Unsteady Aerodynamic Forces Mixed Method for Aeroservoelasticity Studies on an F/A-18 Aircraft

TWO classical methods are often used in the aeroservoelasticity studies for the conversion of unsteady aerodynamic forces from the frequency into Laplace domain. These two methods are the least squares (LS) and the minimum state (MS) [1–3]. These methods were also improved and modified. Extended versions of the LS and MS methods were renamed extended LS methods (ELS) [4] and extended modified matrix Padé method (EMMP) [5]. In these extended versions, different restrictions were imposed to the aerodynamic force approximations to pass through certain points. These approximations should be exact in zero and in two other points which may represent the estimated flutter frequency and the estimated gust frequency. The MS method was modified [6] to take into consideration two weighting types of aerodynamic generalized data. In the first weighting type, the aerodynamic generalized forces data were normalized to the maximum unit value of each aerodynamic coefficient. In the second weighting type, the effect of the incremental error of the aerodynamic coefficients on the aeroelastic characteristics of the system was considered. Qualities of the MS method [7] such as its generality, accuracy, and flexibility were found in all its applications on subsonic and supersonic aircraft. Results obtained following the application of theMSmethod [8] in the equations of motion of an active flexible wing wind tunnel model showed that very good mathematical models may be obtained with fewer augmenting aerodynamic equations than traditional approaches by a factor of 10. This reduction facilitates the lower order control systems integration in aeroservoelastic systems. Different modal based aeroservoelastic modeling techniques [9] were combined to conceive an integrated design optimization algorithm. To study the transient response of both openand closedloop nonlinear aeroelastic systems, a generalized direct simulation method using a discrete time-domain state-space approach was developed. Other aerodynamic force approximations were realized with several MS approximations by Poirion [10], for several Mach numbers and by use of spline interpolation methods. The most known aeroservoelastic codes such as ADAM [11], ISAC [12], STARS [13], ASTROS [14], and ZAERO [15] implemented one of the classical LS and MS method algorithms. Another code called FAMUSS [16] implemented a new method, different from LS and MS methods. In this method, the state-space matrices elements in the aeroservoelastic code FAMUSS [16] were calculated by a pk flutter solution and linear and nonlinear LS fits of the direct solution of the system’s transfer function frequency response. A new approximation method based on a Padé approximation gave an approximation error of 12–40 times smaller than the error given by the MS method for the same number of augmented states. This method depended on the choice of the order reduction method [17] and is more expensive in computer time than the MS method. Cotoi et al. [18] used Chebyshev polynomials and their orthogonality properties to conceive a new approximation method, and excellent results were obtained by this method in comparison with results obtained by the Padé method. A new method of a combination of pchip and fuzzy clustering techniqueswas conceived byHiliuta et al. [19] for the unsteady force interpolations on a range of nonevenly spaced reduced frequencies. These forces remain in the frequency domain and we will convert them from the frequency into Laplace domain by classical methods such as LS or MS. We present in this paper a newmethod based on the mixing of two classical methods LS and the MS. The method presented here gives better results in terms of execution speeds and precision in comparison to the results obtained by the LS method for an F/A-18 aircraft.