# Systems Theory

## Objectives

Upon conclusion the student will be able to analyse the dynamic behaviour of systems in his area of expertise, and to design and tune control systems of small complexity.The course aims to develop the initiative, critical mind, autonomy and implementation abilities.

## General characterization

2478

6.0

##### Responsible teacher

Fernando José Almeida Vieira do Coito

Weekly - 4

Total - 56

Português

### Prerequisites

Mathematics:

- integral and differential calculus; differential equations

-complex numbers; complex functions

Physics:

- forces and movement; Newton''''''''s Laws

### Bibliography

• Katsyhiko Ogata, System Dynamics, Prentice-Hall
• B. J. Kuo, Automatic Control Systems, Prentice-Hall
• Katsyhiko Ogata, Modern Control Engineering, Prentice-Hall
• Franklin;-- Powell;-- Emami-Naeini, Feedback Control of Dynamic Systems, Addison-Wesley
• Texts for all the chapters  (in portuguese)

• ernando Coito, Lessons on System Theory (in portuguese)

### Teaching method

Theory/Practice class: exposition of theoretical concepts; applicatioon examples.

Practical and laboratorial classes: propblem resolution, realization of practical works to understand the concepts; realization of short projects.

### Evaluation method

The approval on the Signal Theory course can be achieved in one of two alternative ways:

1. Average grade higher than 9.5 values ​​(scale 0-20 values) in the evaluation of 2 tests to be carried out during the semester.

2. Conducting a final exam (“recurso”) with a minimum grade of 9.5.

The course doesn’t have a frequency evaluation. All students who do not get approved on tests may attend the final exam.

Tests and Exam:

Both the tests and the exam will have two evaluation components: theoretical-practical component and laboratory component. The evaluation of the laboratory component will focus on the work carried out in practical / laboratory classes . This component corresponds to 25% of the evaluation (5 points).

For the purposes of consultation, students may take only one A4 sheet with them for the tests and exam. The A4 sheet can include any material that the student considers useful, namely formulas, tables or information about laboratory work.

Practical classes / laboratory:

The frequency of practical classes / laboratory is not mandatory.

In laboratory classes, practical work will be carried out with evaluation. Students who respond to class work are exempt from answering the questions of the laboratory component of the exam or tests.

## Subject matter

1. Introducing dynamic systems:

1.1. Introduction

1.2. Relevant test signals

1.3. System properties (linearity, time invariance, causality)

1.4. Dynamic systems 1.5 Introduction to the discrete-time signals and systems.

2. Mathematics:

2.1. Complex numbers 2.2. Laplace transform

3. Time analysis:

3.1. First order systems 3.2. Second order systems 3.3. Higher order systems

4. Control systems in the time domain:

4.1. Feedback 4.2. Set-point tracking 4.3. Stability. 4.4. PID controllers

5. Control systems in the frequency domain:

5.1. Frequency behavior 5.2. Bode diagrams 5.3. The relationship between time and frequency  5.4. Control system specifications 5.4. Nyquist criterion 5.5. Gain and phase margins

## Programs

Programs where the course is taught: