# Difference between revisions of "CDS 101/110, Fall 2015"

 Introduction to Control Systems Instructors Richard Murray (CDS/BE), murray@cds.caltech.edu Lectures: MWF, 1-2 pm, 104 ANB Office hours: Wed 2-3 pm (please e-mail to confirm) Teaching Assistants Ania Baetica (CDS), Benson Christalin (CDS), Jerry Cruz (CDS) Contact: cds110-tas@cds.caltech.edu Office hours: TBD

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

### 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 FBS-2e 1.1-1.5 HW 1 (PDF) Due: 5 Oct Week 2 5 Oct 7 Oct 9 Oct* Modeling, Stability State space models Phase portraits and stability Introduction to MATLAB FBS-2e 3.1-3.2, 5.1-5.3 HW 2 Due: 12 Oct 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-2e 6.1-6.4 HW 3 Due: 19 Oct Week 4 19 Oct 21 Oct 23 Oct* State Feedback Reachability State feedback and eigenvalue placement FBS-2 7.1-7.4 HW 4 Due: 26 Oct Week 5 26 Oct 28 Oct 30 Oct Output Feedback State estimation Trajectory generation, feedforward Midterm review FBS-2e 8.1-8.3 Midterm exam Due: 3 Nov Week 6 2 Nov 4 Nov 6 Nov* Transfer Functions Frequency domain modeling Block diagram algebra Bode plots FBS-2e 9.1-9.4 HW 5 Due: 9 Nov Week 7 9 Nov 11 Nov 13 Nov* Loop Analysis Loop transfer function and the Nyquist criterion Stability margins FBS-2e 10.1-10.3 HW 6 Due: 16 Nov Week 8 16 Nov 18 Nov* 20 Nov PID Control Simple controllers for complex systems Integral action and anti-windup FBS-2e 11.1-11.4 HW 7 Due: 23 Nov Week 9 23 Nov 25 Nov* Loop Shaping, I Sensitivity functions Feedback design via loop shaping FBS-2e 12.1-12.4 HW 8 Due: 30 Nov Week 10 30 Nov 2 Dec 4 Dec Loop Shaping II Fundamental limitations Modeling uncertainty Performance/robustness tradeoffs FBS-2e 12.6-12.7, 13.1-13.2 Final exam Due 11 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 Mondays by 5 pm to the box outside of 109 Steele. A two day grace period is allowed to turn in your homework. Late homework beyond the grace period 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 by Åström and Murray (2008). This book is available in the Caltech bookstore and via download from the companion web site. 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.