CDS 101/110, Fall 2015

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Introduction to Control Systems


  • Richard Murray (CDS/BE),
  • Lectures: MWF, 2-3 pm, 105 ANB
  • Office hours: Wed 3:30-4:30 pm (please e-mail to confirm)

Teaching Assistants

  • Ania Baetica (CDS), Benson Christalin (CDS), Jerry Cruz (CDS), Daniel Guo (EE)
  • Contact:
  • Office hours: Sun, 3-4 pm in 106 ANB, Mon, 3-4 pm in 243 ANB and Tue, 7-8 pm in 106 ANB

This is the course homepage for CDS 101/110, Fall 2015.


  • 8 Dec: Solutions to HW #8 are posted
  • 23 Nov: HW #8 and lecture notes posted
  • 16 Nov: HW #7 and lecture notes posted
  • 9 Nov: HW #6, midterm solutions and lecture notes posted
  • 8 Nov 2015: Homework and exam statistics for the first half of the class
    • HW 1: CDS 110: average 34/40; CDS 101: average 28/30
    • HW 2: CDS 110: average 28/33; CDS 101: average 18/20
    • HW 3: CDS 110: average 21/25; CDS 101: average 8/9
    • HW 4: CDS 110: average 34/38; CDS 101: average 16/20
    • Midterm: CDS 110: average = 59/75, σ = 10.7; CDS 101: average = 36/40, σ = 2.3
  • 19 Oct 2015: Corrected version of HW 3 (PDF) posted: references corrected on problem 1
  • 12 Oct 2015: HW 3 (PDF) has been posted; due 21 Oct (Wed), 2 pm
  • 10 Oct 2015: Corrected version of HW 2 (PDF) posted: references to equations and sections corrected
  • 5 Oct 2015: HW 2 (PDF) has been posted; due 14 Oct (Wed), 2 pm
  • 30 Sep 2015: Office hours for CDS 101/110 are Mon, 3-4 pm in 243 ANB and Tue, 7-9 pm in 106 ANB
  • 28 Sep 2015: HW #1 has been posted; due 7 Oct (Wed), 2 pm
  • 28 Sep 2015: the student mailing list and Piazza invitations have been sent out; if you didn't get one then send e-mail to Richard

Course Syllabus

CDS 101/110 provides an introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear versus nonlinear models, and local versus global behavior.

CDS 101 is a 6 unit (2-0-4) class intended for advanced students in science and engineering who are interested in the principles and tools of feedback control, but not the analytical techniques for design and synthesis of control systems. CDS 110 is a 12 unit class (3-0-9) that provides a traditional first course in control for engineers and applied scientists. It assumes a stronger mathematical background, including working knowledge of linear algebra and ODEs. Familiarity with complex variables (Laplace transforms, residue theory) is helpful but not required.

Lecture Schedule

Date Topic Reading Homework
Week 1

28 Sep
30 Sep*
2 Oct

Introduction and Review
  • Introduction to feedback and control
  • Review of differential equation and linear algebra
  • Feedback principles and examples
FBS-1e 1.1-1.2, 1.4-1.5
FBS-2e 1.1-1.5 (skim), 2.1-2.4
HW 1 (PDF)
Due: 7 Oct, 2 pm

Solutions (PDF) (Caltech access only)

Week 2

5 Oct
7 Oct
9 Oct*

Modeling, Stability
  • State space models
  • Phase portraits and stability
  • Introduction to MATLAB
FBS-1e 2.1-2.2, 3.1 4.1-4.3
FBS-2e 3.1-3.2, 4.1, 5.1-5.3
HW 2 (PDF)
Due: 14 Oct, 2 pm

Solutions (PDF) (Caltech access only)

Week 3

12 Oct*
14 Oct*
16 Oct*

Linear Systems
  • Input/output response of LTI systems
  • Matrix exponential, convolution equation
  • Linearization around an equilibrium point
FBS-1e 5.1-5.4
FBS-2e 6.1-6.4
HW 3 (PDF)
Due: 21 Oct, 2 pm

Solutions (PDF) (Caltech access only)

Week 4

19 Oct
21 Oct
23 Oct*

State Feedback
  • Reachability
  • State feedback and eigenvalue placement
FBS-1e 6.1-6.4
FBS-2e 7.1-7.4
HW 4 (PDF)
Due: 28 Oct, 2 pm

Bicycle dynamics

Solutions (PDF) (Caltech access only)

Week 5

26 Oct
28 Oct
30 Oct

State space control design
  • Trajectory generation, feedforward
  • Integral feedback
  • State estimation (if time)
  • Midterm review
FBS-1e 7.1-7.3
FBS-2e 8.1-8.3
Midterm exam
Due: 3 Nov, 5 pm

Solutions (PDF) (Caltech access only)

Week 6

2 Nov
4 Nov
6 Nov*

Transfer Functions
  • Frequency domain modeling
  • Block diagram algebra
  • Bode plots
FBS-1e 8.1-8.4
FBS-2e 9.1-9.4
HW 5 (PDF)
Due: 11 Nov, 2 pm

Solutions (PDF) (Caltech access only)

Week 7

9 Nov
11 Nov
13 Nov*

Loop Analysis
  • Loop transfer function and the Nyquist criterion
  • Stability margins
FBS-1e 9.1-9.3
FBS-2e 10.1-10.3
HW 6 (PDF)
Due: 18 Nov, 2 pm

Solutions (PDF) (Caltech access only)

Week 8

16 Nov
18 Nov*
20 Nov

PID Control
  • Simple controllers for complex systems
  • Integral action and anti-windup
FBS-1e 10.1-10.4
FBS-2e 11.1-11.4
HW 7 (PDF)
Due: 25 Nov, 2 pm

Solutions (PDF) (Caltech access only)

Week 9

23 Nov
25 Nov*

Loop Shaping, I
  • Sensitivity functions
  • Feedback design via loop shaping
FBS-1e 11.1-11.3
FBS-2e 12.1-12.4
HW 8 (PDF)
Due: 4 Dec, 2 pm

Solutions (PDF) (Caltech access only)

Week 10

30 Nov
2 Dec
4 Dec

Loop Shaping II
  • Fundamental limitations
  • Modeling uncertainty
  • Performance/robustness tradeoffs
FBS-1e 11.4, 12.1-12.4
FBS-2e 12.6-12.7, 13.1-13.3
Final exam
Due 11 Dec, 5 pm
  • Will be handed out in class on 4 Dec


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.