Dynamics and Control of Space Structures

Synthetic program:

L'insegnamento mira a fornire una visione completa della modellazione dinamica e del controllo attivo di strutture dei sistemi strutturali aerospaziali, unificando lo schema di descrizione dei sistemi continui con quello di sistemi discreti a più gradi di libertà. Un elemento fondamentale del corso è lo studio delle modalità di integrazione del modello dinamico con sistemi non solo strutturali, termici e aerodinamici, e del loro utilizzo per la realizzazione di sistemi di controllo.

Introduction.
Description and motivation of the course objectives and topics through practical examples, including a review of the basics of dynamics of aerospace systems.

Dynamics of space structures.
Initial/boundary value problem of a flexible 3-D body (small strain assumption). Initial/boundary value problems of some structural components of space systems (rods, beams, bars and plates). Solution through modal analysis: the differential eigenvalue problem, mode displacement method and mode acceleration method. Discretization techniques: lumped parameter method, Ritz-Galerkin discretization, assumed-modes method, finite element method. Dynamic response by modal analysis: modal superposition, damping models, mode displacement method, mode acceleration method. Numerical solution of the eigenvalue problem. Direct time integration methods. Dynamic response to non-deterministic loads: random vibrations. Introduction and classification of random processes. Random processes through LTI systems. Covariance function. Ergodic processes. White noise process. Lyapunov equation. Frequency representation of random processes: power spectral density, spectral factorization. Miles' equation.

Actively controlled space structures.
State space representation of structural models. Nodal (physical) and modal formulations including additional dynamics. Output and performance equations. State space fundamentals: general solution, impulse response, transformation of state variables, canonical forms, controllability/observability matrices and grammians, model order reductions of state-space systems. Review of classical control design (attitude control of a spacecraft): control scheme and objectives, general design guidelines, closed-loop requirements, phase and gain stabilization. State-space approach to control system design: introduction, pole-placement technique, steady-state linear quadratic control (LQR), steady-state tracking, state reconstruction (linear observer), compensator design through separation principle, spillover effects, stochastic LQR, the optimal observer, direct output optimal control, guidelines for the selection of weighting matrices, finite-horizon optimal control.

Introduction to multi-field problems.
Electromechanical systems, thermoelasticity, aeroelasticity, acoustoelasticity, sloshing