Modeling and analysis of rolling missiles with a single control surface plane

Abstract

In this paper, modeling and analysis is performed for a rolling missile controlled by a single surface plane. An approximative model of the missile dynamics in a non-rolling frame is obtained. This model is obtained by averaging the force and momentum equations over one roll revolution. It is assumed that the control signal is a sinusoid of a certain amplitude and phase. The amplitude is chosen to control the turn radius of the missile and the phase to control the direction of the turn. The obtained model depends non-linearly on the missile’s speed, roll rate, and aerodynamical derivatives in a simple way, and can be expressed as a linear fractional transformation (LFT) model. The order of this model can be made lower than when computing an LFT model without first using averaging. This is important if the objective is to use the LFT model for controller design, since the computational time is increasing rapidly with the LFT order. Later in the paper, it is motivated, using the averaged model, that the missile cannot fly ih a trimmed circle without feedback.. However, using a non-dynamic feedback from two rate gyros this is shown possible. One feedback gain has to be chosen to a certain value in order to obtain a circle and the other can then be chosen in order to obtain, e.g., stability.