Dither in a rolling airframe flight vehicle with a two-position actuator: An amplitude distribution approach

Rolling airframe manoeuvring is a type of manoeuvre in which the missile provides continuous roll during flight. Cross-coupling between the angle of attack and sideslip in rolling airframe missiles (RAMs) yields a coning motion around the flight path. As the pitch and yaw cross-coupling effect decreases, the radius of this coning motion decreases and the accuracy of the control system increases. Two-position (on–off) actuators are used in most RAMs. The presence of a two-position actuator in a feedback system makes its characteristics non-linear. A high-frequency signal so-called dither is applied to compensate for the non-linearity effect of the actuator characteristic in the feedback system and to stabilize the coning motion. The amplitude distribution function (ADF) method in dither analysis shows that the smoothed non-linearity characteristic can be computed as the convolution of the original non-linearity and the ADF of the dither signal. According to the four-degrees-of-freedom (4-DOF) equations of RAMs in a non-rolling frame and regarding various dither signals through the ADF approach on a two-position actuator, an analytical condition for dither amplitude in coning motion stability of RAMs is derived. It was shown that the triangular signal with specified amplitude and high enough frequency led to a smoother response of two-position actuators. Finally, by applying beam-riding guidance to a RAM, the performance of dithers for decreasing the distance of the missile from the centre of the beam is validated through simulations. It is illustrated that applying the triangular dither resulted in minimal error.