By the end of this course, students will gain the following knowledge and skills: - Knowledge of the concept of dynamical system together with its mathematical representations (state equations and transfer functions) - Skills in deriving mathematical models of linear dynamical systems - Skills in computing the solution of the system state equations - Skills in evaluating the behaviour of a dynamical system through numeric simulation - Knowledge of structural properties (stability, reachability, observability) of dynamical systemes - Skills in studying the structural properties - 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 - Skills in analyzing stability and performance of feedback control systems - Knowledge of the design techniques of feedback controllers based on the state space representation through static feedback control laws of the state - Skill in designing state feedback controllers - Knowledge of the state estimation procedures by means of asymptotic state observers - Skills in designing asymptotic state observers - Skills in designing static feedback control laws of the estimated state - Knowledge of the design techniques of feedback controllers based on lead and lag functions - Skills 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 - Skills in designing sampled data control systems - Skills in evaluating the behaviour and performance of controlled systems through numerical simulation

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 knowledge of Matlab. Signal and sampling theory. Z-transform.

- Introduction to continuous-time dynamical systems. State space representation, solution of state equation through Laplace transform, transfer function. (10 hr) - Modal analysis and stability of linear systems. Steady state analysis. Prototype systems. (12 hr) - Introduction to output feedback control; block algebra. (5 hr) - Bode, polar, Nyquist and Nichols diagrams. Nyquist stability criterion. Stability margins. (12 hr) - Feedback systems response in the presence 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. (15 hr) - Control systems design by means of sinusoidal tools using lead, lag and PID functions (15 hr) - Introduction to discrete-time dynamical systems: state space representation, Z transform, transfer function, stability (3 hr) - Design of digital control systems through the emulation approach. (10 hr) - Control systems design by means of state space methods using static feedback of the state. Reachability, observability. State estimation through asymptotic state observers . Control systems design using static feedback of the estimated state (15 hr) - Non-linear systems: computation of the equilibrium points and stability (3 hr)

Lessons: we illustrate the theory and the methodologies and we solve several practical examples, by using MATLAB. Laboratory activities (indicatively, each two tweeks): the aim is to develop the student’s skills through proper training. Students are supposed to practice individually to solve the proposed problems. The primary purpose of the laboratory activities is to apply the methodologies presented during the lessons, through the use of MATLAB. During the last week of the course, an exam simulation in the laboratory is offered.

Lecture slides and laboratory practice handouts are available on the “Portale della didattica”. The main reference textbooks are: 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; Lab exercises;

Exam: Computer lab-based test;

Part I: up to a maximum of 6 theoretical and practical exercises. The goal of this part is to verify the understanding of the fundamental theoretical topics of analysis and design of feedback control systems. The student know-how is verified through questions proposed by means of the Moodle exam platform, in the form of, e.g., multiple-choice, numerical response questions. Maximum score: 16/30. Part II: control design problem. The goal of this part is to verify the students' skills in designing a digital feedback control system via loopshaping approach. Evidence of the design procedure must be provided in the terms of the Matlab files developed for the design. A text document that reports the main steps of the design may be required. Maximum score: 17/30. The final grade is the sum of the scores achieved in the two parts. A mark of 30L/30 is given if the final score is equal to 33. During the exam it is allowed to use a formulary provided by the instructor. The exam is given in Laib using the Exam platform. The course instructor reserves the right to perform an oral examination in specific cases at her/his discretion. Detailed instructions and rules are presented during the course.

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.