Linear Systems (UW ME 547)

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.

Prerequisites

• Undergraduate controls from, e.g., UW ME 471 or ME 545
• Engineering mathematics including calculus, linear algebra, and ordinary differential equations from, e.g., ME 564 Mechanical Engineering Analysis or EE 510 (can be taken concurrently)

Textbook

• Xu Chen and Masayoshi Tomizuka, “Introduction to Modern Controls – with Illustrations in MATLAB and Python,” 2023, ISBN: 9798860587496.
  • Book website
  • Hardcopy from Amazon
  • eBook

Lecture notes

• Single-file course reader (dark theme – battery saving for screen viewing)
• Single-file course reader (light theme – ink saving for printing)
• Review of linear algebra for controls: notes, slides

Reference

• Matlab Control Turorial
• Python Control Toolbox

Lectures

• Module 1 (can be skipped if familiar with undergraduate control systems)
  • The power of controls
  • Basic concepts
  • Modeling of dynamic systems
• Module 2 (can be skipped if proficient with undergraduate control systems)
  • Laplace transform
  • Inverse Laplace transform
• Module 3
  • Z transform
  • Inverse Z transform
• Reading and extension: Chapters 1-3
• Module 4
  • Introduction to the state space
  • From the state space to transfer functions
• Module 5
  • State-space system representations
• Reading and extension: Chapters 4-5
• Module 6-7
  • Solution of state equations
• Reading and extension: Chapter 6
• Module 8
  • Discretization of state-space systems
  • Discretization of transfer functions
• Reading and extension: Chapter 7
• Module 9
  • Stability I: the method of eigenvalue/pole locations
• Module 10-11
  • Stability II and III: Lyapunov’s approach to stability, Lyapunov Equation, continuous- and discrete-time Lyapunov stability theory
• Reading and extension: Chapter 8
  • Midterm review
• Module 12
  • Controllability and observability
• Reading and extension: Chapter 9
• Module 13-14
  • Kalman Decomposition
  • State feedback
• Reading and extension: Chapters 10, 11
• Module 15-16
  • Observers and observer-state feedback
• Reading and extension: Chapter 12
• Module 17-18
  • linear quadratic optimal control
• Reading and extension: Chapter 13

Youtube Lecture List

Additional References

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

• 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.