UW ME 547 Linear Systems

Introduction

ME547 is a first-year graduate course on modern control systems focusing on: state-space description of dynamic systems, linear algebra for controls, solutions of state-space systems, discrete-time models, stability, controllability and observability, state-feedback control, observers, observer state feedback controls, and when time allows, linear quadratic optimal controls. ME547 is a prerequisite to most advanced graduate control courses in the UW ME department.

Lecture notes

• Single-file course reader
• “Essentials of Modern Controls,” Course Pack for ME 547, available for purchase at the University Bookstore, 4326 University Way NE, Seattle, WA 98105
• Review of linear algebra for controls: notes, slides

Reference

• Linear Systems Theory and Design (4th Ed) by Chi-Tsong Chen, Oxford University Press
• Matlab Control Turorial
• Python Control Toolbox

Lectures

• Week 1
  • The power of controls
  • Basic concepts
  • Modeling of dynamic systems
  • Laplace transform
  • Inverse Laplace transform
  • Z transform
  • Inverse Z transform
  • Reading and extension: Course Pack Chapters 1-3
• Week 2
  • Introduction to the state space
  • From the state space to transfer functions
  • State-space system representations
  • Reading and extension: Course Pack Chapters 4-5
• Week 3
  • Solution of state equations
  • Reading and extension: Course Pack Chapter 6
• Week 4
  • Discretization of state-space systems
  • Discretization of transfer functions
  • Stability I: the method of eigenvalue/pole locations
  • Reading and extension: Course Pack Chapters 7, 8.1, 8.2
• Week 5-6
  • Stability II and III: Lyapunov’s approach to stability, Lyapunov Equation, continuous- and discrete-time Lyapunov stability theory
  • Reading and extension: Course Pack Chapter 8
  • Midterm review
• Week 7
  • Controllability and observability
  • Reading and extension: Course Pack Chapter 9
• Week 8
  • Kalman Decomposition
  • State feedback
  • Reading and extension: Course Pack Chapters 10, 11
• Week 9
  • Observers and observer-state feedback
  • Reading and extension: Course Pack Chapter 12
• Week 10
  • linear quadratic optimal control
  • Reading and extension: Course Pack Chapter 13

Youtube Lecture List

Additional References

• Joao P. Hespanha, Linear Systems Theory, Princeton, 2009

• William L. Brogan, Modern Control Theory, 3rd Ed., Prentice Hall.

• P. J. Antsaklis and A. N. Michel, Linear Systems, McGraw Hill.