Digital Control

Code:

EEC0078

Acronym:

CDIG

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

Instance: 2016/2017 - 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	120	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.

3. Introduction to Optimal Control.

Formulation of the linear quadratic optimal control problem.
Geometric interpretation.
Optimality conditions and computation of the solution in  feedback form.
The principle of optimality.
Conditions of optimality given in the form of Hamilton-Jacobi-Bellman equation.
Dynamic programming.

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

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	50,00
Teste	20,00
Trabalho escrito	30,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Elaboração de projeto	26,00
Estudo autónomo	100,00
Frequência das aulas	63,00
Total:	189,00

Eligibility for exams

Frequency is obtained through the participation in the classes and in the mini-project.

Calculation formula of final grade

The evaluation is composed by two components:
- theoretical component T = 0.2 Test + 0.5 Exam
- laboratorial component L = 0.3 min (project report, T+3)

Final grade = T + L

The Test (which is a mini-test) is done during the semester. The program that is evaluated in the Test is not covered by the first Exam.
The second exam has two goals:
1. For the case that the student was not approved, the second exam (that covers all the program) can be used to evaluate one of the components (Test and/or first exam).
2. For the case that the student was approved, the second exam can be used to improve the grade. In this case, the final grade is only the grade of this exam.

Examinations or Special Assignments

Mini-project: design a control system using MATLAB

Internship work/project

NA

Classification improvement

There exist two options:
1. Performing the second exam, which is valued up to 20/20.
2. Performing the Test (which is valued up to 5/20) and the first exam (which is valued up to 15/20)

Observations

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