# Systems Theory

2478

### Department

Departamento de Engenharia Electrotécnica

6.0

### Teacher in charge

Fernando José Almeida Vieira do Coito

5

78

Português

### 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.

### 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

### 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)

• Problems (in portuguese)
• Experiments workbook (in portuguese)

### Teaching method

Theoretical 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 evaluation of knowledges will be done in the progressive form in accordance with the sequence below. There will be 3 types of components of evaluation:

A - Practical (Pi) - it will consist of 6 sets of problems assessed with 1 point. The problems will involve programming in computer and, done in group, the answers will be individual. The presence in the practical classrooms (> 8) and a at least classification of 3 values secures the frequency.

B - Test in the Moodle - there will be 2 tests (Mi) in the Moodle for 2 values each.

C - written Test - there will be 2 written tests (Ei) for 5 values each done in the theoretical classroom.

The evaluation will be done sequentially in accordance with the scheme:
P1 - P2 - M1 - P3 - E1 - P4 - P5 - M2 - P6 - E2
and the classification done accumulatively, being approved with 9.5 of least note.
This scheme means that the note will be able, at most, to be developed in the next form:
1 - 2 - 5 - 6 - 10 - 11 - 12 - 13 - 16 - 20.
There is no obligatoriness of effectuating any of the evaluations, but there is a requirement of a minimum of 6 in the theoretical component (E+M).
The stidents who, having obtained frequency, have not been approved that they will be able to take an exam for 14 values.
The improvements of note, for who has been already approved, will be done by an examination for 20 v.