- 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 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.

Basics of differential and integral calculus, basics of linear algebra (matrices, eigenvalues), complex numbers, polynomial and rational functions, basic notions of mechanics and electric circuits. Some experience with MATLAB is desirable, although this is 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 and laboratory practicums. 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 on automotive applications. 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. In the case of online teaching, the students can either use virtual LAIB (vLAIB) with preinstalled software or download Matlab with Campus licence to their home computers.

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: Written test via vLAIB using the PoliTo platform;

Duration of the exam is 2 hours. Allowed material: tables of Laplace transforms, single A4 sheet with formulas. Matlab programs, printed lecture notes and exercise solutions are not allowed. The students can upload only files created on vLAIB virtual machine during the exam. The exam is organized as a computer-based tests with 4-5 multiple choice questions (for their solution, Matlab functions can be useful) and 2-3 exercises on controller design in Matlab (the solution is a Matlab m-function). The students use virtual LAIB integrated with the university Exam platform. The multiple choice questions give about 24 points, covering the main topics of the course, in particular, derivation of dynamical equations, state-space models and their linearizations; Laplace transforms and transfer functions; modal analysis, stability analysis in the time domain (eigenvalues) and frequency domain (Nyquist); reponse to harmonic and polynomial inputs, disturbance rejection; controllability and observability; discretization. The design exercises give another 8 points and test a student's capability of designing controllers and observers that satisfy predefined specification by using pole placement and LQR methods. The answer to the design problem should be a Matlab script, returning the coefficients of a controller and/or observer. The examples of controller design will be considered during LAB sessions. The minimal grade needed to pass the exam is 18/30.

Exam: Computer lab-based test; Written test via vLAIB using the PoliTo platform;

Duration of the exam is 2 hours. Allowed material: tables of Laplace transforms, single A4 sheet with formulas. Matlab programs, printed lecture notes and exercise solutions are not allowed. The students cannot bring their own computers and upload files other than created on the LAIB computer or vLAIB virtual machine during the exam. The exam is organized as a computer-based tests with 4-5 multiple choice questions (for their solution, Matlab functions can be useful) and 2-3 exercises on controller design in Matlab (the solution is a Matlab m-function). In the case of online exam, the students will use virtual LAIB integrated with the university Exam platform. The multiple choice questions give about 24 points, covering the main topics of the course, in particular, derivation of dynamical equations, state-space models and their linearizations; Laplace transforms and transfer functions; modal analysis, stability analysis in the time domain (eigenvalues) and frequency domain (Nyquist); reponse to harmonic and polynomial inputs, disturbance rejection; controllability and observability; discretization. The design exercises give another 8 points and test a student's capability of designing controllers and observers that satisfy predefined specification by using pole placement and LQR methods. The answer to the design problem should be a Matlab script, returning the coefficients of a controller and/or observer. The examples of controller design will be considered during LAB sessions. The minimal grade needed to pass the exam is 18/30.