Linear Feedback Control

IMPORTANT MESSAGES:

  • We are back to classroom teaching/learning, although part of the lectures will still be provided remotely
  • Each week, slides and/or videos will be uploaded
  • Grading will be based on three (3) quiz and one (1) final exam

Learning Objectives:

  • Study how to model linear systems using state-space models;
  • learn fundamental system properties: stability, controllability, observability;
  • design feedback controllers for linear systems.

Instructor:

  • Prof. Kai Cai (Engineering Building F-610)
  • Email: cai@omu.ac.jp
  • Office hour: anytime appointment by email

Lecture Schedule:

  • Period: Sep. 2022 -- Feb. 2023
  • Day and Time: Tuesdays 13:15-14:45

Textbook / Reference:

Lecture notes in class will cover all contents. Two excellent references are:

  1. B.A. Francis, "Systems Control", lecture notes, Department of Electrical and Computer Engineering, University of Toronto, 2008. (PDF posted for study purpose: part1, part2, part3, ECE557_part4.pdf, part5, part6)
  2. J.P. Hespanha, " Linear Systems Theory", Princeton University Press, 2009. (Copies to be lent by request)

Software:

Matlab (download the Windows 64bit version here, with university campus license). After installing the software, you also need to make a change according this document.

Prerequisites:

Linear Algebra, Introduction to Control Engineering

Course Outline:

    Dates              Topics
  1. 2022.09.27 Introduction (+ self-review of state models and linearization)
  2. 2022.10.04 Lypunov stability, asymptotic stability
  3. 2022.10.11 Matrix exponential: diagonalizable and non-diagoonalizable cases
  4. 2022.10.18 Stability criteria
  5. 2022.10.25 Tutorial 1
  6. 2022.11.08 Quiz 1, reachability, controllability
  7. 2022.11.15 Control canonical form, state-feedback control by eigenvalue assignment
  8. 2022.11.22 Stabilizability, Kalman decomposition
  9. 2022.11.29 State reconstruction, observability, detectability
  10. 2022.12.06 Observer, output-feedback control
  11. 2022.12.13 Tutorial 2
  12. 2022.12.20 Quiz 2, reference tracking, regulator equations
  13. 2023.01.10 Optimal control
  14. 2023.01.17 Tutorial 3
  15. 2023.01.24 Quiz 3, multi-agent systems
  16. 2023.01.31 Exam, consensus