The purpose of this course is to provide the students with the principles and tools of feedback control: sensitivity, steady-state error, vector locus, Bode plots, internal stability, Nyquist criterion, stability margin, robustness, loop shaping, PID control and two degree-of-freedom control. The students will be introduced to the computational tools for dynamical systems available in Control System Toolbox (MATLAB/Simulink).
Topics covered include analysis in time and frequency domains, design in the frequency domain, and these basic principles and techniques can be employed in a wide variety of applications. This course provides an introduction to the concept of loop shaping using PID control and phase lead-lag compensation as a mechanism for designing controllers in the frequency domain. PID control is by far the most common design technique in control systems and a useful tool for any student. A key reason for using feedback is to reduce the effects of uncertainty which may appear in imperfect models. The students will also be introduced to the key concept of robustness analysis of feedback systems.
By the end of this course, students will be able to:
１） Explain advantages of feedback control.
２） Explain characteristic of feedback systems: sensitivity and steady-state behavior.
３） Understand frequency response of systems and represent vector trajectory and bode diagram.
４） Understand internal stability of feedback systems and apply nyquist stability criterion.
５） Explain model uncertainty and robustness analysis of feedback systems.
６） Acquire the fundamentals of loop shaping, PID compensation and phase lead-lag compensation and apply to design feedback systems.
７） Explain two degrees-of-freedom control systems.
Feedback, Stability, Frequency Response, Robustness, Loop Shaping, Two Degrees-of-Freedom Control
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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- | - | ✔ | - | ✔ |
At the beginning of each class, lectures on the course objectives are given while focusing on interactions with students. Towards the end of class, students are given exercise problems related to the lecture.To prepare for each class, students should read the textbook and check what topics will be covered. To allow students to get a good understanding of the course contents and practice application, MATLAB-based homework are provided.
Course schedule | Required learning | |
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Class 1 | Introduction: what is feedback, benefits of feedback control and exercise - Feedback control, feedforward control | Review the dynamical systems. |
Class 2 | MATLAB/Simulink Exercise - How to use Control System Toolbox | Review how to make simulation by using transfer function representation. |
Class 3 | Property of feedback systems: sensitivity, steady-state error and exercise - Sensitivity function, closed-loop transfer function, loop transfer function, steady-state error | Compute transfer function, steady-state error. [1] p. 85 exercise 5, [2] p. 50 example 4.3. |
Class 4 | Property of feedback systems, frequency response: steady-state error, root locus, frequency response, transfer function and exercise - Vector locus, Bode diagram, gain diagram | Understand vector locus and Bode diagram. |
Class 5 | Frequency response: vector locus, Bode diagram and exercise - Bode diagram, gain diagram | Explain and illustrate the fundamental vector locus and Bode diagram. |
Class 6 | Frequency response: vector locus, Bode diagram and exercise - Bode diagram, gain diagram | [1] p. 104 exercise 6 and [2] p. 71 5.8. |
Class 7 | Internal stability of feedback systems: internal stability, Nyquist stability criterion and exercise - Internal stable, characteristic polynomial, Nyquist stability criterion | Explain internal stability and Nyquist stability criterion. |
Class 8 | Internal stability of feedback systems: internal stability, gain margin, phase margin and exercise - Phase margin, gain margin, phase crossover frequency, gain crossover frequency | Derive gain margin and phase margin from Bode diagram, and understand the relationship with stability. |
Class 9 | Stability analysis of feedback systems using MATLAB/Simulink - Solve some examples of Bode diagram and Nyquist stability criterion | Test level of understanding and self-evaluate achievement for classes 1–8. |
Class 10 | Robustness analysis of feedback systems: uncertainty and robustness and exercise - Robustness, uncertainty, nominal model, model set nominal performance, robust performance | Explain uncertainty and robustness. |
Class 11 | Robustness analysis of feedback systems: uncertainty, robustness and exercise - Robust stability, sensitivity function, complementary sensitivity function, nominal performance, robust performance | Understand and explain robust stability, nominal performance and robust performance. |
Class 12 | Feedback systems design: PID compensation, phase lead-lag compensation and exercise - Design process, performance evaluation, loop shaping | Understand PID compensation, the methods of performance evaluation, the concept of loop shaping. |
Class 13 | Feedback systems design: PID compensation, phase lead-lag compensation and exercise - Phase lead-lag compensation | Explain the design methods of phase lead and lag compensations. |
Class 14 | Feedback systems design: PID compensation, phase lead-lag compensation and exercise - Phase lead-lag compensation | Explain the design method of phase lead-lag compensation. [1] p. 167 exercise 7, 8. |
Class 15 | Feedback systems design: PID compensation, phase lead-lag compensation, two degree-of-freedom control and exercise - Feedforward, feedback, 2 degree-of-freedom control | Explain the property and design method of 2 degree-of-freedom control. |
[1] Sugie Toshiharu, Fujita Masayuki. Introduction to Feedback Control. Tokyo: Coronasha; ISBN: 4-339-03303-0. (Japanese)
[2] Sugie Toshiharu, Kagiwara Hiroyuki. Exercise in System Control Engineering. Tokyo: Coronasha; ISBN: 978-4-339-03306-9. (Japanese)
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Students' knowledge of analysis, design methods for feedback systems and the ability to apply them to problems will be assessed.
Exercise, homework and also your interaction with the TAs and instructor 20%, midterm and final exams 80%.
Students must have successfully completed Fundamentals of Dynamical Systems (SCE.C.201), Mathematics for Systems and Control A (SCE.A.201) and Information Processing and Programming (Systems and Control) (SCE.E.202) or have equivalent knowledge.
Lecture Homepage: http://www.hfg.sc.e.titech.ac.jp/course/FC/index.html