Dynamics and Control of Flexible Aircraft

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.

Definition of modal response problems:
- Structural models, linear or linearized, either constrained or in unperturbed free average motion, with prescribed loads, including thermal ones
- Fundamentals of structural damping modeling
- General aspects of response problems using reduced modal models
- Computation of free vibration modes, experimental verification and their importance
- Computation of structural response up to structural verification, convergence of motion and stresses, truncation and residualization, acceleration modes, use of static modes

Numerical methods for the direct integration of the response on large models:
- Response via direct integration, basic methods and their properties, stability, accuracy
- Need of unconditional stability with algorithmic dissipation, comparison with modal response, pros and cons
- Frequency domain solution, limitations and critical aspects in terms of efficiency, some utilities Response to non-deterministic inputs
- Need for stochastic response analysis, typical aeronautical applications
- General characterization of stochastic inputs, with specific reference to ergodic ones
- Ergodic response of asymptotically stable problems using input-output relationships, in time and frequency domains, in state-space representation
- Equivalent response indicators for design and structural verification

Reduced Order Models
- Importance of reduced order models from large, detailed models
- Fundamentals of eigenanalysis
- Generalization of modal reduction, reduction based on frequency content (slow and fast subsystems), need for modal space
- Model reduction by truncation and residualization, quasi-steady models, time-frequency justification
- State-space models: from the quadruple to the "decuple", model reduction, verification hierarchy
- Modeling of sensors and actuators Active control of aerospace structures
- Optimal Control in state-space form (regulator): infinite horizon, solvability conditions and solution, robustness (phase and gain margins) [or lack of it], rivisitation with optimization on some families of disturbances with "algebraic" approach
- Need of state reconstruction, observer and its use as compensator
- Design of steady optimal observer, “algebraic” approach, duality with controller
- Loss of robustness of controller-observer - Spillover
- Techniques for the selection of the cost functions and their connection with design requirements
- Optimal control for direct measurement feedback, pros and cons
- Order reduction of the controller based on frequency and balanced observability-detectability, fundamentals of digital implementation

Addition of configuration/motion dependent forcing terms (only linear or linearized):
- Thermo-elastic coupling
- Integrated coupling caused by motion-dependent boundary conditions
- Aeroelastic coupling
- Aerodynamic loads and their coupling with deformable structures
- Unsteady aerodynamics linearized solution and its transformation in input-output relationship, in time and frequency domain
- Direct input-output formulation using integral methods in frequency domain
- Simplified aerodynamic models, lifting surface, airfoils and strip theory, distributed piston theory
- Controls and servo-controls
- Classic aeroelastic formulation (frequency domain) and its slow-fast hyerarchization
- Deformable aircraft "trim"
- Static aeroelasticity, main problems, simple examples: loads, response, structural verification, regulations
- Dynamic aeroelasticity, flutter and response (deterministic and stochastic), solution techniques, regulations and structural verifications