ECE 682 - Fall 2013

ECE 682 - Multivariable Control Systems

Instructor: Daniel Miller (EIT3116; ext. 35215; miller@uwaterloo.ca)

Schedule: Lectures: Tuesday 11:30am - 2:30pm (EIT3151)

Calendar Description: An introduction to control theory for linear time-invariant finite-dimensional systems from both the state-space and input-output viewpoints. State-space theory: the concepts of controllability, observability, stabilizability, and detectability; the pole-assignment theorem; observers and dynamic compensation; LQR regulators. Input-output theory: the ring of polynomials and the field of rational functions; the algebra of polynomial and rational matrices; coprime factorization of transfer matrices; Youla parametrization. Introduction to optimal control.

Text: I will provide course notes; I will place some relevant textbooks on reserve in the library.

Tentative Grading: There will an assignment per chapter (30%), a course project (20%), and a final exam (50%).

Assumed Background: ECE380 (or equivalent) and familiarity with basic linear algebra.

Detailed Description (Tentative):

  1. Introduction to Linear Multivariable Systems
    Some detailed examples include electrical systems and mechanical systems, including an inverted pendulum.
  2. Mathematical Preliminaries
    Vector spaces, matrices, matrix manipulations, norms, solving linear differential matrix equations.
  3. Multivariable LTI Systems: An Input-Output Approach
    State-space to transfer function, similarity transformations, Jordan forms, discretizing a continuous-time system, poles and zeros of a multivariable system.
  4. Controllability
    Controllability, reachability, PBH test, equivalence of pole placement and controllability, controllable canonical form.
  5. Observers and Observability
    Observability, detectability, PBH test, observers, separation principle.
  6. LQR Optimal Control
    Cost functions, dynamic programming, Riccati equation, optimal LQR feedback, properties of the optimal LQR feedback.
  7. Youla Parametrization and its Applications
    Matrix fractional descriptions of transfer functions, Bezout identity, parametrization of all stabilizing controllers, an introduction to L1, H∞ and H2 optimal control.

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