Learning objectives
<br />The course teaches elementary concepts of control theory. Focusing on continuous-time linear time-invariant systems some techniques on the analysis and synthesis of scalar feedback control systems will be presented.
Prerequisites
<br />Analisi Matematica C, Teoria dei Segnali B.
Course unit content
<br />1) Fundamental concepts: systems and mathematical models. Block diagrams. Feedforward and feedback. Robustness of feedback with respect to feedforward. Mathematical modelling of physical systems: examples from electric networks, mechanical systems, and thermal systems.<br />2) Analysis methods of LTI (linear time-invariant) systems. Ordinary differential equations and Laplace transform. Inverse Laplace transform of rational functions. Generalized derivatives and elements of impulse function theory. Relations between the initial conditions of a differential equation. First and second order linear systems.The concept of dominant poles.<br />3) Frequency-domain analysis: the frequency response function. Relation between the impulse response and the frequency response. Bode’s diagrams. Nyquist’s or polar diagrams. Asymptote of the polar diagrams. Bode’s formula and minimum-phase systems.<br />4) Stability to perturbations and BIBO (bounded-input bounded-output) stability of LTI systems: definitions and theorems. The Routh criterion. Properties of feedback systems. The Nyquist criterion. Phase and magnitude margins: traditional definitions and their extensions. The Padé approximants of the time delay.<br />5) The root locus of a feedback systems: properties for the plotting. Generalization of the root locus: the “root contour”. Examples. Stability degree on the complex plane of a stable systems.<br />6) Control system design: the approach with fixed-structure controllers. Specification requirements and their compatibility. Phase-lead and phase-lag compensation. Pole-zero cancellations and the internal stability of a feedback connection. The PID regulator. The inversion formulae for the synthesis of lead and lag compensators. Synthesis with Diofantine equations.
Bibliography
<br />1) A. Piazzi, “Controlli Automatici A: lucidi delle lezioni”, UniNova, Parma, 2004.<br />2) G.Marro, ``Controlli Automatici'', quinta edizione, Zanichelli, Bologna, 2004.<br />3) P. Bolzern, R. Scattolini, N. Schiavoni, “Fondamenti di Controlli Automatici”, seconda edizione, McGraw-Hill, 2004.<br />4) A. Ferrante, A. Lepschy, U. Viaro, “Introduzione ai Controlli Automatici”, UTET, 2000.<br />5) J.C. Doyle, A. Tannembaum, B. Francis, “Feedback Control Theory”, MacMillan, 1992.<br />6) A. Cavallo, R. Setola, F. Vasca, “La nuova Guida a MATLAB: Simulink e Control Toolbox, Liguori, 2002.
Teaching methods
<br />
Oral lessons and exercitations at the blackboard on the analysis and synthesis of control systems. A glimpse on computer aided control systems design using MATLAB and Control Systems Toolbox.<br />
Written examination in the middle of the course lessons. Final written examination at the end of the course. Optional complementary oral exam.
