The subject provides an introduction to the basic/intermediate principles and tools for the design and analysis of feedback systems, many of which, in daily use are relatively complex ones, including mechanical, electronic, computer hardware/software and possibly other components as well. Systems engineers study the whole rather than one particular component, through mathematical modeling, design, analysis and implementation in order to get the fulfillment of given requirements. Further topics include: (a) quantitative models of mechanical, electrical and electronic physical systems, described by linear, ordinary differential equations; (b) stability, steady state and transient performance analysis of single input, single output open loop and closed control systems; (c) steady-state and transient requirements translation; (d) frequency domain controllers design through phase-lead and phase lag networks. We have attempted to keep the mathematical prerequisites to a minimum while being careful not to sacrifice rigor in the process. We have also attempted to make use of examples from a variety of disciplines, illustrating the generality of the introduced methods and tools. A major goal of this course is to present a concise and insightful view of the current knowledge in feedback and control systems. Summarizing, the objective of this course is to apply knowledge of mathematics and engineering to analyze and design a control system to meet desired specifications.

By the end of this subject , students will gain the following knowledge and skill: - Knowledge of the concept of a dynamical system together with its mathematical representations such as state equations and transfer functions. - Skill in deriving mathematical models of linear dynamical systems. - Skill in computing the solution of the system state equations. - Skill in evaluating the behaviour of a dynamical system through numeric simulation. - Knowledge of structural properties (stability, reachability, observability) of dynamical systems - Skill in studying the structural properties of dynamical systems. - Knowledge of the concept of feedback control of dynamical systems. - Knowledge of the main performance requirements of feedback systems. - Knowledge of the main analysis techniques in the frequency domain for the study of the stability and performance of feedback systems. - 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 and lag networks. - Knowledge of sampled data control systems. - Skill in designing sampled data control systems. - Skill in evaluating the behaviour and performance of controlled systems through numerical simulation.

Knowledge of differential and integral calculus of vector valued real functions, and the basic concepts of physics (mechanics, electric circuits, ...). Basic results of complex numbers, functions of a complex variable, the Laplace transform and a good knowledge of linear algebra and the theory of polynomial and rational functions. Basic skill of Matlab and Simulink.

- Subject organization. Prerequisites. Subject description. Exam rules. Major topics and course outline (1.5 hr). - Control problem formulation (1.5 hr). - Introduction to dynamical systems. State space representation. Examples of state space representation of physical systems (4.5 hr). - Solution of state equations. Transfer function (4.5 hr). - Modal analysis and stability of linear systems (9 hr). - Minimality, reachability and observability, realization (1.5 hr). - Bode, polar, Nyquist and Nichols diagrams (9 hr). - Nyquist stability criterion. Stability margins (4.5 hr). - Feedback systems response to polynomial inputs; steady state tracking errors, disturbance attenuation and rejection (4.5 hr). - Transient and steady state requirements translation (4.5 hr). - Control design in the frequency domain through lead and lag functions (9 hr). - Introduction to sampled data control systems design. (6 hr).

Theoretical and methodological lessons are delivered, on a weekly scheduled basis, by face-to-face instruction in the classroom. Computer laboratory activities are scheduled in order to develop 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, Simulink and the Control System Toolbox. Some exam simulations are presented in the last two weeks of the course.

Selected chapters from: (a) A. Isidori, Sistemi di controllo, volume primo, Siderea. (b) G. F. Franklin, J. D. Powell and M. L. Workman, Digital Control of Dynamic Systems, Addison-Wesley. (c) P. Bolzern, R. Scattolini, N. Schiavoni, Fondamenti di controlli automatici, McGraw-Hill Libri Italia. Lecture slides will be available as well as laboratory practice handouts.

Modalità di esame: Elaborato scritto individuale;

Exam: Individual essay;

... Written examination in computer laboratory: based on computer aided analysis and design of a feedback control system, adequately documented through a written report. More precisely, it is required to (A) Understand and translate the design specifications (12 - 16 points); (B) Design a controller that guarantees fulfillment of the assigned requirements (6 - 8 points); (C) Report the obtained performance of the designed feedback control system (5 - 7 points); (D) Carry out further performance analysis of the designed control system against given disturbances (5 - 7 points); (E) Provide orderly and clear presentation with legible handwriting (2 points). During the examination, lasting 4 hours, the student may consult the lecture slides provided by the lecturer. Detailed instructions and rules are presented in due 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.

Modalità di esame: Prova scritta tramite l'utilizzo di vLAIB e piattaforma di ateneo;

Online written exam, based on computer aided analysis and design of a feedback control system, adequately documented through a written report, with orderly and clear presentation with legible handwriting. The exam is split into two parts Part 1 (A.1) Understand and translate the design specifications into suitable design parameters. (A.2) Discuss the sign of the generalized steady-state gain Kc for which the control system is stabilizable with dynamical networks (phase-lead and/or phase-lag). Part 2 (B) Design a controller that guarantees fulfillment of the assigned requirements. (C) Report the obtained performance of the designed feedback control system. (D) Discuss problems on modal analysis and stability. Detailed instructions and rules are presented in due course.

Modalità di esame: Elaborato scritto individuale; Prova scritta tramite l'utilizzo di vLAIB e piattaforma di ateneo;

Online written exam, based on computer aided analysis and design of a feedback control system, adequately documented through a written report, with orderly and clear presentation with legible handwriting. The exam is split into two parts Part 1 (A.1) Understand and translate the design specifications into suitable design parameters. (A.2) Discuss the sign of the generalized steady-state gain Kc for which the control system is stabilizable with dynamical networks (phase-lead and/or phase-lag). Part 2 (B) Design a controller that guarantees fulfillment of the assigned requirements. (C) Report the obtained performance of the designed feedback control system. (D) Discuss problems on modal analysis and stability. Detailed instructions and rules are presented in due course.