2019 Robust Control

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Academic unit or major
Graduate major in Systems and Control Engineering
Fujita Masayuki 
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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 control systems available in Robust Control Toolbox (MATLAB).
The applications of robust control theory are spreading to diverse areas such as aerospace systems, chemical processes, automobiles, mechatronics and power networks. This course will focus on an introduction to the fundamentals of robustness, uncertainty and design method of H∞ control. H∞ control minimizes H∞ norm of the feedback systems and to reduce its sensitivity in front of perturbations and uncertainties. Since robust control theory has been one of the most active research area, the students will be provided the fundamentals of mainstream control 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 multivariable feedback control systems.
6) Understand robust performance.


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

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
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Class flow

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

Course schedule/Required learning

  Course schedule Required learning
Class 1 Multivariable feedback control, nominal stability - MIMO system, σ-plot, internal stability, Q-parametrization Understand the property of MIMO system and explain nominal stability.
Class 2 Nominal performance - Sensitivity minimization, performance weight Explain the relation between the specification of feedback systems and sensitivity minimizing problem.
Class 3 Robustness, uncertainty - Stability margin, set of models, uncertain weight Understand the inherent uncertainty in a model and explain its representation.
Class 4 Robust stability, loop shaping, fundamental limitations - Small gain theorem, robust stabilization, mixed sensitivity problem Understand robust stability, the loop-shaping approach, mixed sensitivity problem and fundamental limitations of feedback systems.
Class 5 H∞ Control - Generalized plant,H∞ control problem, DGKF Understand the basic idea of H∞ control problem and explain the fundamentals.
Class 6 Design Example 1 - Spinning satellite: design of feedback system by H∞ control Design control system by Robust Control Toolbox based on the knowledge of H∞ control.
Class 7 Robust performance - Robust performance, structured singular value μ, μ-analysis and synthesis Understand the concepts of robust performance, μ-analysis and μ-synthesis
Class 8 Design Example 2 - HiMAT: design of feedback system by H∞ control Design control system by Robust Control Toolbox based on the knowledge of H∞ control.


[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.
[M17] Robust Control Toolbox User's Guide R2017a. 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 45%, 2nd report 55%.

Related courses

  • SCE.C501 : Optimal Control
  • SCE.C401 : System Identification and Estimation

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.


Lecture Homepage: http://www.hfg.sc.e.titech.ac.jp/course/ROC/index.html

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