EML 5311 (section 2B69,2484,6060) - Spring 2015
Control System Theory
Instructor: Dr. Prabir Barooah
Office: MAE-B 330
E-mail: pbarooah at ufl.edu
Office Phone: 352.392.0614
Mobile Phone: 805 259 9643
Class time: period 4 (10:40-11:30 am) MWF
Class location: NEB 201
Office Hours: 1:00 pm - 2:00 pm, MWF
Course website
Please check the course website in e-learning (Canvas, not Sakai) regularly for updates and announcements.
Teaching Assistant
Jonathan Brooks (email: brooks666@ufl.edu)
TA office hours and location: MAE-B 227, T/Th 12-1 pm.
Course description
The course is meant to provide a graduate-level introduction to control theory. The material will focus
on LTI (linear time invariant) systems, with some discussion of non-linear dynamics, justification of
linear approximations, and its limitations. The emphasis will be more on understanding the role of
feedback in dynamic systems, and deriving design guidelines from them, rather than on mastering all
control design methods.
The following is a tentative list of topics that will be covered in the class.
Part A: Classical control design/analysis through frequency-domain techniques
Module A1: control design for stability (main tool: Laplace transforms)
1. Dynamic systems, LCCODE (linear, constant coefficient ordinary differential equation) models
of dynamic systems, review of Laplace transform methods for solving such ODEs.
2. Transfer functions, poles and zeros, BIBO stability,
3. Stabilization through feedback control. PID compensators.
Module A2: controller design for tracking (main tool: Fourier transforms)
• Frequency response Arbitrary signals as sum of sinusoids, Bode plots, asymptotic tracking of
constant and sinusoidal references.
• Control design issues/techniques: Robustness, sensitivity and complementary sensitivity functions, tracking requirements, Loop shaping design. Lead/Lag compensators.
• Fundamental limitations: Bode integral formula, Internal model principle.
• Putting a factor of safety in the design: Nyquist stability criteria, gain and phase margins.
• Data-driven modeling: System identification from input-output data, in particular, the sinesweep method.
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Part A will span approximately 16 lectures.
Part A is intended to be a brisk review of so-called classical control design techniques that you are
expected to have learned in your undergraduate control systems course. The next part will enable you
to apply these techniques on “real” plants that are described by non-liner ODEs.
Part B: Modern control design/analysis techniques (main tool: linear algebra)
1. Mathematical models of dynamic systems: State-space description of non-linear dynamic sysc
tems, simulations in MATLAB
, equilibrium points, kinds of equilibria, stability of an equilibrium point, Lyapunov stability theorem.
2. A very brief but intense review of linear algebra: matrices as linear maps between vector spaces,
range and null spaces, four fundamental subspaces, span, basis, linear independence, eigenvalues
and eigenvectors.
3. Linear systems: linearization around an equilibrium point, linearization around a trajectory,
LTI vs LTV systems, Lyapunov vs. BIBO stability of LTI systems, eigenvalues and Lyapunov
equation.
4. State-space design: Controllability and state feedback, Observability and output-feedback. Luenberger observer, separation principle.
5. Connections between time domain and Laplace domain: state-space to transfer function and vice
versa (of LTI systems), minimal realization, canonical decomposition.
6. From C(s) to C-code Discrete-time systems, sampling and state-space representation, stability.
Implementing continuous-time control design through digital computers.
7. Optimal Control
(a) The general optimal control problem.
(b) LQR : The Linear Quadratic Regulator problem, derivation of the ARE and DRE, finite
and infinite horizon problems.
Part B will span approximately 25 lectures.
Course prerequisites
Since this course is a graduate level introduction to control theory, students are required to have
taken an undergraduate level controls course. In particular, the students are expected to have some
familiarity/understanding of transfer functions, poles and zeros, frequency response, Bode plots, and
LTI state-space models. Part A, particularly Module A1, will therefore mostly be a quick review.
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Familiarity with MATLAB
is also required, as we will be using it extensively.
Evaluation criteria
Grading will based on three exams: homeworks (10%), mid-term 1 (25%), mid-term 2 (25%) and final
exam (40%). The mid-terms will be “in-class” tests (each of 1.5 hours duration, held in the evening),
while the end of term exam will be a take home test.
The mid-terms will be closed book tests. You are allowed to bring x pages of handwritten notes/formula
sheet to Test x. (x = 1, 2). One page means one side of US letter-sized paper, not both sides. Handwritten means written with your own handwriting, not typewritten or photocopied from someone else’s.
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The first two mid-term exams are scheduled on Feb 4 and March 18, 2015. The dates may change
if emergencies arise, but otherwise change is unlikely. The take-home final exam will involve comc
putational parts (requiring MATLAB
or some other scientific computing software). The final exam
will be given on April 22, and you will have to submit it within the time specified (usually 24 or 48
hours). Distance students will have a 3 day window following the in-class exam dates to schedule and
complete the exams with their proctor.
In each homework, only one problem chosen at random will be graded. Your score for that homework
will based on the score you receive on that problem.
Grading scale: A: > 80, A-: 75 − 80, B+: 70 − 75, B: 65 − 70, B-: 60 − 65, C+:55 − 60, C: 50 − 55,
C-: 45 − 50, D: 40 − 45, E:< 40.
Textbook:
There is no required textbook for this course. The following books are recommended:
1. Linear System Theory and Design by Chi-Tsong Chen, Oxford University Press, 3rd edition,
ISBN 0195117778 (graduate level material).
2. Linear System Theory and Design by João P. Hespanha, Princeton University Press, ISBN
978-0-691-14021-6 (graduate level material).
3. Modern Control Systems by Dorf and Bishop (undergraduate-level material).
4. Control Systems engineering by Norman S. Nise.
For Module A1, pdf notes will be provided. Handouts on various topics will also be periodically
provided.
If you are not completely conversant with the undergraduate material on control systems, it is very
important that you review the basic undergraduate controls systems topics such as transfer functions,
frequency response etc.
EML5311ID: In the beginning of the course, you’ll receive a number assigned to you for this course,
which we will call the “EML5311ID”. It will be provided to you as a gradebook entry through elearning, though it has nothing to do with your grades. When you submit your homeworks or tests,
please write your EML5311ID on the front page. Do not write either your name or your UF ID
anywhere in your submitted work. Please remember to bring your EML5311ID with you to all the
tests.
Make up exams etc.
If you have to miss an exam, you must see the instructor and make arrangements in advance unless an
emergency makes this impossible. No make-ups will be given for reasons other than medical emergencies or University business. The latter includes a college athlete having to miss a test due to his/her
required participation in a college athletics program, but does not include a student going to watch a
football game. In case of such an emergency, you must provide written evidence of the said emergency
within 7 days of the scheduled test date for you to qualify for a make up.
Computers, Calculators etc.
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MATLAB
- or some software like it - is required to solve some home work problems, and will be
essential for the take home parts of the exams. You may want to purchase the student version of
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MATLAB
, which contains the control systems toolbox. The full version (including many toolboxes)
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is available in the MAE Undergraduate Computer Lab in NEB 109, and at CIRCA computer clusters
campus-wide (labs.circa.ufl.edu).
Other possibilities for computational software are GNU Octave and Scilab, both of which are free and
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MATLAB
-like. Yet another possibility is to write programs in python, which has good libraries for
scientific computing, including solving ODE. Of course, you can also use C, C++ or Fortran.
You should bring a calculator to class and to the exams. Cellular phones, PDAs, etc. will NOT be
allowed in place of calculators.
Students with Disabilities
The University of Florida provides high-quality services to students with disabilities, and we encourage
you to take advantage of them. Students with disabilities needing academic accommodations should
1) Register with and provide documentation to Disability Resources (392-1261), and 2) Bring a letter
to the instructor from this office indicating that you need academic accommodations. Please do this
as soon as possible, preferably within the first week of class.
Academic Integrity
All students admitted to the University of Florida have signed a statement of academic honesty
committing themselves to be honest in all academic work and understanding that failure to comply
with this commitment will result in disciplinary action. Academic honesty is therefore taken quite
seriously in this class.
No collaboration of any sort is allowed in the take home exams. I highly recommend discussing the
home work problems with your colleagues, especially after you have you have spent some time attempting them yourself.
Changes to syllabus policy
Modifications to this syllabus may be made during the semester. Any changes to the syllabus will be
posted on the course web site and announced in class.
UF Counseling Services
Resources are available on-campus for students having personal problems or lacking clear career and
academic goals. The resources include:
• UF Counseling & Wellness Center, 3190 Radio Rd, 392-1575, psychological and psychiatric
services
• Career Resource Center, Reitz Union, 392-1601, career and job search services.
Software Use
All faculty, staff and student of the University are required and expected to obey the laws and legal
agreements governing software use. Failure to do so can lead to monetary damages and/or criminal
penalties for the individual violator. Because such violations are also against University policies and
rules, disciplinary action will be taken as appropriate. We, the members of the University of Florida
community, pledge to uphold ourselves and our peers to the highest standards of honesty and integrity.
Email policy I will not reply to emails with requests for explanations about homework/test problems
or about doubts on lecture material. I have office hours for this purpose.
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