Syllabus Electrical Engineering Department EE 653: Robust Control – Semester 162

Type

Time

Days

Where

Scheduled Meeting Times Date Range

Class

5 PM-6:15 PM

TU

Building #59 - 1005

February 5th 2017 to May 25th 2017

Schedule Type Lecture

Instructors SALIM IBRIR (Associate Prof.)

Instructor Dr. Salim Ibrir - B-59-1076, G floor - Email: [email protected] or [email protected] Office Hours: Monady, Wednasday and Thursday from 10 am to 12 noon I am available 15 min after the lecture

Course Content: Elements of robust control theory. Norms of signals and systems. Performance specifications. Modeling of uncertain linear systems and system parameterization. Model uncertainty and robustness. Polytopic uncertainties and norm-bounded uncertainties. Domain stability, 𝐻∞ norm, and 𝐻2 norm. Linear matrix inequalities and their numerical solutions. Stability of uncertain linear systems in continuous time and discrete time. 𝐻∞ Filtering, Loop transfer recovery. 𝐻∞ Control, Mixed 𝐻2 − 𝐻∞ control. Case studies. Text: 1. Jeffrey B. Burl, Linear optimal control, 𝐻2 and 𝐻∞ methods, Addison-Wesley, 1999. 2. K. Zhou, J. Doyle, and K. Glover. Robust and Optimal Control. Prentice Hall, Englewood Cliffs, New Jersey, 1996. Other texts and publications: 1. Katsuhiko Ogata, Matlab for control engineers, Prentice Hall, 2008. 2. Brian D. O. Anderson, and John B. Moore, Optimal control: linear quadratic methods, Prentice Hall International, Inc, 1989. 3. Arthur E. Bryson Jr., and Yu-Chi Ho, Applied optimal control, optimization, estimation, and control, Taylor & Francis, 1975. 4. G. Chesi. LMI techniques for optimization over polynomials in control: a survey, IEEE Transactions on Automatic Control, 55(11):2500–2510, 2010. 5. S. Ibrir, Convex optimization approach to observer-based stabilization of uncertain linear systems, Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, Vol. 128, pp. 989-994, December 2006. (Available on the web site of the Instructor). 6. S. Ibrir, Design of static and dynamic output feedback controllers through Euler approximate models: Uncertain systems with norm-bounded uncertainties, IMA Journal of Mathematical Control and Information, Elsevier, Vol. 25, pp. 281-296, 2008. 7. S. Ibrir and S. Diop, Novel LMI conditions for observer-based stabilization of Lipschitzian nonlinear systems and uncertain linear systems in discrete-time, Applied Mathematics and Computation, Vol. 206, no. 2, pp. 579-588, December 2008.

8. B. Barmish. Necessary and sufficient conditions for quadratic stabilizability of an uncertain system. J. Optimization Theory and Applications, 46(4), Aug. 1985. 9. D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou. A new robust D-stability condition for real convex polytopic uncertainty. Systems & Control Letters, 40(1):21–30, May 2000. Course outcomes: 1. 2. 3. 4. 5.

Synthesize of uncertain linear systems in continuous time and discrete time. Define, isolate, and formalize the system uncertainties. Learn how to add more control objectives and get a possible solution. Design, assess, and simulate linear robust feedback under system uncertainties. Construct, demonstrate, analyze, synthesize, and implement robust feedback under system uncertainties. 6. Assess and apply modern optimal and robust 𝐻2 and 𝐻∞ feedbacks. 7. Understand the difference between robust and adaptive control. Grading Policy: Home-works: 15% Project: 25% Mid-Term Exam: 25% Final Exam: 35%

Tentative schedule Week

1

2

3

4

5

6

7

8

Topics

February 5

th

February 12th

February 19th

February 26th

March 5th

March 12th

March 19th

March 26th

Signal norms, Different norms of transfer function, Positive-definite matrices and their properties, The Algebraic Ricatti Equation (ARE), State-space modeling, Lyapunov function, exponential stability. Different types of system uncertainty, Modeling of uncertain linear systems, External uncertainties, Systems with uncertain parameters, Controlling under system uncertainty conditions. Norm-bounded uncertainties, Polytopic uncertainties, 𝐻2 and 𝐻∞ norms of transfer functions, SISO and MIMO systems. Stability of uncertain continuous-time linear systems, stabilizability of linear continuous-time systems. Linear Matrix Inequalities (LMIs) in Control, Convex optimization, The search of possible numerical solutions, LMIs versus AREs. Stability of discrete-time uncertain systems, stabilizability issues, Limitation of linear statespace feedbacks. Prescribed degree of stability, optimal pole placement, Domain stability, Multi-objective control designs. Presentation of robust control package of Matlab and convex-optimization routines of Matlab, Case studies.

Reading Assignment

Assignments and Projects

Lecturer Notes 1

Lecturer Notes 2

Homework 1 Projects distribution and selection

Lecturer Notes 3

Deadline of project selection

Lecturer Notes 3

Homework 1 due by the end of week 4.

Lecturer Notes 4

Homework 2

Lecturer Notes 5

First progress reports of the projects are due (Literature Review must be completed by the end of week 6)

Lecturer Notes 6

Homework 2 is due

Simulation

Distribution of Homework 3

Last day of classes – March 30th, 2017 - Mid-Term Vacation: April 2nd, to April 9th, 2017 April 9th

9

10 11 12

April 16th

April 23th April 30

th

May 7th

13 14 15

May 14th

May 21th

𝐻∞ Control of linear systems, Design examples, Numerical simulations. The continuous time and the discrete-time cases. 𝐻2 Control of linear systems, Design examples, Numerical simulations. The continuous time and the discrete-time cases. Mixed 𝐻2 -𝐻∞ control objective. The continuoustime case Mixed 𝐻2 -𝐻∞ control objective. The discrete-time case 𝐻∞ filtering, Observer-based control, problems and limitations of robust linear feedbacks.

Lecturer Notes 7 Lecturer Notes 8

Homework 3 is due by the end of week 10

Lectures notes 9

Major Exam

Lecturer Notes 10

Projects due by the end of week 13. Final report must be submitted as hard copy.

Project presentations and discussions. Oral presentations followed by questions. Review session May 25th, 2017: Last day of classes Final Exam: Refer to the registrar web site

Important point to remember Pre-requisite: Upon entering this course, all the students should be able to:  Demonstrate a good understanding of the fundamental theory of linear systems in continuous-time and discrete time;  Demonstrate basic understanding of system stability theory in state space;  Demonstrate a good knowledge of differential equations and basic notions of linear algebra;  Perform numerical simulations using Matlab/Simulink software.

Projects: One or two students can select one common project. All the projects may cover one or more topics in system design and control. The project cannot be changed after selection. Academic dishonesty is a serious offense which should not be taken lightly. Cheating, falsification, and plagiarism are both forms of academic dishonesty. Please note that academic dishonesty has grave consequences which may include receiving “no grade” on the project. Attendance: According to the university regulations, any student that exceeds 20% (9 lectures) of the scheduled class meeting without an official excuse will receive a grade DN in the course. Official excuses: All official excuses must be submitted to the instructor no later than one week of the date of the official excuse. The instructor may not accept late excuses. Lecturer notes: The lecturer notes that are distributed in class or sent as electronic files are supporting documents that enhance the content or clarify the difficult aspects of the course. The lecturer notes can be also the electronic files of the slides discussed in course.