CONTROL OF DESIGNED TARGET SEEKER, USED IN SELF-GUIDED ANTI-AIRCRAFT MISSILES, BY EMPLOYING MOTORS WITH A CONSTANT TORQUE

This paper presents the results of research on control of a designed target seeker (Gapiński, D. 2008), which was carried out using of the so-called “signum” function. The technical feasibility of controlling the seeker axis in the phase of searching the air space with the simultaneous consideration of the process of scanning through the optoelectronic system of the head was verified. The numerical analysis of the device dynamics was presented and the analysis of the possibility of practical application previously mentioned method for the control of the designed seeker was conducted. The results are presented in a graphical form as well.


Introduction
Structural solutions for optical scanning heads are being continuously improved by the biggest armaments companies in the world, as proven by most recent European and American patents published in the years 2006(Bar-enz et al. 2012Rueger, zoz 2012;Anderson et al. 2010). It emerges among others from the dynamic technological development of air attack means. On present battlefields, the opponent has the equipment enabling to carry out air combat missions with greater and greater precision and with greater velocities. Furthermore, for several years, disruptions caused by the target have been applied in order to mislead the seeker optical system (ostensible targets). The paper presents the design of such a device, while its innovation, structure and principles of operation were presented in the patent specification (Gapiński 2008). The paper discusses the possibility of controlling the designed scanning and tracking head with the use of electric motors with a constant torque, whose rotary velocity directions are specified according to the method based on the so called function "singnum", and described among others in (Osiecki, Stefański 2003, 2008Stefański 2004). Figure 1 presents a 3D visualisation of the designed head. A detailed description of the design, including the list of parts, is included in the patent solution (Gapiński 2008). The main components of the seeker include: complete spherically-shaped outer housing (1), complete spherically-shaped inner housing (2), as well as gyroscope rotor together with the optoelectronic system (3). The inner and outer housing constitute the Cardan joint, due to which the rotor, together with the optoelectronic system, is separated from the missile base (maintains the set direction in space), and it is possible to precisely control the seeker axis. The designed head has two modes of operation. In the first mode, the head searches the air space in order to detect and locate a flying object, whereas in the second mode, it tracks the located target. In this article, the first mode of operation is analysed, during which the control of the head axis with the "signum" function was performed.

Design of the scanning and tracking head
The moments of inertia of individual elements of the seeker have been calculated in relation to respective axes of the adopted systems of coordinates (Fig. 2). The beginnings of all such systems overlap and are at the intersection of the axis of rotation of the outer housing with the axis of rotation of the inner housing of the head. Maximum torques of individual motors, controlling the outer and inner housing, have been determined based on the previous analysis of the seeker dynamics.
The process of scanning the air space by the optoelectronic system of the device in its first mode of operation is shown in  Figure 3 presents the diagram of the gyroscope of the designed scanning and tracking head, including the adopted systems of coordinates and angles of rotation of those systems in relation to each other.

Mathematical model
The following systems of coordinates have been marked on figure 2:  Angles of rotation and their order are as follows: ψ is the angle of rotation ψ ϑ j specify the location of the gyroscope rotor in relation to the system of coordinates The equations of gyroscope motion have been introduced based on the adopted physical model using the Lagrange equations of the second kind (Awrejcewicz, Koruba 2012;Chatys, Koruba 2005). They employed equations are as follows:  In order to increase the area of scanned space, the seeker axis is set in the programmed motion, for example on the surface of an unwinding spiral. The control of the motion of the head axis was carried out based on the method described in (Osiecki, Stefański 2003, 2008Stefański 2004). The presented method of controlling the motion of the axis of the designed target seeker uses phase trajectories of control deviations. This method involves switching, with the use of control signals u and v , control moments, constant in terms of value, at the appropriate points of phase surface. The switching should bring the control deviations to zero. During this control phase, angles , Z Z ϑ ψ determine the set (desired) motion which should be made by the axis of the scanning head.
The converted equations of motion of the seeker (1a-c) will be written in the following form:  Control signals u and v have been formulated as follows: where 1 e and 2 e indicate control deviations which have the form of:

Presentation of analysis results
Numerical research was conducted for the first operation mode of the designed scanning seeker intended for close-range surface-to-air missiles.

Numerical data of the optical target seeker
The numerical data obtained from the optical target seeker were as follows:  [deg].

Fig. 4. Direct detection of air target
If the target is not detected directly through the optoelectronic system of the seeker, the optical axis of the head will be automatically set according to the programmed motion and, as a result, the scope of scanned space will be increased.
Control of the seeker axis was realized by setting its motion on the surface of a circular cone and on the surface of the unwinding coil. The torques of the controlling motors then assume a constant value of 0.8 [Nm].
Figures 5−10 present the results of digital simulation of the scanning head axis control by setting its motion on the surface of a circular cone at the same time taking into consideration air space scanning by the optoelectronic system of the device. The target was moving at a 200 [m/s] velocity and was 2000 [m] away from the firing position. Figure 5 presents the diagram of the set angular velocity of the seeker axis moving on the surface of a circular cone. In the initial phase of control, the scanning head axis accelerates until the moment it achieves the set angular velocity amounting to 360 [deg/s]. In the further phase of control, the angular velocity of the axis is maintained at a constant level of 360 [deg/s].

Review of analysis results
From the conducted numerical simulations it appears that the control of the designed target seeker with the use of electrical controlling motors with constant torques is done with sufficient precision for self-guidance. The use of the above indicated motors significantly simplifies the whole system of controlling the head. Due to this solution, it is possible to replace the voltage controller with a very simple and fast led or semi-conductor system. The task of such a system is only limited to generating control signals in the form of electrical impulses of the values: 1, 0 or -1. The control signals are generated on the basis of control deviations, which are systematically determined by the fibre-optic sensors of angular displacements installed in the device. From the analysis of the course of control moments presented in figures 9, 10, 18 and 19, it appears that the frequency of controlling impulses does not exceed 10 [kHz]. This proves the technical feasibility of the method of seeker axis control presented in the article as semi-conductor switches currently present in the market are able to generate control impulses with such a frequency.