Mathematical Models for a Missile Autopilot Design

Abstract : This report considers the derivation of the mathematical model for a missile autopilot in state space form. The basic equations defining the airframe dynamics are non-linear, however, since the non-linearities are "structured" (in the sense that the states are of quadratic form) a novel approach of expressing this non-linear dynamics in state space form is given. This should provide a useful way to implement the equations in a computer simulation program and possibly for future application of non-linear analysis and synthesis techniques, particularly for autopilot design of missiles executing high g-manoeuvres. This report also considers a locally linearised state space model that lends itself to better known linear techniques of the modem control theory. A coupled multi-input multi-output (MIMO) model is derived suitable for both the application of the modern control techniques as well as the classical time-domain and frequency domain techniques. This is validated by comparing the model with the other published results, and through both open and closed- loop systems simulations. The models developed are useful for further research on precision optimum guidance and control. It is hoped that the model will provide more accurate presentations of missile autopilot dynamics and will be used for adaptive and integrated guidance & control of agile missiles.