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'''Lecture 10'''  

Revision as of 03:44, 29 January 2020

EE-561: Digital Control Systems
Spring 2020


Talha Manzoor, Assistant Professor, Center for Water Informatics & Technology (WIT)


Office: 9-252, Tesla Wing, 2nd Floor, SSE Bldg

TA: Muhammad Mateen Shahid, MS Electrical Engineering


Office: Control Systems Lab, Tesla Wing, 2nd Floor, SSE Bldg

Course Details

Year: 2019-20

Semester: Spring

Category: Graduate

Credits: 3

Elective course for electrical engineering majors. Core course for electrical engineering students pursuing an MS in the "Systems and Controls" stream.

Course Website:

Course Description

This course involves the design and analysis of control to be implemented by digital computers for systems that operate on continuous signals. The first part of the course focuses on the analysis of sampled-data systems and the tools employed to study them. These include the language of difference equations, the z-transform, discretization methods for continuous-time systems, dynamic response of discrete-time systems and the effects of sampling and quantization. The second part of the course covers the design of feedback control in discrete time domain which includes emulation of controllers designed in continuous time domain and direct design in discrete-time domain using both transform based and state space techniques.

Learning Outcomes

  • Represent and describe discrete-time systems using difference equations and z-transforms
  • Analyze discrete-time and sampled-data systems in order to deduce system behavior
  • Implement controllers designed using continuous-time techniques for application to discrete-time systems
  • Apply and evaluate different techniques for controller design directly in the digital domain


  • EE-361. Feedback Control Systems (for undergrads)
  • A working knowledge of ordinary differential equations and linear algebra will be assumed while delivering the lectures.
  • Experience in programming with MATLAB will be required to solve some components of the assignments.

Text book

The course will be taught from the following textbook.

(Franklin) Digital control of dynamic systems by Franklin, Powell and Workman (3rd edition), Addison Wesley, 2000.

Other references

(Strang) Computational Science and Engineering, Wellesley-Cambridge Press, 2007

(FranklinF) Feedback Control of Dynamics Systems, Pearson Prentice Hall, 2013

(Astrom) Computer Controlled Systems, Prentice Hall, 1997

(Ogata) Modern control engineering, Pearson Prentice Hall, 2010

Grading Scheme

Homeworks+Quiz : 20%

Course project: 25%

Midterm: 25%

Final : 30%

Policies and Guidelines

  • Quizzes will be announced. There will be no makeup quiz.
  • Homework will be due at the beginning of the class on the due date. Late homework will not be accepted.
  • You are allowed to collaborate on homework. However, copying solutions is absolutely not permitted. Offenders will be reported for disciplinary action as per university rules.
  • Any appeals on grading of homeworks, quiz or midterm scores must be resolved within one week of the return of graded material.
  • Attendance in lectures is strongly recommended but not mandatory. However, you are responsible for catching the announcements made in the class.

Course Delivery Method

Lectures. Mon, Wed: 12:30pm-1:45pm. 10-202. SSE Bldg


Week 1 Jan 20 Lecture 1 Motivation: The control design problem, structure of a digital control system, the need for a dedicated theory of digital control, Categories of systems: discrete, sampled-data, digital; Overview of course contents

Lecture 2 Difference Equations: Difference equation of a resistive ladder (notes), numerically solving difference equations, Method of undetermined coefficients, From ODE’s to difference equations (approximating an integral), The computer solution to an ODE

Astrom Ch 1, Franklin Ch 1, Ch 2.2
Week 2 Jan 27 The z-transform: Definition of the transform, transform of elementary signals, the transfer function, interpretation of z as a time-delay operator, block diagram of trapezoid integration, Relation between transfer function and pulse response, convolution

Lecture 4 Pole location and system response: Poles and zeros, Stability (internal and external), Transform of elementary signals, transform of the general sinusoid, relation of pole locations with the time response (radius and angle).

Franklin Ch 2.3, Ch 2.5

Week 3 Feb 03 Lecture 5

Lecture 6

Week 4 Feb 10 Lecture 7

Lecture 8

Week 5 Feb 17 Lecture 9

Lecture 10

Week 6 Feb 24 Lecture 11

Lecture 12

Week 7 Mar 02 Project Proposal Presentations

Lecture 13

Week 8 Mar 09 Lecture 14

Mid-term Exam

Week 9 Mar 16 Mid-semester Break.
Week 10 Mar 23 Lecture 15

Lecture 16

Week 11 Mar 30 Lecture 17

Lecture 18

Week 12 Apr 06 Lecture 19

Lecture 20

Week 13 Apr 13

Lecture 21

Lecture 22

Week 14 Apr 20

Lecture 23

Lecture 24

Week 15 Apr 27

Final Project Presentations

Lecture 25

Week 16 May 04

Lecture 26

Lecture 27

Week 17 May 11 Final-exam Week
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