The course will address the fundamentals of dynamical systems analysis and of the design of simple analogic and digital feedback controllers.

- Knowledge of the concept of dynamical system together with its mathematical representations such as state equations and transfer functions
- Skill in deriving mathematical models of linear dynamical systems
- Skill in computing the solution of the system state equations
- To evaluate the behaviour of a dynamical system through numeric simulation
- Knowledge of structural properties (stability, reachability, observability) of dynamical systemes
- Skill in studying the structural properties
- Knowledge of nonlinear dynamical systems and the relavant properties of equilibrium solutions.
- Knowledge of the concept of feedback control of dynamical systems
- Knowledge of the main performance requirements of feedback systems
- Knowledge of the main feedback system analysis techniques based on sinusoidal tools
- Skill in analyzing stability and performance of feedback control systems
- Knowledge of the design techniques of feedback controllers based on lead and lag functions
- Skill in designing feedback controllers for single input single output systems through lead, lag and PID functions
- Knowledge of sampled data control systems and realization through digital filters
- Skill in designing sampled data control systems
- To evaluate the behaviour and performance of controlled systems through numerical simulation

Requirements: differential and integral calculus of vector valued real functions, basic concepts of physics (mechanics, electric circuits, ...), complex numbers, complex functions, Laplace transform, real rational functions, linear algebra, basic skill of Matlab.

Course topics and relevant credits
- Introduction to dynamical systems. State space representation. Examples of state space representation of physical systems. (1 cr)
- Solution of state equations, modal analysis and stability of linear systems. Transfer function. (1,5 cr)
- Minimality, reachability and observability, realization. (0,5 cr)
- Nonlinear dynamical systems. Equilibrium solution, linearization around an equilibrium solution, stability of equilibrium solutions through the linearization approach. (1,0 cr)
- Introduction to Output feedback control. Block algebra. (0,5 cr)
- Bode, polar, Nyquist and Nichols diagrams. Nyquist stability criterion. Stability margins (1,5 cr)
- Feedback systems response in face of polynomial inputs; steady state tracking errors, disturbance attenuation and rejection. Time and frequency response of first and second order systems. Feedback systems performance: transient and steady state. (1,0 cr)
- Control design by means of sinusoidal tools and using lead, lag and PID functions (1,5 cr)
- Analysis and design of sampled data control systems. (1,0 cr)
- Short accounts of control design in state space. (0,5 cr)

Exercise sessions will be carried out in computer laboratory by means of Matlab Tools (Control System Toolbox, Simulink) and are centered on the development of academic and applicative examples.

Textbooks
N. S. Nise: "Control System Engineering", 5th Edition, Wiley, 2008.
R. C. Dorf, R. H. Bishop: "Modern Control Systems", 10th Edition, Prentice Hall, 2005.
G. F. Franklin, J.D. Powell, A. Emami-Naeini, "Feedback Control of Dynamic Systems", 5th Edition, Prentice Hall, 2006.
K. Ogata, "Modern Control Engineering", 4th Edition, Prentice Hall, 2002.
P. Bolzern, R. Scattolini, N. Schiavoni, Fondamenti di controlli automatici, Ed. McGraw-Hill Libri Italia, Milano, 3a edizione, 2008
G. Calafiore, Elementi di Automatica, CLUT, Torino, 2007, II ediz.
G. Calafiore, Appunti di Controlli Automatici, CLUT, Torino, 2006.
A. Isidori, Sistemi di Controllo – Vol. Primo, Ediz. Scientifiche Siderea, Roma, 1992. II ediz.

Lecture slides will be available as well as laboratory practice handouts

Written examination carried out in computer laboratory and made up by:
- 3 mulitple choice exercises (9 points)
- 1 open question on conceptual topics (10 points)
- 1 control system design problem (14 points)
During the exam, is allowed only the use of a formulary provided by the teacher.