CDS 110/ChE 105, Spring 2024
Analysis and Design of Feedback Control Systems  
Instructors

Teaching Assistants

This is the course homepage for CDS 110, Spring 2024. This course is cotaught with ChE 105 (Dynamics and Control of Chemical Systems).
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 twodegree 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 
Introduction and review

FBS2e 1.11.5 (skim), 2.12.4

HW #1

Week 2 8 Apr* 
Modeling, Stability

FBS2e 3.13.2, 4.1, 5.15.3

HW #2

Week 3 15 Apr 
Linear Systems

FBS2e 6.16.4

HW #3

Week 4 22 Apr 
State Feedback

FBS2e 7.27.5

HW #4

Week 5 29 Apr 
State estimation

FBS2e 8.18.4

HW #5

Week 6 6 May 
Trajectory generation and tracking

FBS2e, 7.1, 8.5 OBC, Ch 1, 2.1, 2.2, 4.3 
HW #6

Week 7 13 May 
Frequency domain analysis

FBS2e 9.19.4, 10.110.3

HW #7

Week 8 20 May 
Robustness and fundamental tradeoffs

FBS2e, 12.112.3, 13.3, 14.2, 14.4  HW #8

Week 9

PID control

FBS2e, 11.111.4

HW #9 (Sophomores, Juniors)

Week 10 5 Jun 
Final review and applications


Final exam (Seniors, Graduate Students)

Finals week (Sophomores, Juniors) 
None  Final exam (Sophomores, Juniors)

Grading
The final grade will be based on homework sets, a midterm exam, and a final exam:
 Homework (60%): Homework sets will be handed out weekly and due on Wednesdays by 2 pm via Gradescope. 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 receive 50% credit. Python (or MATLAB) code is considered part of your solution and should be printed and turned in with the problem set (whether the problem asks for it or not).
 (Sophomores and juniors only) The lowest score on your homework sets will be dropped.
 Final exam (40%): The final exam will be a 12 hour, inclass, closedbook exam.
 Seniors and graduate students: the final exam will be on 7 Jun (Fri), 24 pm
 Sophomores and juniors: the final exam will be on 12 Jun (Wed), 24 pm
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. Python (or MATLAB) scripts and plots are considered part of your writeup and should be done individually (you can share ideas, but not code).
ChatGPT and other AI tools may be used in the same manner as a fellow student in the class: you are allowed to consult online tools and use them to understand the topics, but all solutions should be written up individually. You cannot use online tools to generate solutions for coding problems (cutting and pasting from templates or materials handed out in class and editing them as appropriate is OK).
No collaboration is allowed on the final exam.
Course Text and References
The primary course text is
 [FBS2e] K. J. Astrom and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Second Edition. Princeton University Press, 2021.
This book is available via free download.
The following additional references, also available for free, may also be useful:
 [Lew], A. D. Lewis, A Mathematical Approach to Classical Control, 2003. Online access.
 [OBC] R. M. Murray, "OptimizationBased Control", 2023. Online access
 [LST] Richard M. Murray, Feedback Systems: Notes on Linear Systems Theory, 2020. (Updated 30 Oct 2020)
In addition to the books above, the textbooks below may also be useful. They are available in the library (nonreserve), from other students, or you can order them online.
 B. Friedland, Control System Design: An Introduction to StateSpace Methods, McGrawHill, 1986.
 G. F. Franklin, J. D. Powell, and A. EmamiNaeni, Feedback Control of Dynamic Systems, AddisonWesley, 2002.