ECE 460 Control Theory and Systems II, Dr. Pan Agathoklis

Department of Electrical and Computer Engineering

ECE 460 (1 1/2) CONTROL THEORY AND SYSTEMS II

Syllabus:

Sampling in Control Systems. The z-transform and response between sampling instants. Analysis of sampled data systems and stability testing. State-space analysis and design of continuous and discrete systems. Controllability, observability and zero input stability analysis. Pole placement techniques. (Prerequisite: ECE360 or ELEC360 or MECH380)

Click here for the Course Outline document.

Classes:

Mondays and Thursdays, 8:30- 9:50 am, ELL 060.
Demos:
Mid-term:

Monday, February 24, 8:30- 9:40 am, Ell 060.
Two pages (a page is one side of a sheet) of notes and copies of z-transform tables are permitted.
For the solutions in pdf format, see here.
For last year's midterm in pdf format, Click here.
Final Exam:

Friday, April 11, 7:00pm - 10:00pm, ECS 125.
Four pages (a page is one side of a sheet) of notes and copies of tables (2.1 and 2.2) are permitted.
For an old Exam, Click here.

Review for Final Exam:

Thursday, April 10, 10:00am - 12 noon, ECS 104.

Office hours:

Wednesdays, 10:00am-11:00am; The Wednesdays Office hours will be in person EOW 423.
Fridays, 1:30pm-02:30pm; The Friday Office hours will be on Zoom (Link TBA).

Assignments
Copies of Lectures Slides
Textbook
Useful Links
Assessment
Links to Policies and Regulations

Assignments

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 18)

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 25) :

Questions B-2-7, B-2-12, B-2-17 from the textbook.
For the solution in pdf format, Click here.

Assignment #3 (Due Sunday, February 2) :

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 B-3-4, B-3-6, B-3-7, B-3-15, B-3-19 from the textbook.

For the solution in pdf format, Click here.

Assignment #4 (Due Sunday, February 9) :

Questions B-3-20, B-4-4, B-4-8 from the textbook.
For the solution in pdf format, Click here.

Assignment #5 (REVISED Due: Thursday, February 20)

Study Examples 7.26 and 7.27 form K. Ogata, "Modern Control Engineering" and Example 4-12 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 B-4-10 (Use PI control) and B-4-15 from the textbook.
The .m files ass_5.m, lead_c.m, lag_c.m, and ass_5.out are helpful for compensator design B-4-15.

For the solution of B-4-10 and B-4-15 in pdf format, Click here.
Assignment #6 (Due Sunday, March 9) :

Questions B-5-4, B-5-5, B-5-8 (except the dagonal form) and B-5-15 from the textbook.
For the solution in pdf format, Click here.

Assignment #7 (Due Wednesday, March 19) :

Questions B-5-18, B-5-22, B-6-1, B-6-3 and B-6-5 from the textbook.
For the solution in pdf format, Click here.

Assignment #8 (Due Wednesday, March 26):

Questions B-6-11, B-6-12 from the textbook.

Determine the feedback gain matrix for the model of B-6-11 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 Thursday, April 3) :

Question B-6-17 from the textbook (Compare Fig. 6-24 with figure in slide B68).

Design a full order prediction observer with deadbeat response for the system of Question B-6-13 in the textbook.

For the solution of Ass #9 in pdf format, Click here.

Copies of Lecture Slides

Copies of the lecture slides (in pdf format) are available here for downloading.

ECE460.pdf (Sections A,B,C combined; about 2.8 MB)
z Transform Tables
Double_Integral_Example

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 re-circulated 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.

Textbook

1. Required
Title : Discrete Time Control Systems, 2^nd Edition

Author : K. Ogata

Publisher : Prentice-Hall

Year : 1995

2. Recommended
Title : MATLAB student Version

Publisher : The MathWorks

See also https://www.mathworks.com/academia/students.html

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

Useful Links

A brief history of Feedback Control
The Impact of Control Technology
IEEE Control Society Video Library
Control Engineering Virtual Library

Course Assessment

Assignments : 5%

Mid-term : 35% Monday, February 24

Final : 60%

The final grade obtained from the above marking scheme for the purpose of GPA calculation will be based on the percentage-to-grade 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.

Links to Policies and Regulations

General Information on Policies and Regulations can be found in the Course Outline.

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Continuously modified: January-April, 2025.

	Title	: Discrete Time Control Systems, 2^nd Edition
	Author	: K. Ogata
	Publisher	: Prentice-Hall
	Year	: 1995

	Title	: MATLAB student Version
	Publisher	: The MathWorks
	See also	https://www.mathworks.com/academia/students.html

Department of Electrical and Computer Engineering

ECE 460 (1 1/2) CONTROL THEORY AND SYSTEMS II

Syllabus:

Click here for the Course Outline document.

Classes:

Mondays and Thursdays, 8:30- 9:50 am, ELL 060.

Demos:

Demo 1: Thursday, February 10, 8:30am in ELW A359.

Problem for Demo #1: Design and implement a position control system with a digital compensator. The open loop system G(s)=K/[s(s+a)] with a=3.4, K=120.52. Design specifications: sampling period T=0.05495, Kv=15 and phase margin > 45 deg For copies of the slides in pdf format, Click here.

Demo 2: Thursday, March 27, 8:30am in ELW A359.

For copies of the Demo2 Slides in pdf format, Click here.

Mid-term:

Monday, February 24, 8:30- 9:40 am, Ell 060. Two pages (a page is one side of a sheet) of notes and copies of z-transform tables are permitted. For the solutions in pdf format, see here. For last year's midterm in pdf format, Click here.

Final Exam:

Friday, April 11, 7:00pm - 10:00pm, ECS 125. Four pages (a page is one side of a sheet) of notes and copies of tables (2.1 and 2.2) are permitted. For an old Exam, Click here.

Review for Final Exam:

Thursday, April 10, 10:00am - 12 noon, ECS 104. Office hours: Wednesdays, 10:00am-11:00am; The Wednesdays Office hours will be in person EOW 423. Fridays, 1:30pm-02:30pm; The Friday Office hours will be on Zoom (Link TBA).

Office hours:

Wednesdays, 10:00am-11:00am; The Wednesdays Office hours will be in person EOW 423. Fridays, 1:30pm-02:30pm; 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 18)

Assignment #2 (Due Saturday, January 25) :

Questions B-2-7, B-2-12, B-2-17 from the textbook. For the solution in pdf format, Click here.

Assignment #3 (Due Sunday, February 2) :

Questions B-3-4, B-3-6, B-3-7, B-3-15, B-3-19 from the textbook.

For the solution in pdf format, Click here.

Assignment #4 (Due Sunday, February 9) :

Questions B-3-20, B-4-4, B-4-8 from the textbook. For the solution in pdf format, Click here.

Assignment #5 (REVISED Due: Thursday, February 20)

Study Examples 7.26 and 7.27 form K. Ogata, "Modern Control Engineering" and Example 4-12 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 B-4-10 (Use PI control) and B-4-15 from the textbook. The .m files ass_5.m, lead_c.m, lag_c.m, and ass_5.out are helpful for compensator design B-4-15.

Assignment #6 (Due Sunday, March 9) :

Questions B-5-4, B-5-5, B-5-8 (except the dagonal form) and B-5-15 from the textbook. For the solution in pdf format, Click here.

Assignment #7 (Due Wednesday, March 19) :

Questions B-5-18, B-5-22, B-6-1, B-6-3 and B-6-5 from the textbook. For the solution in pdf format, Click here.

Assignment #8 (Due Wednesday, March 26):

Questions B-6-11, B-6-12 from the textbook.

Determine the feedback gain matrix for the model of B-6-11 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 Thursday, April 3) :

Question B-6-17 from the textbook (Compare Fig. 6-24 with figure in slide B68).

Design a full order prediction observer with deadbeat response for the system of Question B-6-13 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. ECE460.pdf (Sections A,B,C combined; about 2.8 MB) z Transform Tables Double_Integral_Example

Course Lecture Notes

1. Required

Title : Discrete Time Control Systems, 2nd Edition Author : K. Ogata Publisher : Prentice-Hall Year : 1995

2. Recommended

Title : MATLAB student Version Publisher : The MathWorks See also https://www.mathworks.com/academia/students.html

General Information on Policies and Regulations can be found in the Course Outline.

Problem for Demo #1:
Design and implement a position control system with a digital compensator.
The open loop system G(s)=K/[s(s+a)] with a=3.4, K=120.52.
Design specifications: sampling period T=0.05495, Kv=15 and phase margin > 45 deg
For copies of the slides in pdf format, Click here.

Monday, February 24, 8:30- 9:40 am, Ell 060.
Two pages (a page is one side of a sheet) of notes and copies of z-transform tables are permitted.
For the solutions in pdf format, see here.
For last year's midterm in pdf format, Click here.

Friday, April 11, 7:00pm - 10:00pm, ECS 125.
Four pages (a page is one side of a sheet) of notes and copies of tables (2.1 and 2.2) are permitted.
For an old Exam, Click here.

Thursday, April 10, 10:00am - 12 noon, ECS 104.

Office hours:

Wednesdays, 10:00am-11:00am; The Wednesdays Office hours will be in person EOW 423.
Fridays, 1:30pm-02:30pm; The Friday Office hours will be on Zoom (Link TBA).

Wednesdays, 10:00am-11:00am; The Wednesdays Office hours will be in person EOW 423.
Fridays, 1:30pm-02:30pm; 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.

Questions B-2-7, B-2-12, B-2-17 from the textbook.
For the solution in pdf format, Click here.

Questions B-3-20, B-4-4, B-4-8 from the textbook.
For the solution in pdf format, Click here.

Study Examples 7.26 and 7.27 form K. Ogata, "Modern Control Engineering" and Example 4-12 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 B-4-10 (Use PI control) and B-4-15 from the textbook.
The .m files ass_5.m, lead_c.m, lag_c.m, and ass_5.out are helpful for compensator design B-4-15.

Questions B-5-4, B-5-5, B-5-8 (except the dagonal form) and B-5-15 from the textbook.
For the solution in pdf format, Click here.

Questions B-5-18, B-5-22, B-6-1, B-6-3 and B-6-5 from the textbook.
For the solution in pdf format, Click here.

Copies of the lecture slides (in pdf format) are available here for downloading.

ECE460.pdf (Sections A,B,C combined; about 2.8 MB)
z Transform Tables
Double_Integral_Example

Title : Discrete Time Control Systems, 2^nd Edition

Author : K. Ogata

Publisher : Prentice-Hall

Year : 1995

Title : MATLAB student Version

Publisher : The MathWorks

See also https://www.mathworks.com/academia/students.html