28527 - Automatic Controls T-1

Course Unit Page

Academic Year 2021/2022

Learning outcomes

The aim of this course is to provide competencies and methodologies for the mathematical modelling of dynamic systems and their analysis in both the time and frequency domain. At the end of the course, the student is able to: 1) determine, through physical-mathematical approaches, state-space models (linear and nonlinear) of physical systems in various physical domains (electrical, mechanical, electromechanical, hydraulic, thermal), 2) analyze the response to given input signals of state-space and input-output models by exploiting the Laplace and Fourier transforms, 3) analyze the stability of linear systems and the stability of equilibrium states of nonlinear systems.

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.


Slides prepared by the teacher, available on Virtuale.

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 https://www.semanticscholar.org/paper/Introduction-to-physical-system-modelling-Wellstead/cec2100e1c5cb9755e00de83a3cecd0ed4414d90 

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


Teaching methods

Traditional and online lectures.

Assessment methods

The final evaluation is based on written (compulsory) and oral (optional) examinations.

Teaching tools

Video projector, PC, webcam.

Office hours

See the website of Roberto Diversi