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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 (post-covid)

Homeworks+Quiz : 20% 35%

Course project: 25% 35%

Midterm: 25% 30%

Final : 30%

General 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 (pre-covid). Mon, Wed: 12:30pm-1:45pm. 10-202. SSE Bldg

Online Lectures (post-covid). YouTube Playlist


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 4.1
Week 2 Jan 27 Lecture 3 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), Infering stability from the impulse response, Jury's stability test, transform of the general sinusoid, relation of pole locations with the time response (radius and angle).

Franklin Ch 4.2, Ch 4.4

Week 3 Feb 03 Lecture 5 Pole location and system response ctd: The discrete sinusoid as a discrete version of a continuous signal, the implied mapping of poles from s-plane to z-plane, damping ratio and natural frequency lines in the z-plane

Kashmir Day Holiday

Franklin Ch 4.4

Week 4 Feb 10 Lecture 6 Sampling related issues: placement of sampling and hold circuits in the digital control system, the phenomenon of aliasing (frequency folding), compensating for aliasing with a band-pass filter, practical anti-aliasing filters, taking into account the approximate dynamics of the filter

Lecture 7 The hold operation: Modelling the sample and hold device in a sampled-data system; C.T transfer function of the zero-order-hold; The D.T representation of a plant coupled with zero-order hold; the spectrum of the sample and hold; Aprroximating the sample and hold with a pure time delay

Franklin Ch 5, Astrom Ch 7.4

Franklin Ch 4.3.1

Week 5 Feb 17 Lecture 8 Realization of Digital Controllers: Devising customized circuitry using adders, multipliers and delay elements; Realization through direct programming; Realization through standard canonical programming; Introduction of the state variables; Control canonical and Observer canonical realizations; State-space description of the canonical forms

Lecture 9 State Space fundamentals: The concept of a state; State transformations; Relation with the transfer function; Poles and eigenvalues; Invariance of the transfer function under non-singular linear state transformations

Project proposal reports due

Franklin Ch 4.2.3, Ch 4.3.3
Week 6 Feb 24 Lecture 10 State space descriptions of sampled data systems: Solution to the homogeneous state equation, the matrix exponential, properties of the exponential, Calculating the exponential by power series, diagonalization and the Laplace transform; Solution of the non-homogeneous state equation; Discretizing the solution; Obtaining the discrete time state space description from the continuous time model with a Z.O.H.

Lecture 11 Discrete-time equivalents to continuous-time transfer functions: Equivalents by numerical integration; forward, backward and bilinear rules; distortion of stable regions; frequency warping in the bilinear transform; Zero-pole mapping equivalents; Hold equivalents

Franklin Ch 4.3.3, Ch 6
Week 7 Mar 02 Lecture 12 Time delayed systems; Classification of time-delayed systems; Rational and irrational transfer functions; Pade's approximation; State space model for a continuous time delay line; Example of a time delay system: shower mixer; Discrete-time equivalent for a time-delayed system; Equivalents for the transfer function representations.

Lecture 13 Equivalent state-space description for a time-delayed system; control design specifications; error coefficients for steady state accuracy; system Type

Franklin Ch 4.3.2, Ch 4.3.4, Ch 7.1
Week 8 Mar 09

Lecture 14 Transient response specifications for control design; Mapping response speifications to pole and gain values; Sample rate selection; Control design through emulation; Efficient coding of a discrete-time transfer function; Evaluating the response for a designed controller

Mid-term Exam

Franklin Ch 7.1 Ch 7.2
Weeks 9-11 Covid Lockdown.
Week 12 Apr 06 Lecture 14 (Repeat) video System specifications; Classification based on system type; Determining error coefficients for sampled-data systems; Transient response specifications for sampled-data systems; Design by emulation (procedure); Guidelines for selection of sample time

Lecture 15 video Design example: Mapping system requirements to response specifications; obtaining a continuous time controller for the emulated system; obtaining the discrete equivalent controller; Implementation issues for discrete-time controllers; Evaluation of design; Degradation in performance due to sampling and incorporating delays due to low sampling in the design process

Franklin Ch 2.1.1, Ch 2.2.2, Ch 4.4.5, Ch 7.1, Ch 7.2 m file (lec 15)

Week 13 Apr 13 Lecture 16 video Introduction to state space design: The control law and estimation design problems; Control law design through algebraic pole placement; Full state feedback in the control canonical form; Ackerman's formula and pole placement Franklin Ch 8.1
Week 14 Apr 20 Lecture 17 video Controllability: pole placement for an uncontrollable system; definitions and test for controllability; controllability and pole cancellation; weak controllability; Controller saturation and guidelines for good pole selection; Pole selection for higher order systems

Lecture 18 video Estimation: Introduction to the estimation problem, design of prediction estimators, observability in discrete time, design of current estimators, introduction to reduced order observers

Franklin Ch 8.1, Ch 8.2, Ch 8.3.2, Ch 8.7 m file (lec 17) m file (lec 18)
Week 15 Apr 27

Lecture 19 videoCombined control law and estimation: The separation principle of estimation and control; The equivalent transfer function representation for the compensator; comparison of compensators based on the prediction, current and reduced-order estimators; Evaluating closed loop system response in simulation; Computing steady state control effort for non-zero reference inputs

Lecture 20 video Introduction of the reference input; reference input with full state feedback; The state command structure; The output error command structure; Comparison with classical compensation techniques

Franklin Ch 8.3 Ch 8.4 m file (lec 19) m file (lec 20)
Week 16 May 04

Lecture 21video Integral control and disturbance estimation; Integral control through state augmentation; Disturbance rejection through disturbance estimation; Rejection of sensor disturbances; Reference following through feedforward

Lecture 22 video Effect of delays; Incorporating sensor delays in control design; Dealing with actuator delays; Summary of state space design

Franklin Ch 8.5, Ch 8.6 m file (lec 21) m file (lec 22)
Week 17 May 11 Project report submission
Week 18 May 18 Final Viva

Project Policy

  • Evaluation based on 2 presentations and a report proposal report, final report and final viva.
  • Project title and scope to be proposed by the students and approved by the instructor.
  • Project must be motivated by a real-life problem.
  • Project must consist of at least the following steps
    • Problem background and formulation of the control/estimation problem
    • Specifications of the system response for control/estimation design, properly contextualized in the domain of application
    • Sensing mechanisms, actuators and sampling related issues
    • Discrete-time/sampled-data model
    • Controller/Estimator Design
    • Evaluation of the designed controller/estimator w.r.t. the response specifications
    • A commentary on the limitations and tradeoffs of the designed control/estimation scheme

Project Ideas

Power and Energy

  • Multisampled Digital Average Current Controls of the Versatile Buck–Boost Converter Paper.
  • Design and Implementation of Digital Control in a Fuel Cell System Paper.
  • Digital Control of Resonant Converters: Resolution Effects on Limit Cycles Paper.
  • Simple and Effective Digital Control of a Variable-Speed Low Inductance BLDC Motor Drive Paper
  • Multisampled Digital Average Current Controls of the Versatile Buck–Boost Converter Paper Haider Ali Tauqeer 19060036


  • Robust digital control for autonomous skid-steered agricultural robots Paper. Muhammad Hammad Ullah 19060027
  • Discrete-time second order sliding mode with time delay control for uncertain robot manipulators Paper
  • Receding Horizon Control for Convergent Navigation of a Differential Drive Mobile Robot Paper
  • A comparison of continuous and discrete tracking-error model-based predictive control for mobile robots Paper Arslan Hassan 19060016

Networked Control

  • Variable Selective Control Method for Networked Control Systems Paper Maham Javed 19060024
  • Consensus Problems for Discrete-time Agents with Communication Delay Paper Mahnoor Aftab 18060035
  • On Kalman-Consensus Filtering With Random Link Failures Over Sensor Networks Paper
  • Robust Discrete-Time Markovian Control for Wheeled Mobile Robot Formation Paper

Environment and Agriculture

  • Optimal irrigation management for large-scale arable farming using model predictive control Paper
  • Adaptive Sampling for Energy Conservation in Wireless Sensor Networks for Snow Monitoring Applications Paper Hassam Arshad 19060045
  • Distributed Model Predictive Control of Irrigation Systems using Cooperative Controllers Paper
  • Ecological monitoring in a discrete-time prey–predator model Paper Bilal Ahmad 19060021


  • Data-Driven Digital Direct Position Servo Control by Neural Network With Implicit Optimal Control Law Learned From Discrete Optimal Position Tracking Data Paper
  • Structures within the Quantization Noise: Micro-Chaos in Digitally Controlled Systems Paper
  • Chatter Stability in Robotic Milling Paper
  • Chattering-free discrete-time sliding mode control Paper Talha Nadeem 19060015
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