ECE 682 - Fall 2015

ECE 682 - Multivariable Control Systems

Instructor

Professor Daniel Miller
Office: EIT-3116
Phone: (519) 888-4567 extension 35215
e-mail: miller@uwaterloo.ca

Schedule

Lectures will be Mondays from 2:30pm - 5:30pm in room EIT 3141.

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 on LEARN; I will place some relevant textbooks on reserve in the library.

Grading

  • There will be exercises spread throughout the notes. Depending on the size of the class, I will mark some of them to yield an assignment mark (20%).
  • There will be an individual project worth 30%. It will entail modelling a physical system, designing a state estimator(s) and a controller(s), and carrying out some MATLAB simulations. Details will be provided in the second or third week of class.
  • There will be a final exam worth 50%.

Assumed Background

ECE 380 (or equivalent) and familiarity with basic linear algebra.

Detailed Description

  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 and difference vector equations.

  3. Multivariable LTI Systems: An Input-Output Approach

    State-space to transfer function, similarity transformations, discretizing a continuous-time system, poles and zeros of a multivariable system.

  4. 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, prop- erties 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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