This course examines the modeling of linear systems and using feedback to improve their performance. The progression of topics in the course includes the relationship between transfer function poles and system specifications; closed-loop pole placement to meet specifications; differences between open-loop and closed-loop control using a DC-motor-based case study; use of feedback to improve tracking, mitigate the effects of unwanted signals (disturbances), and render a system less sensitive to changes in system parameters; PID controllers; and stability testing with Root Locus and the Nyquist criterion. When time permits, additional topics include state-space design to demonstrate the applicability of linear algebra methods for representing and manipulating control systems, and using matrix representations to characterize system response and lead to the use of state feedback for system stabilization or control.

This course builds on knowledge from earlier courses, with the course in signals and systems, ELEC-323 (or MATH-332) as a formal prerequisite, along with additional background in linear algebra, differential equations and electric circuits in APSC-174, MATH-235, and ELEC-221.
In particular, it is presumed that, prior to taking this course, a student knows what a transfer function is, how to get the Laplace transform of ordinary differential equations, how to calculate transfer functions for basic RLC circuits, and what Bode plots are. Prerequisites: ELEC-323 or MATH-332.

Course Learning Outcomes (CLOs)
  • Determine the transfer function of a complex block diagram
  • Understand the relationship between pole location in a transfer function and system performance
  • Know how to use feedback to alter the location of closed-loop poles to meet performance specifications
  • Know how to use a variety of techniques to test if a control system is stable
  • Have an intuitive understanding of how feedback works and why closed-loop control can achieve better tracking, disturbance rejection and lower sensitivity than open-loop control can
  • Have an appreciation for the difficulties of tuning PID controllers
  • Be able to determine steady-state error in a control system
  • Draw a root locus of a control system and derive from this an intuitive feel for how poles or zeros should be added in closed-loop to stabilize a system
  • Draw a Nyquist plot and relate the results of Nyquist criterion to results visible on a root locus plot
  • Use state-space methods to represent systems and state feedback to control them
  • Feel comfortable with a variety of techniques for modeling control systems, for testing stability and for using feedback to alter the performance of a system or to stabilize a system
Credit Breakdown

Lecture: 3
Lab: 0.75
Tutorial: 0.5

Academic Unit Breakdown

Mathematics 0
Natural Sciences 0
Complementary Studies 0
Engineering Science 15
Engineering Design 36