Robust Control Course
E-courses Dr. Hamid D. Taghirad  

 Description   Contents   References   Assignments   Documents   Programs   Software   Papers   Links 


 
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Course Description
   
Course Name:  Robust Control
Course No.  EE - 43131
Professor:  Dr. Hamid D. Taghirad
Semester:  Fall 94
Room and Time:  Mon-Wed: 9:00-10:30 Room 304
Office Hours:  Mon-Wed: 8:00-9:00

Course Contents (pdf)

In this course the stability and performance analysis of feedback system in the presence of model uncertainty are introduced, and robust controller synthesis methods for uncertain systems are presented. The scope of the course is limited to linear systems, LFT type of uncertainty, H control and μ-analysis and synthesis. In addition to elaborate the required theory, the students learn how to use Robust Control Toolbox of Matlab. Moreover, a comprehensive design project is thoroughly accomplished by the students as a term project.

The tentative course contents are as following.
Time:   Contents
Week 1

Introduction:  Modeling, uncertainty and robustness,  Sensitivity function,  General regulator problem,  Small-gain theorem and H

Week 2 Normed Spaces:  Norms of signals, Norms of systems, Relation between signals and systems norm, Computing 2 and norms, Multivariable norms, Hilbert and Banach spaces.
Week 3

Robust problems Modeling: Plant uncertainty, different types of uncertainty, parametric uncertainty, unstructured uncertainty, illustrative examples.

Week 4

Robust problems Analysis:  Internal stability, Robust stability, based on Sensitivity functions, H norms, and structured singular values.

Week 5

Robust controller synthesis:  Controller parameterization, Design constraints, algebraic constraints, analytic constraints, interpolation conditions, waterbed effect.

Week 6

Mixed Sensitivity Problem:  Definition to mixed sensitivity, the augmented state-space model.

Week 7

Solution to general regulator problem (Methods): H2, H solutions based on Ricatti Equations. H solutions based on LMI, H2/ H solutions.

Week 8

Solution to general regulator problem (Methods): H solutions based on LMI, H2/ H solutions.

Week 9

      Midterm Exam

Week 10

Solution to general regulator problem (implementations): Design for SISO and Non-minimum phase, Comprehensive case study.

Week 11

Solution to general regulator problem (implementations): Design for unstable and Non-minimum phase systems and disturbance rejection, Comprehensive case study.

Week 12

μ Analysis: Structured singular values,  μ -Analysis.

Week 13

μ synthesis:  μ -Synthesis, Comprehensive case studies.

Week 14

Case studies: Control of F14 Aircraft, robust problem formulation, controller synthesis, performance evaluation and improvement.

Week 15

Case studies: Three inertia system: robust modeling and identification, weighting function selection, H and H2/ H controller design and improvement, μ synthesis, controllers performance evaluations.

 

 

References:

1

کنترل مقاوم H ، حمیدرضا تقی راد، محمد فتحی و فرینا زمانی اسگویی، انتشارات دانشگاه صنعتی خواجه نصیرالدین طوسی، چاپ دوم، 1393.

2

Doyle, Francis, Tannenbaum, “Feedback Control Theory” ,Macmillan Publishing, 1990 .

3

Zhou K., with  J. Doyle, "Essentials of Robust Control", Prentice Hall, 1998.

4

Skogestad S. and I. Postlethwaite "Multivariable Feedback Control", John Wiley & Sons, 1996.

5

G.E. Dullerud and F. Paganini, "A course in Robust Control Theory: A convex Approach" , Springer Verlag, 1991.

6

P.R. Belanger, “Control Engineering, A modern approach”,  Saunders College, 1995.

7

“Robust toolbox", user manual, version 3.1.1, Mathworks, 2006.

8

Selected papers and handouts.

Assignments

Assignments (pdf) Solved Problems Projects (pdf) Exams (pdf)
Assignment 1   Solution SP1, SP2, SP3  CP1    Midterm
Assignment 2   Solution KTH  CP2  Final exam date   Final
Assignment 3   Solution Stuttgart    
Assignment 4   Solution Purdue     Final Grades
Assignment 5   Solution SamplePapers    

Course Evaluation

For Those of you who wants to provide me your valuable course evaluation and comments.

Course Documents:

 
 
 Main Textbook (pdf):
 part 1, part 2, part 3, part 4, part 5, part 6, part 7, part 8, part 9, part 10, part 11, part 12, Refs.
 Matlab Toolboxes user manuals (pdf):
 Robust control Toolbox  LMI toolbox µ-synthesis toolbox
Other handouts (pdf):

Mixed H2-H

Dr. Zames Handout on Bode Theorem and Non-min phase systems
An Introductory Tutorial to QFT (pdf)

Developed Programs

Course Examples (m-files):
Robust stability 1, Robust stability 2, mixed sensitivity, flexible beam, mu-analysis, space shuttle, HIMAT  (zip)
Mu-synthesis file formats: (zip)

Software

 Mathworks Matlab:
 LMI Toolbox Guide, µ-synthesis Toolbox Guide, QFT Toolbox Guide, Robust Toolbox Guide
 Matlab Toolboxes user manuals (pdf):
 µ-synthesis toolbox  LMI toolbox      

Related Papers

1.

State-space solutions to standard H/sub 2/ and H/sub infinity / control problems, Doyle, J.C.; Glover, K.; Khargonekar, P.P.; Francis, B.A. Source: IEEE Transactions on Automatic Control, v 34, n 8, Aug. 1989, p 831-47

2.

State-space formulae for all stabilizing controllers that satisfy an H/sub infinity /-norm bound and relations to risk sensitivity, Glover, K.; Doyle, J.C. Source: Systems & Control Letters, v 11, n 3, Sept. 1988, p 167-72

3. Simplifying the H/sup infinity / theory via loop shifting, Safonov, M.G.; Limebeer, D.J.N. Source: Proceedings of the 27th IEEE Conference on Decision and Control , 1988, p 1399-404 vol.2
4.

Optimal, constant I/O similarity scaling for full-information and state-feedback control problems, Packard, A.; Kemin Zhou; Pandey, P.; Leonhardson, J.; Balas, G. Source: Systems & Control Letters, v 19, n 4, Oct. 1992, p 271-80

5. An LMI-based parametrization of all H/sub infinity / controllers with applications; Gahinet, P.; Apkarian, P. Source: Proceedings of the 32nd IEEE Conference on Decision and Control (Cat. No.93CH3307-6), 1993, pt. 1, p 656-61 vol.1
6. All controllers for the general H/sub infinity / control problem: LMI existence conditions and state space formulas; Iwasaki, T. ; Skelton, R.E. Source: Automatica, v 30, n 8, Aug. 1994, p 1307-17
7. Multiobjective output-feedback control via LMI optimization, Scherer, C.; Gahinet, P.; Chilali, M. Source: IEEE Transactions on Automatic Control, v 42, n 7, July 1997, p 896-911
8.

H/sub infinity / design with pole placement constraints: an LMI approach; Chilali, M.; Gahinet, P. Source: IEEE Transactions on Automatic Control, v 41, n 3, March 1996, p 358-67

9. mu -analysis and synthesis Toolbox ( mu -tools), Balas, G.J. Doyle, J.C.; Glover, K.; Packard, A.; Smith, R. Source: Automatica, v 30, n 4, April 1994, p 733-5
10.

The complex structured singular value; Packard, A. ; Doyle, J. Source: Automatica, v 29, n 1, Jan. 1993, p 71-109

11. H.D. Taghirad and P.R. Belanger, H∞ -based robust torque control of harmonic drive systems, Journal of Dynamic Systems, Measurements, and Control, ASME Pub., 123(3) pp 338-345, Sept. 2001.
12. H.D. Taghirad and s. Gholampour, Robust position control of hydraulic robotic shoulder, In the Proceedings of  the  12th International Conference on Electrical Engineering, May 2004, Mashad.
13. M. Tavakoli, H. D. Taghirad and M. Abrishamchian, Parametric and Nonparametric Identification and Robust Control of a Rotational/Translational Actuator, In Proceedings of The Fourth International Conference on Control and Automation (ICCA'03), pp. 765-769, June 2003, Montreal, Canada.
14. H.D. Taghirad and A. Shariati, H∞ control of active suspension system for Ľ car model with hydraulic actuators,  in the proceeding of 12th  International conference of Electrical Engineering, Shiraz, May 2003, Vol 3, pp 60-67.
15. H.D. Taghirad and GH. Bakhshi, Composite-H∞ Controller Synthesis for Flexible Joint Robots, Submitted to the IEEE International Conference on Intelligent and Robotic Systems, 2002.
16. H.D. Taghirad and S. Afshar, Linear identification and PID controller design and implementation on a SCARA robot, Proceedings of 8th International Conference on Electrical Engineering, May 1999, Isfahan.
17. H.D. Taghirad and P.R. Belanger, Robust friction compensation for harmonic drive system, Proceedings of IEEE international Conference on Control Application, pp 547-551, 1997, Trieste, Italy.
18. H.D. Taghirad and P.R. Belanger, H∞-based robust torque control of harmonic drive systems, Proceedings of IEEE international Conference on Control Application, pp 990-994, 1997, Trieste, Italy.
19. H.D. Taghirad and P.R. Belanger, Intelligent torque sensing and robust torque control of harmonic drive under free-motion, In Proceedings of the IEEE International Conference on Robotics and Automation, 2:1749-54, April 1997.
20. H.D. Taghirad and P.R. Belanger, Robust torque control of harmonic drive under constrained-motion, In Proceedings of the IEEE International Conference on Robotics and Automation, 1:248-253, April 1997.

Related Links
 A tribute to Dr. G. Zames
.Robust Control at Stuttgart University by Dr Frank Allgöwer (2009)
 Robust Control at Eindhoven University of Technology by B.A. Cornelissen (2005)
 Introduction to Robust Control by V. Balakrishnan (2003).
 Robust Control at EPFL by Dr. Karimi
 Process Control at University of Newcastle. Robust Control Study Notes by M. Tham (1998).
 JAVA applets for control by W. Rugh et al. (2000).
 Carsten W. Scherer homepage at Delft university
   

 


 Description   Contents   References   Assignments   Documents   Programs   Software   Papers   Links 

Copyright © Dr. Hamid D. Taghirad
K.N. Toosi University of Technology
Last Updated Monday September 14, 2015