Nonlinear Stochastic Control for Space Launch Vehicles

In designing a robust ascending control for space launch vehicles, uncertainties such as variations in aerodynamics, jet effects, hinge moments, mass property, and navigation processing, etc., have to be considered, and normally, time and labor intensive Monte Carlo simulations are used in order to achieve a desired tracking performance distribution. In this paper, a systematic stochastic control design method is applied based upon a direct quadrature method of moments. In conjunction with a nonlinear robust control and offline optimization through nonlinear programming, any order of stationary statistical moments can be directly controlled. Compared with existing stochastic control methodologies, the advantages of the proposed method are 1) the closed-loop tracking system is asymptotically stable, 2) any (attainable) higher order steady-state moments of the state/output variables can be controlled, 3) the system is stable up to the order of the highest moment selected in the design, 4) the state process can be unknown and is not required to be Gaussian, and 5) no Monte Carlo analysis is required in the design. Two simulation scenarios of the X-33 3-DOF attitude control in ascending phase have been used to demonstrate the capabilities of the proposed method, and the results are validated by Monte Carlo runs. Although the method is only evaluated in this paper in the attitude control of the reusable launch vehicle's ascending phase, the method will be applicable to a wider class of aero and space systems such as aircraft, unmanned aerial vehicle, missile, and satellite attitude control.