An Application of Stochastic Control Theory to the Gust-Alleviation System for a Transport Airplane

Abstract

The optimal control law that minimizes the gust responses of an airplane's longitudinal motion is obtained, making assumptions that the airplane is approximated as a point and that aeroelastic problem is ignored. The airplane gust-alleviation problem has been treated mainly in the frequency domain because of the simplicity of the input-output relations for the power spectra. But in the optimal control problem, the approach in the time domain, applying the optimal stochastic control theory, seems to have more advantages for investigating such a complex control as gust-alleviation. The system state equations consist of the short-period equation of an airplane and the gust shaping filter. The optimal linear control law is derived by applying the Matrix Minimum Principle which minimizes the R.M.S. values of the normal acceleration and the pitch rate at the center of gravity. The results of the numerical calculation for two types of control systems, one being the linkage-control system and the other the independent-control system, are shown in the case of a conventional transport. The latter system is ascertained to have a fairly better performance. The optimal system is also ascertained to have very low sensitivity to the change of the scale of turbulence.