OVERVIEW

The course presents the basic notions and concepts related to the analysis and control of dynamic systems.

AIMS AND CONTENT

LEARNING OUTCOMES

The course provides the basics regarding the theory of dynamical systems, and their formal representation. The structural properties of the systems are studied, and the concept of feedback is introduced

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 linear time-invariant dynamic systems
• knowing the structural properties of continuous-time linear 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 linear time-invariant systems, by means of algebraic feedback.

PREREQUISITES

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

Mathematics; Physics, Geometry.

TEACHING METHODS

Frontal lessons. Classroom exercises.

SYLLABUS/CONTENT

Dynamic systems: types and representations.

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

Calculation of 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 and BIBO.

Internal representation and state variables: calculation of the transition function. Various types of 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

TEACHERS AND EXAM BOARD

Exam Board

SIMONA SACONE (President)

MICHELA ROBBA

SILVIA SIRI

LESSONS

Class schedule

THEORY OF SYSTEMS

EXAMS

EXAM DESCRIPTION

Written and oral examinations.

ASSESSMENT METHODS

During the exam the student has to solve numerical exercises and to explain the theoretical notions necessary for their solution.

Exam schedule

FURTHER INFORMATION

Pre-requisites :

Mathematical analysis 1 and 2; Physics; Geometry.