Space and astronautical engineering

System analysis. a) Mathematical models. State space representations. Linear models. Nonlinear models and its linearization around equilibrium points and solutions. b) Time domain analysis. Output and state response. Natural modes and modal decomposition. Qualitative evaluation of output response: convergence rate, rise time, settling time and maximal overshooting and undershooting. Frequency domain analysis. Fundamental properties of Laplace transform and more commonly used Laplace transforms with theorems. Transfer functions. Input-output models. c) Stability. Main notions and criteria for linear and nonlinear systems: Lyapunov functions. Routh criterion for linear systems. Modified versions of Routh criterion. Asymptotic behaviour of linear systems. Steady state and transient response. Input-output armonic response. Graphical representation of armonic responses: Bode plots. d) Interconnected systems: series, parallel and feedback interconnections. Zero-pole cancellations and hidden modes. General properties of feedback interconnections. Feedback control system design. a) Time domain design. Control and state reconstruction: controllability and observability. Hautus tests for controllability and observability. Point-to-point control problems. Initial state reconstruction problems. Eigenvalue assignment and state observation. Steady state performances and elementary problems of tracking. b) Frequency domain design. Stability tests for closed-loop systems based on the properties of the open-loop system: polar plots and Nyquist criterion. Proportional, derivative and integral control actions. Root-locus. Stabilization and pole assignment with root-locus methods. Steady state performances: tracking and disturbance compensation and/or attenuation. Transient performances: phase margin and cross-over frequency versus cut-off frequency and resonance peak. Zero-pole control actions for phase margin and cross-over frequency modification.

algebra and math

The contents of the course are extensively and exhaustively contained in ``NOTES ON LINEAR CONTROL SYSTEMS’’ organized in 12 modules, each module containing a specific issue (or bunch of issues) listed in the syllabus with numerous examples, exercises and discussions, both theoretical and graphical. Other textbooks which may be looked up are S. Battilotti, Notes on linear control systems, Esculapio ed., 2016, II ed. G. Marro, Controlli automatici, V ed., Zanichelli ed. A. Isidori, Sistemi di controllo, Siderea ed, 1979. S. Monaco, Sistemi lineari: elementi di analisi, Prog. Leonardo ed.Bologna, 2000. R.C. Dorf, R.H. Bishop, Controlli automatici, Perason, Prentice Hall, 2010. O.M. Grasselli, L. Menini, S. Galeani, Sistemi dinamici, Hoepli, IV ed. Milano, 2012. More specifically focused on exercises are C. Gori Giorgi, S. Monaco, S. Battilotti, S. Di Gennaro, Teoria dei Sistemi: complementi ed esercizi L. Lanari, G. Oriolo, Controlli automatici: esercizi di sintesi, EuRoma.

Free attendance

The student will be evaluated on the base of a written exam, consisting of a certain number of problems (mainly 3), focused on the analysis and design of feedback control systems (2 on the design and 1 on the analysis). The student is asked to solve these problems, in which both theoretical and computational aspects are taken into account. To each problem a score is assigned and the student is given a grade on the base of the overall score.

The course takes place in the classroom, alternating theoretical lessons and application-oriented lessons with examples in different fields

System analysis. a) Mathematical models. State space representations. Linear models. Nonlinear models and its linearization around equilibrium points and solutions. b) Time domain analysis. Output and state response. Natural modes and modal decomposition. Qualitative evaluation of output response: convergence rate, rise time, settling time and maximal overshooting and undershooting. Frequency domain analysis. Fundamental properties of Laplace transform and more commonly used Laplace transforms with theorems. Transfer functions. Input-output models. c) Stability. Main notions and criteria for linear and nonlinear systems: Lyapunov functions. Routh criterion for linear systems. Modified versions of Routh criterion. Asymptotic behaviour of linear systems. Steady state and transient response. Input-output armonic response. Graphical representation of armonic responses: Bode plots. d) Interconnected systems: series, parallel and feedback interconnections. Zero-pole cancellations and hidden modes. General properties of feedback interconnections. Feedback control system design. a) Time domain design. Control and state reconstruction: controllability and observability. Hautus tests for controllability and observability. Point-to-point control problems. Initial state reconstruction problems. Eigenvalue assignment and state observation. Steady state performances and elementary problems of tracking. b) Frequency domain design. Stability tests for closed-loop systems based on the properties of the open-loop system: polar plots and Nyquist criterion. Proportional, derivative and integral control actions. Root-locus. Stabilization and pole assignment with root-locus methods. Steady state performances: tracking and disturbance compensation and/or attenuation. Transient performances: phase margin and cross-over frequency versus cut-off frequency and resonance peak. Zero-pole control actions for phase margin and cross-over frequency modification.

algebra and math

The contents of the course are extensively and exhaustively contained in ``NOTES ON LINEAR CONTROL SYSTEMS’’ organized in 12 modules, each module containing a specific issue (or bunch of issues) listed in the syllabus with numerous examples, exercises and discussions, both theoretical and graphical. Other textbooks which may be looked up are S. Battilotti, Notes on linear control systems, Esculapio ed., 2016, II ed. G. Marro, Controlli automatici, V ed., Zanichelli ed. A. Isidori, Sistemi di controllo, Siderea ed, 1979. S. Monaco, Sistemi lineari: elementi di analisi, Prog. Leonardo ed.Bologna, 2000. R.C. Dorf, R.H. Bishop, Controlli automatici, Perason, Prentice Hall, 2010. O.M. Grasselli, L. Menini, S. Galeani, Sistemi dinamici, Hoepli, IV ed. Milano, 2012. More specifically focused on exercises are C. Gori Giorgi, S. Monaco, S. Battilotti, S. Di Gennaro, Teoria dei Sistemi: complementi ed esercizi L. Lanari, G. Oriolo, Controlli automatici: esercizi di sintesi, EuRoma.

Free attendance

The student will be evaluated on the base of a written exam, consisting of a certain number of problems (mainly 3), focused on the analysis and design of feedback control systems (2 on the design and 1 on the analysis). The student is asked to solve these problems, in which both theoretical and computational aspects are taken into account. To each problem a score is assigned and the student is given a grade on the base of the overall score.

The course takes place in the classroom, alternating theoretical lessons and application-oriented lessons with examples in different fields