Control decoupling analysis for gyroscopic effects in rolling missiles

The complex summation method is used to represent the pitch/yaw dynamic equations for a missile with autopilot. The particular forms of complex motion variables that are used enable cross coupling to be identified with imaginary coefficients in the resulting equations. A designer who wishes to produce uncoupled responses to commands for a maneuver then has a clearcut objective when choosing control laws, namely, to eliminate the imaginary coefficients from the response equations. This paper illustrates the use of this technique with an application to gyroscopic coupling resulting from a rolling airframe. It leads via transfer functions to the proposal of a zero-starred filter as an alternative to a pole/zero cancellation technique for eliminating the major source of coupling when the command is in a nonrolling frame of reference.