching Assistants TBD Office hours: TBD

This is the course homepage for CDS 110, Spring 2024.

Course Syllabus

An introduction to analysis and design of feedback control systems in the time and frequency domain, with an emphasis on state space methods, robustness, and design tradeoffs. Linear input/output systems, including input/output response via convolution, reachability, and observability. State feedback methods, including eigenvalue placement, linear quadratic regulators, and model predictive control. Output feedback including estimators and two-degree of freedom design. Input/output modeling via transfer functions and frequency domain analysis of performance and robustness, including the use of Bode and Nyquist plots. Robustness, tradeoffs and fundamental limits, including the effects of external disturbances and unmodeled dynamics, sensitivity functions, and the Bode integral formula.

Lecture Schedule

Date	Topic	Reading	Homework
Week 1 1 Apr 3 Apr 5 Apr	Introduction and review Course overview and logistics Introduction to feedback and control Review of differential equation and linear algebra	FBS2e 1.1-1.5 (skim), 2.1-2.4	HW #1
Week 2 8 Apr* 10 Apr 12 Apr	Modeling, Stability State space models Phase portraits and stability Introduction to python-control	FBS2e 3.1-3.2, 4.1, 5.1-5.3	HW #2
Week 3 15 Apr 17 Apr 19 Apr	Linear Systems Input/output response of LTI systems Matrix exponential, convolution equation Linearization around an equilibrium point	FBS2e 6.1-6.4	HW #3
Week 4 22 Apr 24 Apr 26 Apr*	State Feedback Reachability State feedback and eigenvalue placement Linear quadratic regulators (LQR)	FBS2e 7.1-7.4	HW #4
Week 5 29 Apr 1 May* 3 May	State estimation Observers, observability Control using estimated state Midterm review (Fri)	FBS2e 8.1-8.3	Midterm
Week 6 6 May 8 May 10 May	Trajectory generation and tracking Two degree of freedom design Gain scheduling Model predictive control	FBS2e, 8.4-8.5 OBC, Ch 1	HW #5
Week 7 13 May 15 May 17 May	Frequency domain analysis Bode and Nyquist plots Stability margins	FBS2e, FBS2e 9.1-9.4, 10.1-10.3	HW #6
Week 8 20 May 22 May 24 May*	Robustness and fundamental tradeoffs Sensitivity functions Bode integral formula	FBS2e, 12.1-12.2, 14.1-14.2	HW #7
Week 9 27 May 29 May* 31 May	PID control Frequency domain design concepts Windup and anti-windup	FBS2e, 11.1-11.4	HW #8 (Sophomores, Juniors) Final (Seniors/Graduate students)
Week 10 3 Jun 5 Jun 7 Jun	Final review and applications Final exam review (Mon) Autonomous vehicles	None	Final (Sophomores, Juniors)

Grading

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 due on Wednesdays by 2 pm either in class or in the labeled box across from 107 Steele Lab. Each student is allowed up to two extensions of no more than 2 days each over the course of the term. Homework turned in after Friday at 2 pm or after the two extensions are exhausted will not be accepted without a note from the health center or the Dean. MATLAB/Python code and SIMULINK/Modelica diagrams are considered part of your solution and should be printed and turned in with the problem set (whether the problem asks for it or not).

• Midterm exam (20%): A midterm exam will be handed out at the beginning of midterms period (28 Oct) and due at the end of the midterm examination period (3 Nov). The midterm exam will be open book and computers will be allowed (though not required).

• Final exam (30%): The final exam will be handed out on the last day of class (4 Dec) and due at the end of finals week. It will be an open book exam and computers will be allowed (though not required).

Collaboration Policy

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor, but you cannot consult homework solutions from prior years and you must cite any use of material from outside references. All solutions that are handed in should be written up individually and should reflect your own understanding of the subject matter at the time of writing. MATLAB/Python scripts and plots are considered part of your writeup and should be done individually (you can share ideas, but not code).

No collaboration is allowed on the midterm or final exams.

Course Text and References

The primary course text is

• K. J. Astrom and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008

This book is available via the Caltech online bookstore or via download from the companion web site. Note that the second edition of this book is in preparation for publication and will serve as the primary text for the course (but almost all of the material we will cover is also in the first edition).

The following additional references may also be useful:

• A. D. Lewis, A Mathematical Approach to Classical Control, 2003. Online access.
• J. Distefano III, A. R. Stubberud and Ivan J. Williams (Author), Schaum's Outline of Feedback and Control Systems, 2nd Edition, 2013.

In addition to the books above, the textbooks below may also be useful. They are available in the library (non-reserve), from other students, or you can order them online.

• B. Friedland, Control System Design: An Introduction to State-Space Methods, McGraw-Hill, 1986.
• G. F. Franklin, J. D. Powell, and A. Emami-Naeni, Feedback Control of Dynamic Systems, Addison-Wesley, 2002.