Fundamentals of automatic control - (9 cfu)

Prof. Aurelio Piazzi Tel. 0521 905733 - Fax. 0521 905723
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The course aims at presenting the fundamental aspects of the theory of automatic control with special reference to the active feedback control of linear dynamical systems.


1) Fundamental concepts: systems and mathematical models. Block diagrams. Feedforward and feedback. Robustness of feedback with respect to feedforward. Mathematical modelling of physical systems: examples from electric networks, mechanical systems, and thermal systems.
2) Analysis methods of LTI (linear time-invariant) SISO (single-input single-output) systems. Ordinary differential equations and Laplace transform. Inverse Laplace transform of rational functions. Generalized derivatives and elements of impulse function theory. Relations between the initial conditions of a differential equation. First and second order linear systems.The concept of dominant poles.
3) Frequency-domain analysis: the frequency response function. Relation between the impulse response and the frequency response. Bode’s diagrams. Nyquist’s or polar diagrams. Asymptote of the polar diagrams. Bode’s formula and minimum-phase systems.
4) Stability to perturbations and BIBO (bounded-input bounded-output) stability of LTI systems: definitions and theorems. The Routh criterion. Properties of feedback systems. The Nyquist criterion. Phase and magnitude margins: traditional definitions and their extensions. The Padé approximants of the time delay.
5) The root locus of a feedback systems: properties for the plotting. Generalization of the root locus: the “root contour”. Examples. Stability degree on the complex plane of a stable systems.
6) Control system design: the approach with fixed-structure controllers. Specification requirements and their compatibility. Phase-lead and phase-lag compensation. Pole-zero cancellations and the internal stability of a feedback connection. The PID regulator. Frequency synthesis with the inversion formulas. The Diophantine equation for the direct synthesis.
7) Digital control systems: The z-transform. Conversion from continuous time to discrete time. Sampling rate and antialiasing filter. Design of digital controllers.

Attività d'esercitazione

Discussion and resolution of exercises at the blackboard on all topics of the course. A glimpse on computer aided control systems design using MATLAB and Control Systems Toolbox.

Modalità d'esame

The exam consists of a written examination and an optional subsequent oral examination. Alternatively, in the middle of the course lessons there is a written test and at the end of the lessons there is a final written examination.


Analisi Matematica 1, Fisica Generale 1.

Testi consigliati

Pdf slides of the lessons on the web site of the course.

Testi d'approfondimento

1) G. Marro, ``Controlli Automatici'', quinta edizione, Zanichelli, Bologna, 2004.
2) P. Bolzern, R. Scattolini, N. Schiavoni, “Fondamenti di Controlli Automatici”, terza edizione, McGraw-Hill, 2008.
3) M. Basso, L. Chisci, P. Falugi, “Fondamenti di Automatica”, CittàStudi, 2007.
4) A. Ferrante, A. Lepschy, U. Viaro, “Introduzione ai Controlli Automatici”, UTET, 2000.
5) J.C. Doyle, A. Tannembaum, B. Francis, “Feedback Control Theory”, MacMillan, 1992.
6) M.P. Fanti, M. Dotoli, “MATLAB: Guida al laboratorio di automatica”, CittàStudi, 2008.
7) A. Cavallo, R. Setola, F. Vasca, “La nuova Guida a MATLAB: Simulink e Control Toolbox, Liguori, 2002.

Ultimo aggiornamento: 05-10-2011

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