The course is taught in English. The course will address the fundamentals of dynamical systems analysis and of the design of simple control systems.

By the end of this course, students will gain the following knowledge and skill: - 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 - Knowledge of the basic properties of the Laplace transform - Skill in computing the solution of the system state equations through the Laplace transform approach - Skill in evaluating the performance 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 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 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 - Skill in designing asymptotic state observers - Skill in designing static feedback control laws of the estimated state

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

- Introduction to dynamical systems. State space representation. Examples of state space representation of physical systems. (6 hr) - Introduction to basic properties of the Laplace transform (3 hr) - Solution of state equations through the Laplace transform, transfer function. (6 hr) - Modal analysis and internal and BIBO stability of linear time invariant systems (8 hr). - Minimality, reachability and observability, realization. (2 hr) - Introduction to output feedback control. Block algebra. (3 hr) - Bode, polar, Nyquist and Nichols diagrams. Nyquist stability criterion. Stability margins. (8 hr) - 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. (10 hr) - Control systems design by means of sinusoidal tools, i.e. loopshaping approach, using lead, lag and PID functions (17 hr) - Control systems design by means of state space methods using static feedback of the state (4 hr) - State estimation through asymptotic state observers (4 hr) - Control systems design using static feedback of the estimated state (4 hr) - Short accounts on the design of digital control systems through the emulation approach. (4 hr)

Theoretical and methodological lessons will be delivered together with example developments by face-to-face instruction in the classroom. Computer laboratory activities are aimed at developing the student’s skill through proper training. Each student is supposed to practice individually with the aid of laboratory work stations. The primary purpose of the laboratory exercises is to apply the methodologies presented in class, through the use of MatLab and Simulink. During the last week of the course, an exam simulation in the laboratory will be offered.

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 will be available on “Portale della didattica” as well as laboratory practice handouts.

Modalità di esame: Test informatizzato in laboratorio;

Exam: Computer lab-based test;

... Written exam in computer laboratory lasting 2 hours divided into two parts. Part I. 5 multiple choice problems. For each problem, 4 possible answers are shown, only one of which is correct. Each problem has a different score based on its difficulty. The maximum score of this part is 17/30. Every exact answer leads to the full score, for every wrong answer a penalty corresponding to the 25% of the ful score is subtracted, every missing answer leads to null score. The goal of this first part of the exam is to verify the understanding of the fundamental theoretical topics of analysis and design of feedback control systems. Part II. 1 control design problem (maximum score: 17/30). The goal of this part of the exam is to verify the student skilness in designing a feedback control system through the loopshaping approach. Evidence of the design procedure must be provided in the terms of the matlab files developed for the design and a text document that reports the main steps of the design. 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 greater or equal than 33. During the exam it is allowed to use a formulary provided by the instructor. Detailed instructions and rules will be presented during the course.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.