Robust Control, Spring, 2016

(ƒƒoƒXƒg§Œδ)
(Course Number: SCE.C402)

Instructor

Prof. Masayuki Fujita

Department of Control and Systems Engineering, Tokyo Tech

Office: S5-303B

Lecture Time and Place

Tuesday 3-4 periods (10:45-12:15), S423 Lecture Room

Credit

Unit: 1-0-0

Teaching Assistants

Riku Funada, Mamoru Doi, Junya Yamauchi (S5-303A)

Email : tateam_at_fl.ctrl.titech.ac.jp

Please send e-mail to above address if you have any questions.

Office Hour

Course Learning Outcomes

1. An ability to formulate, analyze and design fundamental control problems

2. An ability to use a numerical computing environment, such as MATLAB, to solve engineering problems

Grading

Reports on 5th(40%), 7th(45%) and 8th(15%) classes.

Textbook

The course will follow closely:

[SP05] S. Skogestad and I. Postlethwaite, "Multivariable Feedback Control: Analysis and Design, Second Edition," Wiley, 2005 (ISBN: 978-0-470-01167-6).

Reference Books

Other recommended texts are:

[M16] "Robust Control Toolbox Documentation(R2016a)," MathWorks, 2016.
[ZD97] K. Zhou and J. C. Doyle, "Essentials of Robust Control," Prentice Hall, 1997 (ISBN: 0-13-525833-2).
[DP05] G.E. Dullerud and F. Paganini, "A Course in Robust Control Theory: A Convex Approach," Text in Applied Mathematics, Springer, 2005 (ISBN: 978-1-4757-3290-0).

Computer Access and MATLAB

The students can install MATLAB R2016a (MATLAB, Robust Control Toolbox) in your computer. Please see the GSIC's installation guide for more details.

The students can also use MATLAB R2016a at GSIC.

Lecture Schedule

Schedule
Lecture Date Topics Reading Assignment Handouts Report
1st4/5 1. Multivariable Feedback Control
and Nominal Stability
  1.1 Multivariable Feedback Control
  1.2 Multivariable Frequency Response Analysis
  1.3 Internal Stability
  1.4 All Stabilizing Controllers
 [SP05]
Sec. 3.5
Sec. 3.3, A.3, A.5
Sec. 4.1, 4.7
Sec. 4.8
    
2nd4/12 2. Nominal Performance
  2.1 Nominal Performance
  2.2 Sensitivity Minimization
  2.3 Fundamental Limitations 		[SP05]
Sec. 2.8
Sec. 2.8
    
3rd4/19 3. SISO Loop Shaping
  3.1 Computer Controlled System
  3.2 Modeling
  3.3 Example
 [SP05]
Sec. 3.7, 1.4, 1.5
Sec. 2.6, 5.6, 5.7, 5.9

    
4th4/26 4. Robustness and Uncertainty
  4.1 Why Robustness?
  4.2 Representing Uncertainty
  4.3 Uncertain Systems
  4.4 Systems with Structured Uncertainty
 [SP05]
Sec. 4.1.1, 7.1, 9.2
Sec. 7.2, 7.3, 7.4
Sec. 8.1, 8.2, 8.3
Sec. 8.2
    
5th5/10 5. Robust Stability and Loop Shaping
  5.1 Robust Stability and Robust Stabilization
  5.2 Mixed Sensitivity and Loop Shaping
  5.3 1st Report
 [SP05]
Sec. 7.5, 8.4, 8.5
Sec. 2.6, 2.8, 9.1

    
6th5/17 6. H‡ Control
  6.1 General Control Problem Formulation
  6.2 H‡ Control Problem and DGKF Solutions
  6.3 Structure of H‡ Controllers
 [SP05]
Sec. 3.8
Sec. 9.3

    
7th5/24 7. Design Example
  7.1 Spinning Satellite: H‡ Control
  7.2 2nd Report

   
8th
(45min.)		5/31 8. Design Example
  8.1 HiMAT: H‡ Control
  8.2 3rd Report 		     

Tokyo Tech OCW

Check here

Prerequisites

Students are expected to have taken feedback control, modern control and system control theory.

The following texts may be useful for some students.

[AM09] K. J. Astrom and R. M. Murray, "Feedback Systems," Princeton University Press, 2009 (ISBN: 978-0-691-13576-2).
[SF99] T. Sugie and M. Fujita, "Introduction to Feedback ControliƒtƒB[ƒhƒoƒbƒN§Œδ“ό–εj," Corona Publishing Co., LTD., 1999 (ISBN: 4-339-03303-0).

Supplemental Materials

This page augments the main text with discipline-specific materials and additional information.

Theoretical Materials
Topics Handouts
A. SISO Feedback Control
  A.1 Internal Stability and Youla Parameterization
  A.2 Sensitivity and Feedback Perforemance
  A.3 Loop Shaping
Related Book/Paper
A.1 [SP05] Sec. 3.2, 4.1.5, 4.7, 4.8, A.2 [SP05] Sec. 2.2, 5.2,
A.3 [SP05] Sec. 2.4, 2.6 		 
B. Robust Performance
  B.1 ƒΚ-synthesis and DK-iteration
  B.2 Design Example: Spinning Satellite
Related Book/Paper
B.1 [SP05] Sec. 8.12 		 
C. H‡ Loop Shaping Design
  C.1 Perturbations of Coprime Factors
  C.2 Robust Stabilization
  C.3 Loop Shaping Design Procedure
  C.4 Design Example
Related Book/Paper
C.1 [SP05] Sec. 4.1.5, C.2 [SP05] Sec. 9.4.1, C.3 [SP05] Sec. 9.4.2 		 
D. Linear Matrix Inequality (LMI)
  D.1 Convex Optimization
  D.2 Linear Matrix Inequality (LMI)
  D.3 Control Design and LMI Formulation
Related Book/Paper
[SP05] Sec. 12 		 
E. LPV System and Gain Scheduling
  E.1 Linear Parameter Varying(LPV) System
  E.2 Quadratic Stabilization
  E.3 Gain Scheduing
  E.4 Design Example
Related Book/Paper
[DP05] Sec. 11 		 
F. Integral Quadratic Constraints(IQCs)
  F.1 Passivity and Dissipative System
  F.2 IQC Formulation
  F.3 Robust Stability via IQCs
  F.4 Design Examples
Related Book/Paper
[DP05] Sec. 10.1 		 
G. Sum of Squares(SOS)
  G.1 SOS Program: SOS/PSD and SDP
  G.2 Duality, valid ineqalities and Cone
  G.3 Feasibility/Optimization and Ideal
  G.4 Exploiting Structure
Related Book/Paper
  • [BPT13] Chapter 3
    G. Blekherman, P. A. Parrilo and R. R. Thomas,
    "Semidefinite Optimization and Convex Algebraic Geometry"
    MOS-SIAM Series on Optimization, Society for Industrial
    and Applied Mathematics (SIAM), 2013 (ISBN: 978-1-61197-228-3).
  • SOSTOOLS User's guide
    		•  
    Experimental Materials
    Q. Flexible Beam: Mixed Sensitivity
    		  
    R. Flexible Beam: Signal-based H‡ Control
    		  
    S. Magnetic Suspension System: ƒΚ-synthesis
    		  
    T. Magnetic Bearing: Robust Performance
    		  


    Collaboration Policy

    Collaboration on homework assignment is encouraged. But it is forbidden to copy solutions from other students.

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