Lecture Outlines (Introduction to Control Systems)

Bahman Gharesifard
Winter 2017

Lectures:

  • Lecture 1: Examples of control systems
  • Lecture 2: Linear control systems and linearization of nonlinear control systems
  • Lecture 3: Single-input single output linear control systems
  • Lecture 4: Uniqueness of solutions for LTI control systems
  • Lecture 5: Existence of analytic solutions to linear matrix differential equation
  • Lecture 6: Properties of matrix exponentials
  • Lecture 7: Solutions of SISO linear control systems
  • Lecture 8: Kalman's criterion of controllability of LTI systems I
  • Lecture 9: Kalman's criterion of controllability of LTI systems II
  • Lecture 10: Observability for LTI system
  • Lecture 11: Laplace transforms and their abscissa of convergence
  • Lecture 12: Properties of Laplace transforms
  • Lecture 13: Transfer functions for LTI systems
  • Lecture 14: Space of smooth functions with bounded support, distributions, and impulse response to point distributions
  • Lecture 15: Properties of transfer functions related to controllability and observability
  • Lecture 16: Realization theory: Real rational complex-valued proper functions and transfer functions
  • Lecture 17: Canonical controllable and observable realizations
  • Lecture 18: The relationship between frequency response, impulse response, and transfer functions
  • Lecture 19: Frequency response and bode plots
  • Lecture 20: Frequency response and bode plots
  • Lecture 21: Notions of stability for control systems
  • Lecture 22: Internal stability and asymptotic stability for linear control systems
  • Lecture 23: Lyapunov stability for nonlinear dynamical systems I
  • Lecture 24: Lyapunov stability for nonlinear dynamical systems II
  • Lecture 25: Lyapunov equations for linear systems
  • Lecture 26: Control Architectures: Open-loop and closed-loop control
  • Lecture 26♠: Rouche's theorem and continuous dependency of roots of polynomials on their coefficients
  • Lecture 27: Why closed-loop control? Reference tracking along with disturbance rejection
  • Lecture 28: Reference tracking and disturbance rejection for a DC-motor: Pole-placement for controllable LTI systems
  • Lecture 29: Limitations of proportional feedbacks: PD and PID controllers, causality and delay, and wind-up phenomenon
  • Lecture 30: The Principle of Arguments and the Nyquist Theorem I
  • Lecture 31: The Principle of Arguments and the Nyquist Theorem II
  • Lecture 32: The Principle of Arguments and the Nyquist Theorem III
  • Lecture 33: Gain and phase crossovers and margins of stability I
  • Lecture 34: Small gain theorem
  • Lecture 35: Small gain theorem vs. Nyquist theorem
  • Lecture 36: Review session

For questions, contact me with bahman at mast.queensu.ca or with 613-533-2441 (I prefer emails)