# 28527 - Automatic Controls T-1

### Course Unit Page

• Teacher Roberto Diversi

• Learning modules Roberto Diversi (Modulo 1)
Roberto Diversi (Modulo 2)

• Credits 9

• SSD ING-INF/04

• Teaching Mode Traditional lectures (Modulo 1)

• Language Italian

• Campus of Bologna

• Degree Programme First cycle degree programme (L) in Automation Engineering (cod. 9217)

• Course Timetable from Sep 15, 2022 to Nov 11, 2022

Course Timetable from Nov 15, 2022 to Dec 20, 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. 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.

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