Department of Electrical and Computer Engineering
ECE 460 (1 1/2) CONTROL THEORY AND SYSTEMS II
Syllabus:
Sampling in Control Systems. The ztransform and response
between sampling instants. Analysis of sampled data systems and
stability testing. Statespace analysis and design of continuous
and discrete systems. Controllability, observability and zero input
stability analysis. Pole placement techniques.
(Prerequisite: 360)
Click here for the Course Outline document.
Classes:
Mondays and Thursdays, 8:30 9:50 am, COR B129.
Demos:
Demo 1: Thursday, February 15, 8:30am in ELW A359.
Problem for Demo #1:
Design a digital compensator for an open loop
system G(s)=K/[s(s+a)] with a=3.4, K=120.52, T=0.05495 so that Kv=15 and phase margin > 45 deg.
For copies of the slides in pdf format, Click here.
Demo 2: Thursday, March 28, 8:30am in ELW A359.
Problem for Demo #2:
Consider a continuous system {A,b,c} where:
A=[0, 13.71; 0, 3.4], b'=[0, 9.01] and c=[1, 0].
Sampling time, T=0.05495 (same as in demo #1).
 1. Design a digital state feedback controller so that
the output follows the reference signal at steady state and
the step responce has a damping ratio of 0.8 and a settling time of 0.6 sec.
 2. Design a digital integral error feedback controller so that
the output follows the reference signal at steady state and
the step responce has a damping ratio of 0.8 and a settling time of 0.6 sec.
For copies of the Demo2 Slides in pdf format, Click here.
Midterm:
Thursday, February 29, 8:30 9:40 am, COR B129.
Two pages (a page is one side of a sheet) of notes and copies of ztransform tables are permitted.
For the solutions in pdf format, here.
Final Exam:
Thursday, April 18, 2:00pm  5:00pm, ECS 104.
Four pages (a page is one side of a sheet) of notes and copies of tables (2.1 and 2.2) are permitted.
Review for Final Exam:
Wednesday, April 17, 10:00am  12 noon, ECS 130.
Office hours:
Tuesdays, 10:30am11:30pm; The Tuesdays Office hours will be in person EOW 423.
Fridays, 1:30pm02:30pm; The Friday Office hours will be on Zoom (Link TBA).
 Assignement problems (from section B of the textbook) will be posted here.
 Completed assignments should be submitted using UVic's Brightspace site by 6pm the date they are due.
Watch an example of assignment submission.
 Solutions to the assignments will be posted here.
Assignment #1 (Due Saturday, Jan 20)
Problem: Consider the unity negative feedback system with
G(s)=20*K/[s(s+1)(s+20)].
1. Sketch the root locus.
2. Find Kv.
3. Sketch Bode and Nyquist plots.
4. Find K so that zeta=sqrt(2)/2 for the closed loop system.
5. Find phase and gain margins for this K.
6. Sketch the step and ramp responces of the closed loop system for this K.
7. Discuss the connection between Kv, zeta, margins and the responce of the closed loop system.
For the solution in pdf format, Click here.
Assignment #2 (Due Saturday, January 27) :
Questions B27, B212, B217 from the textbook.
For the solution in pdf format, Click here.
Assignment #3 (Due Sunday, February 4) :
 Problem 1: Sample the two signals
x1(t)=sin(2*pi*3*t) and x2(t)=sin(2*pi*0.3*t)
with sampling period T=0.2.
Sketch the spectrum of the continuous signal, the spectrum of the
sampled one and the reconstructed signal
obtained by ideal lowpass filtering of the sampled signal.
Confirm your results with Matlab. For a .m file, Click here.

Questions B34, B36, B37, B315, B319 from the textbook.
For the solution in pdf format, Click here.
Assignment #4 (Due Sunday, February 11) :
Questions B320, B44, B48 from the textbook.
For the solution in pdf format, Click here.
Assignment #5 (Due: Wedmesday, February 21)
Study Examples 7.26 and 7.27 form K. Ogata, "Modern Control Engineering"
and Example 412 from K. Ogata, "Discrete Time Control Systems".
The .m files ex_4_12.m, lead_c.m, lag_c.m and ex_4_12.out are helpful for this.
Solve questions B410 (Use PI control) and B415 from the textbook.
The .m files ass_5.m, lead_c.m, lag_c.m, and ass_5.out are helpful for compensator design B415.
For the solution of B410 and B415 in pdf format, Click here.
Assignment #6 (Due Sunday, March 10) :
Questions B54, B55, B58 (except the dagonal form) and B515 from the textbook.
For the solution in pdf format, Click here.
Assignment #7 (Due Sunday, March 24) :
Questions B518, B522, B61, B63 and B65 from the textbook.
For the solution in pdf format, Click here.
Assignment #8 (REVISED: Due Tuesday, April 2):
Questions B611, B612 from the textbook.
Determine the feedback gain matrix for the model of B611 so that
the closed loop system has settling time of 2sec and overshoot of 18% (T=0.1).
For the solution of Ass #8 in pdf format, Click here.
Assignment #9 (Due Sunday, April 7) :
Question B617 from the textbook (Compare Fig. 624 with figure in slide B68).
Design a full order prediction observer with deadbeat response for the system of Question B613 in the textbook.
For the solution of Ass #9 in pdf format, Click here.
Copies of the lecture slides (in pdf format) are available here for downloading.
Course Lecture Notes
Unless otherwise noted, all course materials supplied to students in this course have been prepared by the instructor and are intended for use in this course only. These materials are NOT to be recirculated digitally, whether by email or by uploading or copying to websites, or to others not enrolled in this course. Violation of this policy may in some cases constitute a breach of academic integrity as defined in the UVic Calendar.
1. Required

Title  : Discrete Time Control Systems, 2^{nd} Edition


Author  : K. Ogata


Publisher  : PrenticeHall


Year  : 1995

2. Recommended
3. For information on Matlab available at UVic computers see here

Assignments  : 5%


Midterm  : 35% Thursday, February 29


Final  : 60%

The final grade obtained from the above marking scheme for the purpose of GPA calculation will be based on the percentagetograde point conversion table as listed in the current Undergraduate Calendar.
Assignment of E grade and supplemental examination for this course will be at the discretion of the Course Instructor.More information and links to the detailed policies can be found in the course outline.
General Information on Policies and Regulations can be found in the Course Outline.
Continuously modified: JanuaryApril, 2024.