2025 (Current Year) Faculty Courses School of Engineering Undergraduate major in Electrical and Electronic Engineering
Linear Control Theorem
- Academic unit or major
- Undergraduate major in Electrical and Electronic Engineering
- Instructor(s)
- Mitsuji Sampei
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- EEE.C361
- Number of credits
- 200
- Course offered
- 2025
- Offered quarter
- 3Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course covers the fundamentals of linear control theory based on state equations, and shows how to analyze systems and how to design controllers for them. In the system analysis, stability, controllability and observability are introduced. In the controller design, state feedback controllers (pole assignment and optimal control), observers and servo controllers are introduced.
The state equation is one of the system descriptions, and many kinds of systems can be described in state equations, for example, mechanical, electrical, chemical and economical systems. This course enables students to derive mathematical models of real systems, and to design controllers for them.
Course description and aims
At the end of this course, students will be able to:
1) Analyze the stability, controllability and observability of the system.
2) Design stabilizing controllers.
Keywords
Linear Control Theory, State Equation
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
- ・Applied specialist skills on EEE
Class flow
Towards the end of class, students are given exercise problems related to what is taught on that day.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | State Equation | Describe systems in state equations. |
| Class 2 | Coordinate Transformation | Describe systems in different coordinates. |
| Class 3 | Controllability, System Decomposition | Check controllability of systems. Decompose systems based on the controllability. |
| Class 4 | Observability | Check observability of systems. |
| Class 5 | Transition Matrix | Describe system responses with transition matrices. |
| Class 6 | State Feedback (Pole Assignment) | Design state feedback controllers using pole assignment method. |
| Class 7 | Pole and Response | Explain the relations between poles and responses. |
| Class 8 | Optimal Control | Design state feedback controllers which minimize performance indexes |
| Class 9 | Lyapunov Function and Stability of Optimal Control | Explain the stability of the optimal control using Lyapunov function |
| Class 10 | Serve Controller | Design servo controllers. |
| Class 11 | Observer | Design observers. |
| Class 12 | Kalman Filter, Duality | Design Kalman Filter. |
| Class 13 | Linearization | Linearize nonlinear systems. |
| Class 14 | Controller Design for Discrete Time System | Design controllers for discrete time systems. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
All materials used in class can be found on Science Tokyo LMS.
Reference books, course materials, etc.
K.J.Astrom and R.M.Murray: Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press
Evaluation methods and criteria
Students’ course scores are based on final exams (50%) and exercise problems (50%).
If the lecture should be conducted on line, course scores are based on exercise problems and reports.
Related courses
- LAS.M102 ： Linear Algebra I / Recitation
- LAS.M106 ： Linear Algebra II
- EEE.C261 ： Control theory
Prerequisites
Students must have successfully completed the followings or have equivalent knowledge.
LAS.M102 ： Linear Algebra I / Recitation
LAS.M106 ： Linear Algebra II