LEARNING OUTCOMES

The course aims at delivering the basic conceptual and methodological tools to deal with the analysis and control synthesis for dynamic systems.

AIMS AND LEARNING OUTCOMES

Knowledge and understanding issues: Provide adequate knowledge in order to understand the role of control systems for linear time invariant SISO (single input - single output) systems. In particular, the expected learning outcomes are related to the understanding of the open and closed loop control architectures. Central are the concepts of stability of SISO dynamic systems, robustness to model uncertainties and exogenous disturbances.

As for the ability to apply knowledge and understanding, at the end of the course the student is expected to have acquired knowledge to:

Model simple dynamic systems, deducing their representation in terms of interconnection of transfer functions.

Use block algebra to deduce the functions of transfer of interest for control purposes, also evaluating all the aspects that characterize them (order, poles / zeros, their stability properties in the open cycle).

Carry out frequency analysis of transfer functions by tracing their Bode and polar diagrams.

Carry out closed loop stability analysis of control systems using all the methods developed (both in the frequency and time domains), checking the consistency between them.

Evaluate the properties of an assigned control system (reduction / cancellation of steady state errors in response to polynomial and sinusoidal signals, evaluation of dynamic behaviors, the terms of dominant poles, pass bands, etc.)

Assess the compatibility of the assigned control specifications with the characteristics of the given system. In case of incompatibility, knowing how to reformulate new specifications compatible with the system and the assigned boundary conditions.

Synthesize a regulator for a given system, capable of meeting the specifications of dynamic and steady-state behavior.

As for judgment autonomy and communication skills: judgment autonomy will have to be demonstrated through the knowledge of the concepts and methods described in the course including applying what is illustrated in the course to any other arbitrary SISO linear time invariant system.

Learning skills: the learning ability will be measured (qualitatively) during lessons, student receptions, and exercises that will be based on the maximum possible active participation. The final learning ability will be assessed globally and quantitatively during through the final exam.

PREREQUISITES

Knowledge of the general concepts and methodological tools developed in the "Teoria dei Sistemi" (Systems Theory) course.

TEACHING METHODS

• Frontal lectures (theory and exercises developed on the blackboard);
• Availability of course lecture notes;
• Written learning tests during the year;
• Class exercises;
• Illustration of the use of existing SW tools for the analysis and synthesis of control systems.

SYLLABUS/CONTENT

Part 1: Introduction to Automatic Controls: general concepts related to open and closed loop control schemes. Introduction to the concept of robustness to exogenous disturbances and parametric uncertainties. Practical examples of plant modeling and their control architectures; necessary plant conditions for its admissibility for closed loop control.

Part 2: Introduction to minimal and non-minimal phase systems including systems with finite delays.

Part 3: Closed loop stability analysis methods: Routh-Hurwitz method; Root Locus method; Nyquist method; phase crossing method; phase and gain margin method.

Part 4: Analysis of the performance, both in the time and frequency domains, of the closed loop control in steady and transient conditions. Methods of approximate evaluation of transfer functions in closed loop.

Part 5: Synthesis of regulators: specifications of a control system; general synthesis methods for minimal phase plants; phase lag and lead regulators, and proportional, integral and derivative (PID) regulator; general synthesis methods for non-minimal phase plants.

Part 6: Introduction to the discretisation of continuous time regulators for their digital implementation.

RECOMMENDED READING/BIBLIOGRAPHY

Course notes will be made available by instructors and are to be considered the main course material. As for additional references on specific topics, candidates should consider the following: 

• G. Marrro: “Controlli Automatici”, Zanichelli, 1997
• P. Bolzern, R. Scattolini, N. Schiavoni: “Fondamenti di Controlli Automatici”, McGraw Hill, 1998
• Karl J. Åström and Richard M. Murray: "Feedback Systems: An Introduction for Scientists and Engineers", Princeton University Press, 2019 (http://www.cds.caltech.edu/~murray/amwiki/Main_Page )