- Basics of Matlab and Simulink; - 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 dynamical systems. - Skill in computing the solution of the system state equations. - Skill in evaluating the behavior of a dynamical system through numeric simulation. - Knowledge of structural properties (stability, reachability, observability) of dynamical systems. - Knowledge of the concept of feedback control of dynamical systems. - Skill in designing feedback controllers via (estimated) state feedback. - Knowledge of the main performance requirements of feedback systems. - Knowledge of the main feedback system analysis techniques based on harmonic tools. - Skill in analyzing the stability and the performances of feedback control systems. - Knowledge about simplest industrial controllers (PID). - Knowledge about sampled data control systems and realization through digital filters. - Skill in designing sampled data control systems. - Skill in evaluating the behavior and performances of controlled systems through numerical simulation.

Linear algebra: operations with vectors and matrices, inverse matrix, determinant, eigenvalues and eigenvectors; Complex numbers; Differential and integral calculus; Basic notions of mechanics and electric circuits is desirable, but not a strict prerequisite.

- Introduction to dynamical systems. - Modeling and state space description. - Solution of state equations. - Modal analysis - Stability of linear systems. - Block algebra. - Reachability (controllability) and observability. - Introduction to feedback control. - Control through feedback of the estimated states - Bode, polar and Nyquist diagrams. - Nyquist stability criterion. - Stability margins. - Feedback systems response due to 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. - Industrial controllers (PID). - Discrete-time systems. Analysis and design of sampled data control systems.

The course consists of lectures, laboratory practicums and seminar-style lectures at the end of the course. Lectures cover -- the theoretical topics of the course (the concepts of dynamical systems, state-space models, linear stability analysis and design of stabilizing controllers, frequency-domain techniques for linear systems, basics of identification, PID controllers); -- some numerical examples and solved problems; -- seminar-style lectures are devoted to practical implementation of digital controllers and filters. In the case of mixed online-offline teaching, the theoretical material will be primarily taught online. The offline lectures will be devoted to consideration of examples and problems (the materials will also be available online). The goal of LAB sessions is to enable students to use MATLAB and Simulink software for numerical simulation, rigorous analysis and design of control systems. The solutions to all problems will be available on the course webpage. The topics of the exercises are: -- derivation and linearization of mathematical equations (state-space models), linearization; -- implementation of models in Simulink, analysis of input-output response; -- analytic and numerical stability analysis; -- transfer functions, Laplace transforms, response to harmonic signals; -- minimal state-space realizations, observability, controllability; -- Nyquist criterion, frequency-domain analysis (stability margins); -- Design of controllers satisfying certain specifications (rise time, overshoots); -- LQR controller design; -- Observer design. The students are recommended to download Matlab with Campus licence to their laptops. The seminar-style lectures at the course are devoted to implementation of digital controllers and filters on programmable logic controllers. An optional project will be proposed for the students (adds extra 2 points to the final exam).

G.F. Franklin, J.D. Powell, A. Emami-Naeini, Feedback Control of Dynamic Systems, Prentice Hall, 2009. N. Nise, Control systems engineering, Wiley, 4th ed., 2004. K. Ogata, Modern Control engineering, Prentice Hall, 4th ed., 2004. G. Calafiore, Elementi di Automatica, CLUT, 2007. Lecture slides and laboratory practice handouts will be available.

Exam: Computer-based written test in class using POLITO platform;

Duration of the exam is 3 hours. Allowed material: a cheat sheet with main equations, Laplace transforms and key definitions (will be disseminated before the exam). It can printed and brought to the exam, also will be available for downloading during the exam. Matlab programs, printed lecture notes and exercise solutions are not allowed. The students should bring their laptops to the exam. Other electronic devices are not allowed. The students can use online Matlab through the exam platform (Matlab cannot be started from their own computers). Simulink is also available in the online version, but is quite slow and not recommended during the exam. The exam is organized as a computer-based tests with 8 open or multiple-choice questions, each gives up to 4 points. Examples will be provided during the lectures and laboratory practicums, typical topics are -- computation of equilibria for nonlinear systems; -- linearization and stability analysis of equilibria; -- solving linear equations via Laplace transforms; -- computation of transfer functions; -- modal analysis; -- pole-placement design of controllers and observers; -- discretization; -- identification of discrete-time systems. Some general theoretical questions can be given, e.g., what is a controllable system or what is the Nyquist curve? A student can also receive 2 extra points (added to the exam mark) for the optional project, hence, the maximal mark is 34. Marks 31-34 are registered as "30 e lode." The minimal mark to pass the exam is 18.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.