Efficient and Robust Inverse Simulation Techniques Using Pseudo-Spectral Integrator with Applications to Rotorcraft Aggressive Maneuver Analyses

Abstract

This paper intends to propose new inverse simulation techniques to cope with the numerical stability and accuracy problems frequently encountered with the integration inverse simulation methods widely used today. To achieve this, the pseudo-spectral method is adopted as a time integrator of the aircraft motion equations. In addition, the quasi-Newton and fixed-point iterative methods are applied to solve the resultant nonlinear algebraic equations in an efficient manner. These algorithms are integrated into a moving horizon framework to guarantee fast numerical convergence. The proposed methods are applied to the analyses of rotorcraft aggressive maneuvers such as popup, pirouette, and depart/abort mission-task-elements defined in the rotorcraft handling qualities requirements, ADS-33E-PRF. Numerical properties of the proposed methods are thoroughly investigated to clarify the effect of the numbers of quadrature nodes and time-horizon segments, and the level of maneuver aggressiveness on the robustness and efficiency of the analyses. Numerical efficiency and robustness of the present method are identified using specially designed performance measures such as the number of iterations to obtain a converged solution, functional residuals at the final solutions, and the variation of the adaptive relaxation factor. The results show that the present approach can provide extremely fast solutions of the inverse simulation problems and presents strong robustness to the level of maneuver aggressiveness, long-term simulation, and solution control parameters. Therefore, it is worthwhile to use the present techniques as one of the inverse simulation methods.