28015 - Automatic Controls T

Learning outcomes

The aim of the course is to provide the basic knowledge for the analysis of signals and linear systems in continuous time for the study of feedback control systems. The first part of the course concerns the illustration of the Laplace transform, the harmonic analysis and the stability criteria.
The second part presents in detail the most important methods for the synthesis of regulators in continuous and discrete 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 relays. The circle criterion.

Readings/Bibliography

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

G.F. Franklin, J.D. Powell. A. Emami-Naeini, Feedback Control of Dynamic Systems - 4rd edition,  Prentice-Hall, 2002.

R.C. Dorf, R.H. Bishop, Modern Control Systems - 11th edition, Prentice-Hall, 2008

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

Teaching methods

Lectures and practical lessons.

Assessment methods

Written and oral examination. Usage of the TFI software.

Teaching tools

Personal Computer.

Office hours

See the website of Umberto Soverini