This course covers the fundamentals of linear system 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 not only shows how to analyze and how to control systems, but also shows their theoretical background, which is necessary knowledge for developing new system theory.
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.
3) Have an understanding of mathematical derivation of the theories, and acquire the ability to develop new system theory
Linear System Theory, Linear Control Theory, State Equation.
Intercultural skills | Communication skills | ✔ Specialist skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
The first two thirds of the course concentrates on how to use theories. The remaining one third of the course gives the detailed mathematical proof of the theories.
Course schedule | Required learning | |
---|---|---|
Class 1 | System Modeling and State Equation | Describe linear systems using state equations. |
Class 2 | Controllability | Check controllability of systems. |
Class 3 | Observability | Check observability of systems. |
Class 4 | Stability | Check stability of systems. |
Class 5 | State Feedback: Pole Assignment | Design state feedback controllers using pole assignment method. |
Class 6 | State Feedback: Optimal Control | Design state feedback controllers which minimize performance indexes. |
Class 7 | Servo Controller and Internal Model Principle | Design servo controller. |
Class 8 | Full Order Observer | Design full order observers for systems. |
Class 9 | Kalman Filter and Duality | Design Kalman Filters for systems. |
Class 10 | Controllability Canonical Form and Observability Canonical Form | Transform the original system into controllability/observability canonical forms. |
Class 11 | Lyapunov Function and Proof of Stability of Optimal Control | Explain the stability of the optimal control using Lyapunov function. |
Class 12 | Proof of Optimality of Optimal Control | Understand the proof of the optimal control. |
Class 13 | Robustness and Asymptotic Characteristics of Optimal Control | Explain the robustness and asymptotic characteristics of optimal control. |
Class 14 | Disturbance Observer and Reduced Order Observer | Design disturbance observers and reduced order observers. |
Class 15 | Stabilizability and Detectability | Check stabilizability and detectablilty of 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 the final exams (100%).
Students will be assessed on their understandings of system analysis (controllablity, observability, etc.) and controller design (state feedback, observer, etc.), and their ability to apply them to solve problems.
Students must have successfully completed the followings or have equivalent knowledge.
LAS.M102 ： Linear Algebra I / Recitation
LAS.M106 ： Linear Algebra II
SCE.C201 ： Fundamentals of Dynamical Systems