Systems Theory and Control

Code:

M3031

Acronym:

M3031

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2021/2022 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	27	Official Study Plan	2	-	6	56	162
			3

Teaching language

Suitable for English-speaking students

Objectives

Objectives:

Initial and basics knowledge in the area of Mathematical Theory of Control, area of application-oriented mathematics that deals with the basic principles underlying the analysis and design of feedback control systems. The discipline provides for computational simulation of systems using CAD tools, namely MATLAB and Simulink

Learning outcomes and competences

1- Determine the representative equations of
elementary systems of the various application areas
(Engineering, Medicine, Biology, among others) and
from them, with the mathematical methods studied,
to identify the type of response, both temporal
and frequency, that is associated with it.
2- Understand the notions associated with feedback
and analyze the behavior and stability in the domain of time 
and frequency, of feedback systems.
3- Design and calibrate controllers.

Working method

Presencial

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

Linear Algebra and Diferential Equations (advised)

Program

Mathematic Models for Dynamical Systems: discrete and continuous time. Nonlinear models; linearization. Examples.
Laplace transform, definition and properties; impulsional response and transfer function of the system.

Frequency Domain Analysis, Bode Diagrams of elementary transfer functions. Bode diagrams of a general transfer function. Influence of Zeros and Poles on the Frequency Response. Notion of Feedback System, block diagram of a Feedback System.

Performance analysis, in steady state, of feedback systems, position errors, speed and acceleration. Stability and Routh criterion.

State Space Analysis: modal analysis, stability, controlability and observability criterions.

State Feedback in Time Domain. State feedback and state observers.

Mandatory literature

João Miranda Lemos; Controlo no espaço de estados. ISBN: 978-989-8481-70-2
Panos J. Antsaklis; A linear systems primer. ISBN: 978-0-8176-4460-4

Teaching methods and learning activities

The syllabus provided will be treated in the theoric and practice classes (TP), which will introduce the relevant proposed concepts and demonstrate some of the results. In the lectures countless problems and application examples will also be solved.

It will be also proposed exercises and it will be  given the necessary support to the students for their understanding and resolution. All learning objectives have direct correspondence with the programmed contents described, being the subject of work in different types of classes provided.

Software

MATLAB

keywords

Physical sciences > Mathematics > Applied mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Trabalho prático ou de projeto	25,00
Teste	75,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Elaboração de projeto	30,00
Estudo autónomo	90,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

Frequency in TP. Justification is accepted for 
everyone depending on individual situation.

Calculation formula of final grade

• Final Grade = CT + CP (grade of each component should be superior to 40%)

• TP evaluation - Practical work, presentation and discussion = 5 marks

Classification improvement

Only CT can me improved