Theory of Systems

The UC TS program was designed with the aim of the student to acquire a set of fundamental knowledge and skills underlying TS. The structure adopted for the classes is sequential, being justified, in some cases, because the acquisition of specific knowledge and the development of certain competences depend on others previously assimilated. However, in general, there are contents for which the order is irrelevant, as they do not require previous knowledge and skills.

In theoretical classes, an exposition of the subject is made, complemented with practical examples, and in theoretical-practical classes, the knowledge acquired in theoretical classes is applied, complemented by the resolution of exercises to apply the acquired knowledge.

The knowledge acquired in this course unit, complemented with the knowledge of others, should allow students to design, implement and carry out both quantitative and qualitative analysis of control systems. Skills: Know the properties of physical signals and systems. Describe and represent physical systems, through mathematical models. Know control actions of automatic industrial controllers. Analyze the responses of physical systems with test signals. Analyze and characterize physical systems represented through mathematical models. Determine the stability of feedback control systems. Analyze the behavior of a system using the root place method. Analyze the behavior of a system using the frequency response method.

1 – Presentation of the UC. Brief historical description of the evolution of systems and control theory. Presentation of motivating examples, particularly in the field of electrical engineering, among others.

2 – Algebra of Block Diagrams, Canonical Form of a Control System, Block Diagram Transformation, Overlapping Multiple Input Signals, Block Diagram Simplification, Block Diagram and Mathematical Models, Mason’s Rule.

3 – Mathematical Models, forms of mathematical representation: differential equation, Laplace transform, transfer function. Linearization. Time response from the transfer function: decomposition into partial fractions, transient regime and pole location of the system. Initial value and final value theorems.

4 – Analysis of open-loop systems in the time domain, study of the behavior of the system described by a differential equation of constant coefficients. Description of a system through its transfer function, analysis of the transient response of first and second order and high order systems, a higher order system than two can be obtained as a linear combination of the lower order responses. Routh-Hurwitz stability criterion, effect of zeros on step response.

5 – Analysis of feedback systems in the time domain. Block diagram algebra, steady state analysis, the root locus method, rules for constructing the root locus diagram.

6 – Analysis of frequency domain systems, open-loop analysis, frequency response graphical representation, polar diagrams, goat diagram, Nyquist stability criterion. Closed-loop analysis, relative stability, delayed feedback systems analysis.

7 – Study on controllers, ways of controlling feedback systems, ON-OFF controllers and linear controllers. Presentation of proportional (P), integral (I) and derivative (D) actions, saturation by effect of integral action, presentation of empirical methods for the calibration or tuning of controllers, open-loop and closed-loop methods. Cascade control and control by feedforward, by compensation for advance or delay of phase and PI action.

NAO

 J. L. Martins de CARVALHO (1993). Dynamical systems and automatic control.  444 p. New York : Prentice Hall. 

Kuo, Benjamin C.. (1995). Automatic control systems. Upper Saddle River,. cop. . 897, I-8 p.. Prentice Hall.

Ogata, Katsuhiko (2003). Engenharia de controle moderno. 4ª ed. São Paulo. 788 p. Pearson/Prentice Hall.

Ogata, Katsuhiko (2008). MATLAB for control engineers. Upper Saddle River, 433 p. Pearson/Prentice-Hall.

Ogata, Katsuhiko (2000). Engenharia de controle moderno. 3ª ed. Rio de Janeiro 812 p. LTC – Livros Técnicos e Científicos. 

Ogata, Katsuhiko (1996). Projeto de sistemas lineares de controle com MATLAB. Rio de Janeiro, 202 p. Prentice-Hall.

Ogata, Katsuhiko (1997). Solução de problemas de engenharia de controle com MATLAB. Rio de Janeiro , 330 p. Prentice-Hall.