- 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); -- Optimal controller design (linear-quadratic regulators); -- 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: Computer lab-based test;

The total duration of exam is 3 hours. The computer-based test includes 6 (six) multiple-choice questions with 3-5 alternatives and 1 (one) design exercise. During the exam, you can use only a table of Laplace transforms. You cannot bring any other printed or handwritten materials. You are not allowed to bring any programs on USB sticks and use any electronic devices except for the laboratory computer (Matlab and Simulink will be installed on it). Each multiple-choice question gives 4 points if answered correctly and 0 points if skipped or answered incorrectly. The questions can be fully theoretical (e.g. what is an observable system?) or require to solve a simple problem (e.g. to find the poles of a given transfer function or to solve a linear time-invariant system using Laplace transforms). The design exercise requires to write and submit a Matlab M-function (potentially, accompanied with a Simulink diagram) that finds the controller and observer with a set of predefined properties and illustrates the behavior of the closed-loop system. The design exercise gives up to 7 points (partial grading applies). The final mark is computed as the sum of points collected for all tasks. Mark 31 corresponds to 30L.

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.

Exam: Written test via vLAIB using the PoliTo platform;

The total duration of exam is 3 hours. The computer-based test includes 6 (six) multiple-choice questions with 3-5 alternatives and 1 (one) design exercise. During the exam, you can use only a table of Laplace transforms. You cannot use any other materials and any electronic devices except for the computer used to take the exam. Please keep it in mind that the computer has to be equipped with camera (to provide video-surveillance during the exam). All programs (Matlab etc.) and files can be opened only on the VLAIB virtual machine. Detailed instructions will be provided. Each multiple-choice question gives 4 points if answered correctly and 0 points if skipped or answered incorrectly. The questions can be fully theoretical (e.g. what is an observable system?) or require to solve a simple problem (e.g. to find the poles of a given transfer function or to solve a linear time-invariant system using Laplace transforms). The design exercise requires to write and submit a Matlab M-function (potentially, accompanied with a Simulink diagram) that finds the controller and observer with a set of predefined properties and illustrates the behavior of the closed-loop system. The design exercise gives up to 7 points (partial grading applies). The final mark is computed as the sum of points collected for all tasks. Mark 31 corresponds to 30L.

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

The total duration of exam is 3 hours. The computer-based test includes 6 (six) multiple-choice questions with 3-5 alternatives and 1 (one) design exercise. During the exam, you can use only a table of Laplace transforms. You cannot bring any other printed or handwritten materials. Students who are doing the exam onsite are not allowed to bring any programs on USB sticks and use any electronic devices except for the laboratory computer (Matlab and Simulink will be installed on it). If you are taking exam online, you can open programs and create files only on the VLAIB virtual machine (detailed instructions will be provided). Each multiple-choice question gives 4 points if answered correctly and 0 points if skipped or answered incorrectly. The questions can be fully theoretical (e.g. what is an observable system?) or require to solve a simple problem (e.g. to find the poles of a given transfer function or to solve a linear time-invariant system using Laplace transforms). The design exercise requires to write and submit a Matlab M-function (potentially, accompanied with a Simulink diagram) that finds the controller and observer with a set of predefined properties and illustrates the behavior of the closed-loop system. The design exercise gives up to 7 points (partial grading applies). The final mark is computed as the sum of points collected for all tasks. Mark 31 corresponds to 30L.