Robust Control, Spring, 2018

Instructor

Prof. Masayuki Fujita Department of Systems and Control 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

Hayato Dan, Made Widhi Surya Atman, Kosei Noda (S5-204A)

Email :

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

Office Hour

• Friday 16:30-17:30, S5-204A

Course Learning Outcomes

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

• Multivariable Feedback Control
• Nominal Stability and Nominal Performance
• Robustness and Uncertainty
• Robust Stability and Loop Shaping
• H∞ Control
• Robust Performance: μ-Analysis (and Synthesis)
• Design Examples

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

Grading

Reports on 2nd(15%), 4th(30%) and 6th(55%) classes.

Textbook

The course will follow closely:

Reference Books

Other recommended texts are:

Tokyo Tech OCW

Check here

Computer Access and MATLAB

The students can install MATLAB R2018a (MATLAB, Robust Control Toolbox) in your computer. Please see the GSIC's installation guide for more details. The students can also use MATLAB R2017a at GSIC.

Collaboration Policy

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

Lecture Schedule

Schedule
Lecture	Date	Topics	Reading Assignment	Handouts	Report
1st	4/10	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
2nd	4/17	2. Nominal Performance   2.1 Weighted Sensitivity   2.2 Nominal Performance   2.3 Sensitivity Minimization   2.4 Remarks on Fundamentals Limitations   2.5 1st Report	[SP05] Sec. 2.8, 3.3, 4.10, 6.2, 6.3 Sec. 2.8, 3.2, 3.3 Sec. 3.2, 3.3, 9.3 Sec. 6.2
3rd	4/24	3. Robustness and Uncertainty   3.1 Why Robustness?   3.2 Representing Uncertainty   3.3 Uncertain Systems   3.4 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
4th	5/1	4. Robust Stability and Loop Shaping   4.1 Robust Stability and Robust Stabilization   4.2 Mixed Sensitivity and Loop Shaping   4.3 2nd Report	[SP05] Sec. 7.5, 8.4, 8.5 Sec. 2.6, 2.8, 9.1
5th	5/8	5. H∞ Control   5.1 General Control Problem Formulation   5.2 H∞ Control Problem and DGKF Solutions   5.3 Structure of H∞ Controllers	[SP05] Sec. 3.8 Sec. 9.3
6th	5/15	6. Design Example 1   6.1 Spinning Satellite: H∞ Control   6.2 3rd Report	[SP05] Sec. 3.7
7th	5/22	7. Robust Performance   7.1 Robust Performance   7.2 Structured Singular Value μ   7.3 μ-Analysis and Synthesis	[SP05] Sec. 7.6, 8.3, 8.4, 8.10 Sec. 8.5, 8.6, 8.8, 8.11 Sec. 7.6, 8.9, 8.10, 8.11
8th (45min.)	5/29	8. Design Example 2   8.1 HiMAT: H∞ Control	[M17]

Supplemental Topics	Handouts
B. Robust Performance   B.1 μ-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 D.1 [SP05] Sec. 4.1.5, D.2 [SP05] Sec. 9.4.1, D.3 [SP05] Sec. 9.4.2

Case Studies	Handouts
Q. Flexible Beam: Mixed Sensitivity
R. Flexible Beam: Signal-based H∞ Control
S. Magnetic Suspension System: μ-synthesis
T. Magnetic Bearing: Robust Performance

Prerequisites

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

The following texts may be useful for some students.

Prerequisites	Handouts
A1. SISO Feedback Control   A1.1 Internal Stability and Youla Parameterization   A1.2 Sensitivity and Feedback Perforemance   A1.3 Loop Shaping Related Book/Paper A1.1 [SP05] Sec. 3.2, 4.1.5, 4.7, 4.8, A1.2 [SP05] Sec. 2.2, 5.2, A1.3 [SP05] Sec. 2.4, 2.6
A2. SISO Loop Shaping   A2.1 Computer Controlled System   A2.2 Modeling   A2.3 Example Related Book/Paper A2.1 [SP05] Sec. 3.7, 1.4, 1.5, A2.2 [SP05] Sec. 2.6, 5.6, 5.7, 5.9

Additional Materials

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

Additional Topics	Handouts
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 SOSTOOLS User's guide
H. System Level Synthesis(SLS) Related Book/Paper System level synthesis: A tutorial SLS Toolbox	wiki

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