The basic objective of anti-air defence is to support military units in conducting operations in the condition of air danger. Antiaircraft units and sub-units are equipped with, among others, anti-aircraft short-range missiles. A significant element of the operation of such missiles is an optical homing head. Its task is to determine the location of a missile relative to a target.[11,17] The most modern anti-aircraft missiles use scanning heads, with its modified design presented in the paper [4]. They allow a missile to be launched into an area of probable target presence, before it is intercepted by the optical system of the head. It is because, in the initial flight phase of a missile undergoes a process of seeking a manoeuvring air target, namely, airspace scanning. This enables shortening the target interception time and increasing the efficiency of the anti-air system operation. Moreover, thanks to a narrow-angle lens, the scanning heads are more resistant to interference and enable precise tracking of a detected air target. The propulsion element of a head is a gyroscope system (GS). The operating precision of such a system impacts the homing accuracy of a missile onto a target. A GS is affected by forces from the missile deck. Friction in suspension bearings and system imbalance have also an adverse effect. Too large deviations of the GS axis from a set position may lead to losing the target from the line of sight of the head's optical system. Therefore, in order to ensure precise and stable target tracking by a head, it is important to optimally select the gyroscope system control parameters, which enables mitigating the impact of such disturbance on the positioning accuracy of its axis.