LEARNING OUTCOMES

The aim of the course is to provide understanding, analytical skills and basic design methodologies regarding automatic systems and industrial automation.

AIMS AND LEARNING OUTCOMES

The learning outcomes of the course refer to the capacity of

-        understanding the main features of the system dynamics;

-        knowing the formal representations of continuous-time and discrete-time linear time-invariant dynamic systems

-        knowing the structural properties of continuous-time and discrete-timelinear time-invariant dynamic systems, with main focus on stability properties

-        analyzing several stability properties of a given system;

-        verifying structural properties (reachability, observability) of a given system;

-        designing stabilizing actions possibly also aimed at improving the dynamics of continuous-time and discrete-time linear time-invariant systems, by means of algebraic feedback.

PREREQUISITES

The course prerequisites refer to basic elements of the following courses:

Mathematics; Physics, Geometry

TEACHING METHODS

Aula lessons

SYLLABUS/CONTENT

Dynamic systems: types and representations.

Generalized functions. Laplace transform: properties, rules, transformation and antitransformation, time limits theorems. Zeta transform: properties, rules, transformation and antitransformation, time limits theorems.

Internal representation and state variables: calculation of the transition function. Calculation of the transition function for linear stationary systems represented in SISO external form. Transfer function, impulse response, frequency response. Feedback and the effect on the poles.

Stability: structural stability and BIBO stability.

Definitions of reachability and observability: criteria and conditions. Effects on the structural properties of the blocks connections and of possible simplifications. Feedback and structural properties.

RECOMMENDED READING/BIBLIOGRAPHY

Sergio Rinaldi: Teoria dei sistemi, CLUP, Milano

Michele Aicardi: Appunti di Teoria dei sistemi, Genova

Luca Benvenuti, Alberto De Santis, Lorenzo Farina: Sistemi dinamici, McGraw-Hill