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
-
Introduction
to
Linear
Multivariable
Systems
Some detailed examples include electrical systems and mechanical systems, including an inverted pendulum.
-
Mathematical
Preliminaries
Vector spaces, matrices, matrix manipulations, norms, solving linear differential and difference vector equations.
-
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.
Controllability
Controllability, reachability, PBH test, equivalence of pole placement and controllability, controllable canonical form.
-
Observers
and
Observability
Observability, detectability, PBH test, observers, separation principle.
- LQR Optimal Control Cost functions, dynamic programming, Riccati equation, optimal LQR feedback, prop- erties of the optimal LQR feedback.
-
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.
General University of Waterloo guidelines
- Academic integrity: In order to maintain a culture of academic integrity, members of the University of Waterloo community are expected to promote honesty, trust, fairness, respect and responsibility.
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- Appeals: A decision made or penalty imposed under Policy 70 (Student Petitions and Grievances) (other than a petition) or Policy 71 (Student Discipline) may be appealed if there is a ground. A student who believes he/she has a ground for an appeal should refer to Policy 72 (Student Appeals).
- Note for students with disabilities: The AccessAbility Services, located in Needles Hall, Room 1132, collaborates with all academic departments to arrange appropriate accommodations for students with disabilities without compromising the academic integrity of the curriculum. If you require academic accommodations to lessen the impact of your disability, please register with the AccessAbility Services at the beginning of each academic term.