28015 - Automatic Controls T

Course Unit Page

  • Teacher Umberto Soverini

  • Credits 9

  • SSD ING-INF/04

  • Teaching Mode Traditional lectures

  • Language Italian

  • Campus of Bologna

  • Degree Programme First cycle degree programme (L) in Electrical Energy Engineering (cod. 5822)

Academic Year 2022/2023

Learning outcomes

At the end of the course the student owns the basic skills regarding feedback control systems and has notions on the Laplace transform, the harmonic analysis and the stability criteria. Moreover, the student owns skills regarding the most important methods for the synthesis of regulators in continuous time, both for linear systems and nonlinear systems with algebraic non-linearity.

Course contents

1. Signals and systems. Block diagrams. Feedforward and feedback control systems. Mathematical models of some dynamical systems.

2. Analysis of linear dynamic systems. Linear differential equations. The Laplace transform and the inverse Laplace transform for rational functions. Responses of first and second order elementary dynamic systems.

3. The frequency response function. Bode plots. The Bode formula. Polar plots. Nichols plots.

4. Definitions and theorems on stability. The Routh criterion. General properties of feedback systems. Steady-state errors and type of systems. The Nyquist criterion. Gain and phase margins. Systems with delays. M and N constant loci. Resonance angular frequency, resonance peak and bandwidth.

5. The root locus method. Definition of the root locus. Properties of the root locus. Some examples. The root contour.

6. Compensators and standard regulators. Performance specifications and their compatibility.The most important RC compensators. Design with lag and lead compensators. Design with lead-lag and bridged-T compensators. Standard regulators. Sensitivity functions on the Bode diagrams.

7. The Fourier series. Nonlinear feedback systems. Equilibrium states and stability. The describing function. Analysis of systems with non linear static blocks . The circle criterion.


G. Marro, Controlli automatici - 5a edizione, Zanichelli, Bologna, 2004.

P. Bolzern, R. Scattolini, N. Schiavoni, Fondamenti di controlli automatici - 4a edizione, Mc Graw Hill Education, 2015.

R. Zanasi, Esercizi di Controlli Automatici - 2a edizione, Progetto Leonardo, Bologna, 2011.

G.F. Franklin, J.D. Powell. A. Emami-Naeini, Controllo a retroazione di sistemi dinamici, Vol. I - EdiSES s.r.l., Napoli, 2004.

R.C. Dorf, R.H. Bishop, Controlli Automatici - 1a edizione, Pearson Italia, Milano, 2010.

Teaching methods

Lectures and practical lessons. Practical lessons with TFI (Transfer Function Interpreter)

Assessment methods

Written and oral examination.

Teaching tools

Personal Computer.

Office hours

See the website of Umberto Soverini