## Courses Catalogue

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Our catalogue provides a description of the courses offered at NOVA as well as useful information about our Schools.

# Systems Theory

2478

### Department

Departamento de Engenharia Electrotécnica

6.0

### Teacher in charge

Fernando José Almeida Vieira do Coito, Manuel Duarte Ortigueira

5

67

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.

### Prerequisites

Main mathematical concepts:

• integrals and derivatives
• series, polynomials and polynomial fractions
• complex analysis
• graphical representation

### 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

2. Mathematics:

2.1. Complex numbers 2.2. Laplace transform

3. Mathematical representation of systems:

3.1. The model 3.2. Properties 3.3. Dynamic systems physical modeling: 3.3.1. Mechanical systems 3.3.2. Electrical systems 3.3.3. Heat and mass flow

4. Time analysis:

4.1. First order systems 4.2. Second order systems 4.3. Higher order systems

5. Control systems in the time domain:

5.1. Feedback 5.2. Set-point tracking 5.3. Stability. Routh-Hurwitz criterion 5.4. PID controllers

6. Control systems in the frequency domain:

6.1. Frequency behavior 6.2. Bode diagrams 6.3. The relationship between time and frequency  6.4. Control system specifications 6.4. Nyquist criterion 6.5. Gain and phase margins 6.6. The lead compensator and the lag compensator 6.7. Loop gain shaping.

7. Introduction to the discrete-time signals and systems.

### 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
• "Manual de Matlab" (in portuguese)
• "Introdução ao Simulink" (in portuguese)
• 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 assessment will have 3 components: tests, practice, and exam

• There will be 3 tests on the Moodle.
• The practice will be constituted by a project and several sets of problems to be done along the semester, using the 2 final hours of the classes.Tthe project will have 2 evaluations.
• Students need a minimum classification of 9,5 in pratice + 7,5 in tests, to have access to the exam.
• There will be two kinds of exams:
One counting with 40% for the final classification for those with at least 9,5 in the tests. The final classification will be done by 0.4*P+0,2*T+0,4*E.
One counting with 60% for the final classification for those with at least 7,5 in the tests. The final classification will be done by 0.4*P+0,6*E.