This paper deals with the active suppression of aerodynamically driven limit cycle flutters. Because of the significant dependence of such outcomes upon flight conditions, an adaptive solution is selected. The related task is accomplished through an Immersion and Invariance (I&I) controller coupled to a sliding mode observer. To simplify its tuning while satisfying robust stability conditions the design of the controller includes attenuating linear filters. The effect of using different fidelity approximations for the aerodynamic subsystem is verified on three different test cases, adopting reduced order models to design their controllers, including the dynamics of sensors and saturating actuators. The resulting active systems are subsequently verified against diverse nonlinear high fidelity aerodynamics, flight conditions and structural parameters. Nomenclature β c Control input ψ Controller regressor χ Uncertain parameter vector λ, c s , μ, γ Con , σ, b d Controller design parameters A r , B r , C r , D r Reduced order matrices of the nonlinear aerodynamics f a Aerodynamic forces scaled by the dynamic pressure q ∞ M a , C a , K a Aerodynamic quasi-steady approximation matrices M s , C s , K s Structural mass, damping and stiffness matrices q Servo-elasto-mechanical degrees of freedom Q, R, Q s , γ Obs Observer design parameters
In this work, a nonlinear state-space-based identification method is proposed to describe compactly unsteady aerodynamic responses. Such a reduced-order model is trained on a series of signals that implicitly represent the relationship between the structural motion and the aerodynamic loads. The determination of the model parameters is obtained through a two-level training procedure where, in the first stage, the matrices associated to the linear part of the model are computed by a robust subspace projection technique, whereas the remaining nonlinear terms are determined by an output error-minimization procedure in the second stage. The present approach is tested on two different problems, proving the convergence toward the reference results obtained by a computational fluid dynamics solver in linear and nonlinear, aerodynamic, and aeroelastic applications, whereas the aerodynamic reduced-order models are coupled with the related structural mechanical systems, demonstrating the ability of capturing the main nonlinear features of the response. The robustness of the reduced-order model is then tested considering a series of inputs with varying amplitudes and frequencies outside the range of interest and computing aeroelastic responses with nonnull pretwist angles. NomenclatureA a , B a , C a , D a = linear subparts of the reduced-order model b = half-chord, c∕2 E a , F a = nonlinear subparts of the reduced-order model f a = aerodynamic loads h, θ = plunge and pitch degrees of freedom k = ωc∕U ∞ ; reduced frequency N a = number of aerodynamic states, size of x a N out = number of aerodynamic output, size of f a q ∞ = 1 2 ρ ∞ U 2 ∞ ; dynamic pressure t = continuous time V = U ∞ ∕ω θ b μ p ; reduced velocity V bif = bifurcation speed x a = aerodynamic state x s = structural dynamics state β LE , β TE = leading-and trailing-edge control surface deflections μ = m∕πρ ∞ b; mass-to-fluid ratio τ = ω θ t; nondimensional time ϕx a = nonlinear functions of the aerodynamic reduced-order model ω i = natural frequency of the ith degree of freedom
Aeroelastic systems have the peculiarity of changing their behavior with flight conditions. Within such a view, it is difficult to design a single control law capable of efficiently working at different flight conditions. Moreover, control laws are often designed on simple linearized, low-fidelity models. A fact introducing the need of a scheduled tuning over a wide operational range. Obviously such a design process can be time consuming, because of the high number of simulations and flight tests required to assure high performance and robustness. The present work aims at proving the high flexibility of neural network-based controllers, testing their adaptive properties when applied to typical fixed and rotary wing aircraft problems. At first the proposed control strategy will be used to suppress the limit cycle oscillations experienced by a rigid wing in transonic regime. Then as a second example, a controller with the same structure will be employed to reduce the hub vibrations of an helicopter rotor with active twist blades.
A technique aimed at neutralizing the presence of free-play effects in a control surface actuation chain is presented. It is based on an adaptive inversion of a function approximating such a nonlinearity. A simple, yet robust, on-line adaptive algorithm is proposed to identify the free-play parameters, i.e. free-play width, the equivalent control stiffness and friction. The procedure is then coupled to an immersion and invariance control law to drastically reduce possible residual closed-loop limit cycle oscillations due to the free-play nonlinearity. Within such a framework, the so chosen compensation technique can be interpreted as a control augmentation, easily extendable to multiple control surfaces. The methodology is then verified on a four-degree-of-freedom airfoil in a transonic regime, characterized by highly nonlinear unsteady aerodynamic loads, producing significant shock motions and large limit cycles, at a relatively high frequency. The presence of both aerodynamic and structural nonlinearities makes such a system bistable, leading to complex responses dependent on the initial conditions and the input used to excite the system. The effective suppression of these auto-induced vibrations becomes even more challenging because the limit cycle oscillations generated by different sources are characterized by differing amplitudes and frequencies
A technique aimed to neutralize the presence of free-play effects in a control surface actuation chain is presented. The procedure is based on the inversion of a function approximating such a nonlinearity. A simple yet robust on-line adaptive algorithm is proposed to identify the free-play parameters, i.e. free-play width and the equivalent control stiffness. To achieve such a compensation, the only measures required are those of the control surface deflection and the hinge torque.The procedure is then coupled with an other adaptive control law to drastically reduce possible residual limit cycle oscillations in closed loop associated to the free-play presence. Within such a framework, the proposed compensation can be interpreted as a control augmentation which can be easily extended to multiple control surfaces.Even if only numerical analyses are considered in this work, measurement noise is taken into account, and both free-play and friction are simulated in the control surface actuation system, aiming to increase the reliability of the presented results. In addition, several offdesign conditions are analyzed, e.g. varying the free-play width and friction amplitude. The proposed methodology is applied to a three degrees of freedom airfoil in transonic regime. This case is characterized by highly nonlinear unsteady aerodynamic loads, producing significant shock motions and large limit cycle oscillations at a relatively high frequency, resulting so in a challenging test for the proposed approach. Nomenclature x aAerodynamic state x s Structural dynamics state A, B a , B c , C y State space matrices implemented in the controller A r , B a,r , B m,r , B c,r , C y,r State space matrices of the real controlled system z β , z m , z act Sensors output A a , B a , C a , D a Aerodynamic reduced order model matrices φ (x a ) Nonlinear terms of the aerodynamic reduced order model
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