2016 | Robust Control - TOKYO TECH OCW

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2016　Robust Control

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Academic unit or major: Graduate major in Systems and Control Engineering

Instructor(s): Fujita Masayuki

Class Format: Lecture

Media-enhanced courses

Day/Period(Room No.): Tue3-4(S423)

Group: -

Course number: SCE.C402

Credits: 1

Academic year: 2016

Offered quarter: 1Q

Syllabus updated: 2016/4/27

Lecture notes updated: -

Language used: English

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Syllabus

Course description and aims

The purpose of this course is to provide the students with the principles and tools of robust control theory: nominal stability, nominal performance, robustness, uncertainty, robust stability, loop shaping, H∞ control, robust performance. The students will be introduced to the computational tools for dynamical systems available in Robust Control Toolbox (MATLAB).

The applications of robust control theory are spreading to diverse areas such as aerospace systems, chemical processes, power networks, and control of fluids. This course will focus on the introduction of the fundamentals of robustness, uncertainty and design method of H∞ control. Any dynamical model of a system will neglect some physical phenomena. Therefore, a model set that includes the true physical plant can never be constructed. A design technique must help make this gap small, and H∞ control focused on this course minimizes H∞ norm of the feedback systems and to reduce its sensitivity in front of perturbations and uncertainties. Since robust control theory was the most active area from the 1970s through the 1990s, the students will be provided with the fundamentals of mainstream systems theory.

Student learning outcomes

By the end of this course, students will be able to:
１） Explain the motivation of robust control.
２） Compute nominal stability and nominal performance.
３） Explain robustness and uncertainty of systems.
４） Explain robust stability and loop shaping.
５） Acquire the fundamentals of H∞ control, and based on this knowledge, design feedback control systems.
6） Understand robust performance.

Keywords

Robustness, Uncertainty, Nominal Stability, Nominal Performance, Robust Stability, Loop Shaping, H∞ Control, Robust Performance

Competencies that will be developed

✔ Specialist skills

Intercultural skills

Communication skills

Critical thinking skills

✔ Practical and/or problem-solving skills

Class flow

The students will be provided with key concepts along with effective examples in each class. To allow students to get a good understanding of the course contents, problems related to the contents of this course are assigned as homework. Always check the required learning for each class and be sure to complete it as a part of preparation and review.

Course schedule/Required learning

	Course schedule	Required learning
Class 1	Multivariable feedback control, nominal stability - MIMO system, internal stability, Q-parametrization	Understand the property of MIMO system and explain nominal stability.
Class 2	Nominal performance - Multivariable frequency response, sensitivity function, sensitivity minimizing problem, performance weight	Explain the relation between the specification of feedback systems and sensitivity minimizing problem.
Class 3	Robustness - Stability margin, modeling, uncertain weight	Understand the inherent uncertainty in a model and explain its representation.
Class 4	Uncertainty, robust stability - Set of models, structured uncertainty, small gain theorem, robust stabilization	Compute the representation of uncertain systems and robust stability.
Class 5	Loop shaping, mixed sensitivity, fundamental limitations - Mixed sensitivity problem, open loop transfer function, unstable zero, unstable pole	Explain the loop-shaping approach, mixed sensitivity problem and understand fundamental limitations of feedback systems.
Class 6	H∞ Control - Generalized plant，H∞ control problem, DGKF	Understand the basic idea of H∞ control problem and explain the fundamentals.
Class 7	Design Examples - Design of feedback systems by H∞ control	Design control systems by Robust Control Toolbox based on the knowledge of H∞ control.
Class 8	Robust performance, further topics - Structured uncertainty, μ-analysis	Understand robust performance and explain the concepts of further topics in robust control theory.

Textbook(s)

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

Reference books, course materials, etc.

[ZD97] K. Zhou and J. C. Doyle. Essentials of Robust Control. Prentice Hall; 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; ISBN: 978-1-4757-3290-0.
[M15] Robust Control Toolbox User's Guide R2015b. MathWorks.

Assessment criteria and methods

Students' knowledge of analysis, design methods for uncertain systems and the ability to apply them to problems will be assessed.
1st report 50%, 2nd report 50%.

Related courses

SCE.C501 ： Optimal Control
SCE.C401 ： System Identification and Estimation
SCE.C502 ： Hybrid Systems Control

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed Feedback Control (SCE.C.202), Linear System Theory (SCE.C.301) or have equivalent knowledge.

Other

Lecture Homepage: http://www.fl.ctrl.titech.ac.jp/course/ROC/index.html

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