34842 - Automatic Controls and Theory of Systems M

Learning outcomes

The course is mainly concerned with the behavior of dynamical systems and analyzes their properties. It treats also some elements of filtering and optimal control.

Course contents

Introduction to systems.

General definitions and properties. State-variable and input-output descriptions. Continuous and discrete-time systems. Equivalent states and systems. Equilibrium states. Equilibrium states. Properties of dynamical systems. Problems considered by system and control theory.

Stability of dynamical systems

Stability of motions and responses. Local stability. Liapunov stability criteria. Bounded-input bounded-state and bounded-input  bounded-output stability. Approximation of continuous-time systems with discrete-time models. The reduced Liapunov criterion.

Linear time-varying systems.

State evolution. Impulse response. Reachability and controllability. Control between states. Observability and reconstructability. Observation of the initial state. Necessary and sufficient conditions for bounded-input bounded-state and bounded-input  bounded-output stability.

Linear time-invariant systems.

Computation of motions. Modes and stability. Discrete-time models of continuous systems. Reachability, controllability, observability and recontructibility subspaces. Changes of coordinates in the state space and Kalman canonical decomposition. Stability criteria. Pole assignment under state and output feedback. Design of asymptotic observers and separation property. Transfer function. Realization of an impulse response and of input-output sequences. Optimal LQ control.

Stochastic systems

Models of linear stochastic processes. State observation in stochastic contexts. Optimal filtering: Kalman filtering. Optimal control in stochastic environments: LQG control.

Readings/Bibliography

G. Marro, Teoria dei Sistemi e del Controllo, Zanichelli Editore, Bologna, 1989.

 E. Fornasini e G. Marchesini, Appunti di Teoria dei Sistemi, Edizioni Libreria Progetto, Padova, 1988.

 M. Tibaldi, Progetto di sistemi di controllo, Pitagora, Bologna, 1995.

 K. Ogata, Modern Control Engineering - Fifth Edition, Prentice Hall - Pearson, 2010.

Teaching methods

Lectures and use of e-learning tools.

Assessment methods

The final evaluation is based on oral examinations possibly integrated by the written solution of exercises and/or non mnemonic questions.

Teaching tools

Course website containing various materials, FAQs and self-evaluation tests. The site address is

http://sting.deis.unibo.it/tds/

Links to further information

http://sting.deis.unibo.it/tds/

Office hours

See the website of Roberto Guidorzi