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.
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
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Towards the end of class, students are given exercise problems related to what is taught on that day
|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.
K.J.Astrom and R.M.Murray: Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press
Students’ course scores are based on final exams (50%) and exercise problems (50%).
Students must have successfully completed the followings or have equivalent knowledge.
LAS.M102 ： Linear Algebra I / Recitation
LAS.M106 ： Linear Algebra II