CDS 101/110, Fall 2015

Introduction to Control Systems
Instructors Richard Murray (CDS/BE), murray@cds.caltech.edu 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: cds110-tas@cds.caltech.edu 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.

Announcements

• 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 Background survey (PDF) Mon lecture notes (PDF), Wed review session notes (PDF)	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 Mon lecture notes (PDF) Wed lecture notes (PDF)	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 Mon lecture slides (PDF) Fri recitation slides (PDF)	HW 3 (PDF) Due: 21 Oct, 2 pm Python: cartpend.py MATLAB: cartpend.m, cartpend_model.m SIMULINK: balance_simple.mdl 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 Mon lecture slides (PDF) MATLAB: L4_1_statefbk.m , predprey.m , predprey_rh.m Python: L4_1_statefbk.py , predprey.py	HW 4 (PDF) Due: 28 Oct, 2 pm Bicycle dynamics MATLAB: bike_linmod.m Python: bike_linmod.py 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 Mon lecture slides (PDF) Fri review session notes (PDF)	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 Mon lecture slides (PDF) Fri recitation notes (PDF)	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 Mon lecture slides (PDF) Wed lecture slides (PDF) Fri PID example (python)	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 Mon lecture slides (PDF) Wed recitation slides (PDF)	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 Mon lecture slides (PDF) Wed lecture slides (PDF) Wed PVTOL example (python)	Final exam Due 11 Dec, 5 pm Will be handed out in class on 4 Dec

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.