Digital Control

Code:

EEC0078

Acronym:

CDIG

Keywords
Classification	Keyword
OFICIAL	Automation, Control & Manufacturing Syst.
OFICIAL	Basic Sciences for Electrotechnology

Instance: 2020/2021 - 2S

Active?	Yes
Responsible unit:	Department of Electrical and Computer Engineering
Course/CS Responsible:	Master in Electrical and Computers Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEEC	134	Syllabus	3	-	7	63	189

Teaching language

Portuguese

Objectives

Analysis and design of linear dynamic control systems in both contexts of continuous time and sampled data.
Proficiency in the use of computational tools to suport the analysis and design of controllers for dynamic linear systems.

Learning outcomes and competences

Once this UC is concluded, students should be able to:

1. Model and analyze linear dynamic control systems by using methods and tools in the frequency domain - Root Locus and Bode Plots - in the context of periodically sampled data, and to design compensators using these tools.


2. Analyze linear dynamic control systems represented in the state space and design linear feedback controllers and linear state estimators in both discrete and continuous time.


3. Formulate linear quadratic optimal control problems and compute their optimal control strategies.


4. Use computacional tools to support the analysis of control systems and the design of controllers.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Linear Algebra, Calculus, Signal Theory, Control Theory

Program

1. Analysis and Design of Dynamic Linear Control Systems in Discrete Time.

Sampled systems: Time and frequency domains.
Block diagram operations involving ``sampler and holder".
Brief overview of key Z Transform concept and rules.
Relation between the Lapace and the Z domains.
Transfer Functions (TF) in Z. Derivation of the TF in the Z domain from the TF in the Laplace domain.
Time response in the Z domain.
Stability. Sampling frequency and stability.
Steady state errors.
Methods of Analyzis in the Z domain: Bode Plot (BP); Root Locus (RL).
Systems compensation in the Z domain: Lead and/or lag compensation using BP and RL.

2. State Space (Systems in continuous and discrete times).

Brief review of pertinent topics in Algebra (eigenvectors, eigenvalues, coordinates change).
The concept of state.
State space modeling: Differential equations of order n and the (A,B,C,D) representation.
Canonical forms: controllable, observable, and diagonal.
Time response: Variation of parameters formula.
Methods to compute the exponential of a matrix.
Poles localization and time response.
Controllability. Observability.
Pole placement: Linear state feedback controller. State estimator by output error linear feedback.
Independence of the designs of the linear controller and estimator.
Linear state estimate feedback controller
Introduction to stability in the state space domain.

Mandatory literature

Ogata, Katsuhiko; Discrete-time control systems. ISBN: 0-13-216227-X
Carvalho, Jorge Leite Martins de; Sistemas de controle automático. ISBN: 85-216-1210-9
Ogata, Katsuhiko; Modern Control Engineering. ISBN: 0-13-598731-8

Teaching methods and learning activities

Exposition classes: Presentation and discussion of the various topics of the curricular unit. Detailed explanation of examples of application of concepts and methods.
Exercises solving classes: Practical execises are solved by the students with the support of the teacher by clarifying the issues that they might raise. Follow-up of the work  in the mini projects support by the use of MATLAB.

Software

Matlab

keywords

Technological sciences > Engineering > Systems engineering > Systems theory
Physical sciences > Mathematics > Applied mathematics
Technological sciences > Engineering > Electrical engineering
Technological sciences > Engineering > Control engineering > Automation

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	70,00
Trabalho prático ou de projeto	30,00
Trabalho escrito	0,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Elaboração de projeto	20,00
Estudo autónomo	110,00
Frequência das aulas	63,00
Total:	193,00

Eligibility for exams

Frequency is obtained through remote participation in at 
least 75% of the PL classes and through participation in 
the mini-project. assessment of PL Class participation 
remotely is done by delivering an exercise from that class 
solved until the following weekend.

In each PL class, 2 students will be drawn to make a 
presentation of the exercise in question separately for 
5 minutes for each one.

Calculation formula of final grade

The final evaluation has two components:

EF - Valuation of the Final Exam on a scale of 0 to 
20 values ​​with a weight of 70%

CC - Valuation of the Continuous Component on a scale 
of 0 to 20 values ​​with a weight of 30%



Final Classification = 0.7 EF + 0.3 CC



The Continuous Component is assessed by the performance 
in the group project and the degree of participation of 
the PL Lesson remotely through the delivery of an exercise 
of that class solved until the following weekend.

In each PL class, 2 students will be drawn to make a 
presentation of the exercise in question separately for 
5 minutes for each one.

Remote participation in classes contributes to the final 
assessment up to 2 points (10%).

Project performance will be valued up to 6 points (30%).

The sum of the evaluation of the project and of the 
Continuous Component cannot exceed 6 values





The appeal exam has two objectives:

1. In case of non-approval, the appeal to the exam may 
discard the continuous component or not, being selected 
the alternative that most benefits the student.

2. In the case of approval, the appeal exam serves for 
grade improvement.

Examinations or Special Assignments

Mini-project: design a control system using MATLAB

Internship work/project

NA

Classification improvement

There are two options:

1. Conducting the resource exam valued up to 20 values

2. Conducting the resource exam valued up to 14 values, 
in case it is more advantageous for the student to 
account for the valuation of the continuous component.

Observations

Pertinnt contents (with emphasis to MATLAB suppport) in: http://www.engin.umich.edu/class/ctms/