Learning objectives
- Understanding of the two principles of active control, feedforward and feedback, and of the broad applications to automation.
- Understanding of the methods, based on Laplace and Zeta transforms, to determine the time-evolution of linear scalar dynamic systems.
- Knowledge of harmonic analysis and of the stability theory for linear systems.
- Knowledge of the main methods of analysis and synthesis for feedback control systems.
In relation to the ability to apply knowledge and understanding, the aims are:
- Skill to analyze feedback control systems.
- Skill to set up and solve simple problems of regulation and control with a single controlled variable.
Prerequisites
Basic elements of mathematical analysis and physics
Course unit content
1) Fundamental concepts: systems and mathematical models. Block diagrams.
Feedforward and feedback. Robustness of feedback with respect to feedforward. Mathematical modelling of physical systems. [4 hours]
2) Introduction to Laplace transform. Elements of complex analysis. Differential equations. Laplace inverse transform. [4 hours]
3) Analysis methods of LTI (linear time-invariant) SISO (single-input single-output) systems. The transfer function. Relations between the initial conditions of a differential equation. First and second order linear systems. The concept of dominant poles. [8 hours]
4) Stability of dynamical systems: stability to perturbations, BIBO (bounded-input bounded-output) stability and related theorems. Routh’s Criterion. [4 hours]
5) 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. [4 hours]
6) Properties of feedback systems. The Nyquist criterion. Phase and magnitude margins: traditional definitions and their extensions. [6 hours]
7) Control system design: the approach with fixed-structure controllers. Specification requirements and their compatibility. Phase-lead and phase-lag Compensation. The pole-zero cancellation technique and the internal stability of a feedback connection. Frequency synthesis with the inversion formulas. The Diophantine equation for the direct synthesis. Regulation of dynamic systems. The PID regulators: frequency design, tuning and implementation. Control of systems with time delay. A glimpse on feedforward-feedback schemes [10 hours]
8) Digital control systems: The z-transform. Conversion from continuous-time to discrete-time. Sampling frequency and anti-aliasing filtering. SISO discrete-time linear systems: free and forced response, stability and Jury’s Criterion. Glimpse on the synthesis of discrete-time controllers. [8 hours]
Bibliography
Books for consultation:
1) G. Marro, ``Controlli Automatici'', quinta edizione, Zanichelli, Bologna,
2004.
2) P. Bolzern, R. Scattolini, N. Schiavoni, “Fondamenti di Controlli
Automatici”, quarta edizione, McGraw-Hill Education, 2015.
3) M. Basso, L. Chisci, P. Falugi, “Fondamenti di Automatica”, CittàStudi,
2007.
4) A. Ferrante, A. Lepschy, U. Viaro, “Introduzione ai Controlli
Automatici”, UTET, 2000.
5) J.C. Doyle, A. Tannembaum, B. Francis, “Feedback Control Theory”,
MacMillan, 1992.
6) M.P. Fanti, M. Dotoli, “MATLAB: Guida al laboratorio di automatica”,
CittàStudi, 2008.
Teaching methods
Theory lectures at the blackboard. In class exercises. Computer lab with Matlab.
Assessment methods and criteria
Assessment of learning is carried out in one of the following forms to be chosen by the student:
1) a written test in the middle of course lessons followed by a final written test at the end of the course.
2) Full written test (at least one for each exam session)
During the assessment tests, it is not permitted to read notes, manuals, books, etc. Some parts of the written tests require the use of a basic scientific calculator.
The final vote is expressed in 0-30 scale and is obtained as a weighted average in the assessment forms that have two distinct parts.
