By the end of this course, students will be able to: ● Describe state-space and transfer-function representations of linear dynamical systems derived from physical models. ● Explain Lyapunov stability, linearization and stability criteria for equilibrium points. ● Illustrate the structural properties of linear systems: stability, controllability and observability. ● Describe the operating principles of PID, state-feedback controllers and dynamical output controllers, including state estimators. ● Define time-domain performance specifications (rise time, overshoot, settling time, steady-state error) and their practical meaning. ● Explain frequency-domain tools — Bode plots, Nyquist diagrams, root-locus techniques — and the concept of stability margins. ● Describe how continuous-time controllers are translated into discrete-time implementations through sampling and discretization. ● Formulate the principle of least-squares parameter estimation from input–output data. Regarding the practical application of the acquired knowledge, students will be able to: ● Derive models of physical systems in state-space and input–output form and simulate them in MATLAB and Simulink. ● Solve linear state equations analytically via the Laplace transform and numerically through simulation. ● Assess stability by applying linearization and appropriate criteria. ● Analyze controllability and observability using standard matrix-based tests. ● Design and tune PID controllers, including self-tuning algorithms in MATLAB. ● Design full-state and estimated-state feedback controllers to meet given performance specifications. ● Construct and interpret Bode, Nyquist and root-locus diagrams to evaluate stability margins and robustness. ● Estimate system parameters from measured data using the least-squares method.

Required: ● Linear Algebra: vector and matrix operations, matrix inversion, determinants, eigenvalues and eigenvectors. ● Complex Numbers: arithmetic operations and representation in the complex plane. ● Calculus: differentiation and integration of single-variable functions. Recommended (not mandatory): ◆ Mechanics and Circuits: basic principles of rigid-body dynamics and elementary electric circuits. ◆ Differential Equations: methods for solving ordinary differential equations.

The course is organized into the following thematic blocks: ● Introduction, mathematical foundations and software tools (5h lectures) ○ Course overview. ○ Review of complex numbers, matrices and differential equations. ○ MATLAB and Simulink for system modeling. ● Dynamical systems modeling and stability (9h lectures) ○ Systems and models. State-space representations and state equations. ○ Linearization around equilibrium points. Lyapunov stability and instability criteria. ● Transfer functions, modal analysis and system responses (10h lectures) ○ Laplace transform and transfer functions. State-space vs. input–output representations. ○ Modal analysis, eigenvalues and partial-fraction expansion. ○ Responses to standard signals. ○ Controllability and observability, minimal realization, external (BIBO) stability. ● Feedback control design (15h lectures) ○ Feedforward vs. feedback control. ○ Pole placement: theory, design specifications and examples. ○ PID controllers: theory and tuning. ○ LQR control. ○ State observers and output feedback. ○ Internal model principle. ● Frequency-domain stability analysis (6h lectures) ○ Introduction to Bode and Nyquist diagrams. ○ Nyquist stability criterion. ○ Stability margins and robustness analysis. ● Discrete-time systems and identification (6h lectures) ○ Discrete-time signals and systems. ○ Discretisation methods. ○ Least-squares parameter estimation and system identification. ● Seminar activities (13h lectures) ○ Seminar on implementation of discrete-time controllers and filters (10h). ○ Solution of past examination papers (3h). ● Laboratory hands-on sessions in MATLAB and Simulink for control analysis and design (15h exercises): ○ State equations and simulation of dynamical systems; ○ Stability analysis via linearization and Nyquist criterion, controllability and observability tests; ○ Transfer functions and Laplace transform; ○ Impulse, step and harmonic responses; ○ Pole-placement, LQR and PID design, observers for state estimation; ○ Least-squares identification; ○ Automotive models and case studies: quarter-car model, lane keeping control, cruise control.

The course is organized into two complementary components: theoretical lectures and hands-on laboratory practicums. The course comprises lectures, laboratory sessions and optional seminar activities: ● Lectures (52h) present the theoretical foundations of automatic control: modeling and state-space representations, stability analysis, transfer functions and modal analysis, feedback control design (pole placement, PID, LQR, observers), frequency-domain stability analysis (Bode and Nyquist diagrams, stability margins), discrete-time systems, discretization and system identification. Each topic is accompanied by numerical examples and fully worked problems. ● Laboratory sessions (15h) provide hands-on experience in MATLAB and Simulink for modelling, analysing and designing control systems. Exercises cover state-equation simulation, stability analysis, transfer functions, controllability and observability tests, time- and frequency-domain responses, pole-placement and LQR design, PID tuning, least-squares identification, and automotive case studies (quarter-car model, lane keeping, cruise control). All lab solutions are posted on the course webpage. Students are encouraged to install MATLAB under the Campus license on their personal laptops. ◆ Seminar activities include the seminar sessions on the implementation of discrete-time controllers and filters (10h), and guided review of past examination papers (3h).

Reference materials: ● Lecture slides and laboratory handouts, available on the course webpage via the teaching portal. The course is self-contained and does not follow any specific textbook. Optional textbooks for further study: ◆ S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and design, 2001. ◆ 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. ◆ P. Bolzern, R. Scattolini, N. Schiavoni, Fondamenti di Controlli Automatici, McGraw-Hill Libri Italia.

Lecture slides; Exercises; Video lectures (previous years);

Exam: Computer lab-based test; Computer-based written test in class using POLITO platform;

The final exam is a computer-based written test held in the university's computer lab (LAIB). The duration of the test is 2 hours. Students have access to the timer built into the examination platform. The exam is designed to verify the acquisition of both knowledge and practical abilities described in the learning outcomes, including: -- modeling and linearization of dynamical systems; -- stability analysis; -- derivation of transfer functions and modal analysis; -- pole-placement and observer design; -- discretization; -- system identification; -- interpretation of frequency-domain tools such as the Nyquist plot. The students are supposed to learn basic MATLAB commands to operate with matrices and linear system. Simulink is not used in the exam questions. Examples of past examination papers will be discussed during the lectures. A cheat sheet containing core equations, Laplace-transform tables and key definitions is provided in advance. Students may print it or download it as a PDF during the exam. No other materials (printed MATLAB scripts, lecture notes, books or exercise solutions) are allowed. Students are not allowed to bring their laptops, tablets or insert flash-drives during the exam. The exam consists of ● nine open-ended or multiple-choice questions, each worth up to 3 points, ● an open-ended question on control design worth up to 4 points, for a maximum of 3*9+4=31 points. A score of 31 is registered as "30 e lode." Open-ended questions can receive partial credit when the final answer is incomplete. Wrong answers in open-ended and multiple-choice questions are not penalized. An optional oral examination in person may be requested by students with a score of 26 or above, but remains at the lecturer's discretion. The oral exam may raise or lower the written score. It consists of at least three questions covering the course program; students may be asked a theoretical question (such as a formulation of a theorem or a definition) as well as to solve an exercise on system analysis or control design and explain the solution.

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.