CDS 110, Spring 2018

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Introduction to Feedback Control Systems


  • Richard Murray (CDS/BE),
  • Lectures: MWF, 2-3 pm, 168 Noyes

Teaching Assistants

  • Karena Cai (CDS), Tung Phan (MCE)
  • Office hours: TBD

This is the course homepage for CDS 110, Spring 2018.

WARNING: CDS 110 is being co-taught with ChE 105 this term. The information below was the original plan for CDS 110, but is reorganized in ChE 105. Unfortunately, no hompage is available for ChE 105.

Course Syllabus

An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Input/output modeling of dynamical systems using differential equations and transfer functions. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. Design of feedback controllers in state space and frequency domain based on stability, performance and robustness specifications.

Lecture Schedule

With the exception of the first week, there will be two 1-hour lectures per week, with the specific days varying from week-to-week. The lecture days for each week will be announced in class and posted here at least 1 week in advance.

Date Topic Reading Homework
Week 1

2 Apr
4 Apr
6 Apr

Introduction and Concepts
  • Course overview
  • Simple examples of feedback control
  • Second order input/output systems
FBS2e, Ch 1 and 2 HW #1
Week 2

9 Apr
11 Apr
13 Apr*

Fundamental Principles
  • Mathematical Models
  • Disturbance Attenuation
  • Reference Tracking
  • Robustness
FBS2e, Ch 2 and 3 HW #2
Week 3

16 Apr
18 Apr*
20 Apr

Modeling, Stability
  • Differential equations with inputs
  • Equilibrium points and stability
  • Phase portraits, linearization
FBS2e, Ch 3 and 5 HW #3
Week 4

23 Apr
25 Apr*
27 Apr

Linear Systems
  • LTI systems, transfer functions
  • Frequency response and Bode plots
  • Block diagram algebra
FBS2e, Ch 6 and 9 HW #4
Week 5

30 Apr
2 May
4 May

Frequency Domain Analysis
  • Loop transfer function, Nyquist criterion
  • Gain, phase, and stability margins
FBS2e, Ch 10 Midterm
Week 6

7 May
9 May
11 May*

PID Control
  • PID control analysis
  • Integrator windup, anti-windup
FBS2e, Ch 11 and 12 HW #5
Week 7

14 May*
16 May
18 May

Frequency Domain Design
  • Sensitivity functions, gang of four
  • Effects of right half plane poles and zeros
  • Bode's integral formula (briefly)
FBS2e, Ch 13 and 14 HW #6
Week 8

21 May*
23 May*
25 May*

TBD (guest lecturer) TBD HW #7
Week 9

28 May*
30 May*
1 Jun*

TBD (guest lecturer) TBD HW #8 (Sophomores, Juniors)
Final (Seniors/Graduate students)
Week 10

4 Jun*
6 Jun*
8 Jun

Final Review + Demos None Final (Sophomores, Juniors)


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

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.