ECE557F Systems Control (Last updated November 23, 2015)

Course Description

Teaching Staff

Prof. M.E. Broucke GB434A LEC 01 broucke at
Zachary Kroeze GB348 TUT 01 zach.kroeze at
Alireza Mohammadi GB348 PRA 01, PRA 02 alireza.mohammadi at

Lecture and Tutorial Schedule

Section Day and Time Location Start Date
LEC 01 Tue 4-5 WB119  
  Wed 4-5 WB119  
  Fri 4-5 WB119 September 11
TUT 01 Wed 5-6 WB119 September 16

Course Notes

ECE557 Course Notes, September 2012.

Course Outline

The following table shows the lecture topics. Note that the lecture schedule may be updated as the semester progresses, so it's a good idea to check the webpage periodically.

Week Lecture Topics
1 1       Introduction to control systems; State equations
2 2 TF to SS conversion; SS to TF conversion
  3 Linearization
  4 Properties of e^At
3 5 Solution of xdot = A x; Computing e^At
  6 Computing e^At
  7 Modal decomposition; Phase portraits of second order systems
4 8 Phase portraits of second order systems
  9 Stability of LTI systems
  10 Stability of LTI systems
5 11 Linear algebra review
  12 Linear algebra review
  13 Linear algebra review
6 14 Linear Algebra review
  15 Controllability: introduction
  16 Controllability: main result
7 17 Controllability: properties
  18 Controllable decomposition
  19 Controllable canonical form
8 20 Pole placement: single-input case
  21 Pole placement: multi-input case
  22 PBH test; Stabilizability
9 23 Stabilization example; Observability
  24 Observability: main result
  25 Observable decomposition
10 26 Observers; Stabilization by measurement feedback problem (SMFP)
  27 Separation principle
  28 SMFP example
11 29 Optimal control: introduction
  30 Optimal control: dynamic programming principle
  31 Optimal control: derivation of controller
12 32 Optimal control: examples
  33 Optimal control: examples
  34 Output regulation
13 35 Output regulation
  36 Output regulation
  37 Output regulation
14 38 Output regulation

Practice Problems

A selection of practice problems will be worked out in tutorial. Solutions will be posted roughly one week after the tutorial.

Problem Set Topics Solutions
Problem set 1 Modeling, state equations, computing e^At, modal decomposition, TF --> SS, linearization Solution 1
Problem set 2 Linear algebra Solution 2
Problem set 3 Controllability, pole placement Solution 3
Problem set 4 Multi-input pole placement, controllable decomposition, PBH test Solution 4
Problem set 5 Observability, observers, output feedback stabilization Solution 5
Problem set 6 Optimal control Solution 6
Problem set 7 Output regulation Solution 7


Labs take place in BA3114 and are performed in groups of two or three students. The labs include a preparation and a report. Each student submits one preparation at the beginning of the lab. The report is due one week after your scheduled lab (one report per group), in a drop box labeled "ECE557", box #15, basement of Sandford Fleming. There are no make-up labs. If you miss a lab you cannot show up at a different lab section.

Section Day and Time Lab 1 Lab 2 Lab 3 Lab 4
PRA 01 Mon 12-15 Sep 21 Oct 5 Oct 19 Nov 9
PRA 02 Thu 9-12 Sept 24 Oct 8 Oct 29 Nov 12

Lab Title Matlab and supporting files
Lab 1 Introduction to the Control Lab  
Lab 2 Pole placement and observer design for a cart ReportFormatLab2.doc
Lab 3 Control design of an inverted pendulum on a cart using Simulink ReportFormatLab3.pdf
Lab 4 Control of an inverted pendulum on a cart ReportFormatLab4.pdf


Labs 15% Includes preparation, lab work, and report  
Homework 5%    
Midterm 1 15% October 14, 4-6pm  
Midterm 2 20% November 18, 4-6pm  
Final Exam 45% December 16, 2-4:30pm  

Miscellaneous Notes