2019 Linear Control Theorem

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Academic unit or major
Undergraduate major in Electrical and Electronic Engineering
Sampei Mitsuji 
Course component(s)
Day/Period(Room No.)
Tue1-2(S423)  Fri1-2(S423)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

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.

Student learning outcomes

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.

Corresponding educational goals are:
(1) Specialist skills Fundamental specialist skills
(4) Applied skills (inquisitive thinking and/or problem-finding skills) Organization and analysis
(7) Skills acquiring a wide range of expertise, and expanding it into more advanced and other specialized areas


Linear Control Theory, State Equation

Competencies that will be developed

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

Class flow

Towards the end of class, students are given exercise problems related to what is taught on that day
to solve.

Course schedule/Required learning

  Course schedule Required learning
Class 1 State Equation Describe systems in state equations.
Class 2 State Equation and Transfer Function Obtain transfer functions of systems described in state equations.
Class 3 Coordinate Transformation and Controllability Check controllability of systems.
Class 4 System Decomposition Decompose systems based on the controllability.
Class 5 Observability Check observability of systems.
Class 6 Stability Check stability of systems.
Class 7 State Feedback (Pole Assignment) Design state feedback controllers using pole assignment method.
Class 8 Pole and Response Explain the relations between poles and responses.
Class 9 Optimal Control Design state feedback controllers which minimize performance indexes
Class 10 Lyapunov Function and Stability of Optimal Control Explain the stability of the optimal control using Lyapunov function
Class 11 Serve Controller Design servo controllers.
Class 12 Observer Design observers.
Class 13 Linearization Linearize nonlinear systems.
Class 14 Analysis of Discrete Time System Analyze controllability, observability and stability of discrete time systems.
Class 15 Controller Design for Discrete Time System Design controllers for discrete time systems.


All materials used in class can be found on OCW-i.

Reference books, course materials, etc.

K.J.Astrom and R.M.Murray: Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press

Assessment criteria and methods

Students’ course scores are based on final exams (50%) and exercise problems (50%).

Related courses

  • LAS.M102 : Linear Algebra I / Recitation
  • LAS.M106 : Linear Algebra II
  • EEE.C261 : Control theory

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

Students must have successfully completed the followings or have equivalent knowledge.
LAS.M102 : Linear Algebra I / Recitation
LAS.M106 : Linear Algebra II

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