Quasi-Optimum Control of a Flexible Booster

Abstract

The problem of minimizing both the in-flight bending moments as well as the terminal drift of a flexible vehicle is considered. The performance criterion V(T) = 12y2(T)+k2 tT M2(ξ)dξ, where y(T) is the drift, and M is the in-flight bending moment, is selected to achieve a compromise between excessive drift and excessive structural loading. The two-point boundary value problem for the design of the rigid-body control system is solved analytically for the linear, time-varying optimum control law. The flexibility of the vehicle is then accounted for, in a model consisting of two rigid sections hinged together with a torsional spring, by augmenting the rigid-body optimum control law with feedback terms proportional to the vehicle flexure and its rate. The results of a digital computer simulation indicate that the quasi-optimum control law obtained by this technique results in satisfactory performance, while the rigid-body control law is inadequate for a vehicle of moderate flexibility.