A Generalized State-Space Aeroservoelastic Model Based on Tangential Interpolation

Abstract

In this work, a new approach for the generation of a generalized state-space aeroservoelastic model based on tangential interpolation is presented. The resulting system of differential algebraic equations (DAE) is reduced to a set of ordinary differential equations (ODE) by residualization of the non-proper part of the transfer function matrix. The generalized state-space is of minimal order and allows for the application of the force summation method (FSM) for the aircraft loads recovery. Compared to the classical rational function approximation (RFA) approach, the presented method provides a minimal order realization with exact interpolation of the unsteady aerodynamic forces in tangential directions, avoiding any selection of poles (lag states). The new approach is applied first for the generation of an aerodynamic model for the bidimensional unsteady incompressible flow in the time domain. Next, an application on the generation of an aeroservoelastic model for loads evaluation of the flutter reduced order assessment (FERMAT) model under atmospheric disturbances is done, showing an excellent agreement with the reference model in the frequency domain. The proposed aeroservoelastic model of minimal order is suited for loads analysis and multivariable control design, and an application to a gust loads alleviation (GLA) strategy is shown.

A structured approach for input derivative index-2 descriptor dynamical model control

“…Based on the descriptor model with polynomial part H, with DAE realization S of dimension n = 168 (embedding E matrix rank of r = 166 and non-null D matrix), as detailed in [11], we can construct the canonical form and obtain…”

“…Then, the complete controller K with realization S K , including the input derivativeu(t), which solves problem (11), is simply given as…”

“…Let us now apply the proposed methodology on a generalized state-space aeroservoelastic model, represented in Figure 1, known as the FERMAT model, which is used to design load alleviation controllers. This latter has been obtained based on tangential interpolation method (see [11] for details). In brief, the resulting DAE system may be reduced to a set of ODE by residualization of the non-proper part of the transfer function matrix.…”

An input-independent method for solving weakly nonlinear partial differential equations in the frequency domain: application to the Euler equations

“…1,2 Other approaches for the generation of linearized ROMs include the eigensystem realization algorithm (ERA) 3 or the Loewner approach. 4 However, the linearized approach presents limitations in cases involving the presence of large shock motions or separation areas and the development of limit cycle oscillations (LCO). The linearized (also known as dynamically linear) approach is equivalent to a first order Volterra functional series expansion of the governing PDE in the incremental variables.…”

Special Issue: Aeroelasticity

“…First, we have reviewed the research that contributed development of the theory and enhanced the fundamental understanding of aeroelastic phenomena. Quero et al [1] introduced the generation of a generalized state-space aeroservoelastic model based on tangential interpolation. The approach provides a minimal order realization with exact interpolation of the unsteady aerodynamic forces in tangential directions and overcomes certain drawbacks of the classical rational function approximation approach.…”