28527 - Automatic Controls T-1

Course Unit Page

Academic Year 2019/2020

Learning outcomes

The aim of this course is to provide competencies and methodologies for the mathematical modelling and simulation of dynamic systems and their analysis in both the time and frequency domain. In particular, the state-space approach is treated over various physical domains: electrical, mechanical, electromechanical, hydraulic, thermal. The analysis in the time/frequency domains will be based on the Laplace/Fourier transforms.

Course contents

Systems and models. Mathematical models as approximation of reality: concept of competent model. Simulation. Modelling and identification. Classification of models. State-space models: linear, non linear, time-invariant. Equilibrium and stability. Linearization. Lyapunov criteria. Constructing state-space models of dynamic systems belonging to different physical domains: electrical, mechanical, electromechanical, hydraulic, thermal. Analysis of linear and time-invariant systems: the Laplace transform. The matrix exponential. Responses of first and second order systems. Transfer functions and state-space models. Block diagrams. Analysis in the frequency domain: Fourier series, Fourier transforms, the harmonic response function. Bode diagrams. Analysis of linear discrete-time systems: the Zeta transform. A brief outline of the numerical solution of differential equations.


Course slides, see the course website:


P. Bolzern, R. Scattolini, N. Schiavoni, "Fondamenti di Controlli Automatici", McGraw-Hill, 2015.

G. Marro, "Controlli Automatici", Zanichelli, 2004.

G. F. Franklin, J. D. Powell, A. Emami-Naeini, "Controllo a Retroazione di Sistemi Dinamici", Vol. I, EdiSES, 2004.

W. J. Palm III, "Control Systems Engineering", Wiley, 1986.

P. E. Wellstead, "Introduction to Physical System Modelling", scaricabile all'indirizzo http://www.control-systems-principles.co.uk/downloads.html

A. Cavallo, R. Setola, F. Vasca, "La nuova guida a MATLAB, Simulink e Control Toolbox", Liguori Editore, 2002.

U. Soverini, "Sistemi Dinamici - Esercizi commentati e risolti", Esculapio, 2013.


Teaching methods

Traditional lectures.

Assessment methods

The final evaluation is based on written and oral examinations.

Teaching tools

Video projector.

Office hours

See the website of Roberto Diversi