Multiple-input describing function technique applied to design a single channel ON-OFF controller for a spinning flight vehicle

Abstract

In this study, the guidance and control problem of a single-channel spinning missile is investigated. The missile utilizes a single ON-OFF actuator to drive a pair of control surfaces (e.g. elevators) and consequently to perform all required lateral maneouvers. An approximated linear response of the so-called non-rotating frame to ON-OFF input, applied to the rotating frame, is derived using the multiple-input describing function technique. It is shown that there is a relationship between the response of the non-rotating frame and that of the equivalent non-rotating body. It is also shown that the two-channel flight controller, designed for the equivalent non-rotating body, can be reduced to a single-channel controller, the output of which is applied to the rotating body. A necessary condition is introduced for this purpose. A proportional navigation guidance law for such a spinning missile is also introduced that generates an angular rate command instead of the acceleration command. Finally, the performance of the proposed controller in the presence of noise and uncertainties is validated through flight simulations.