LAW OF CONTROL AND INDICATORS OF THE MISSILE STABILIZING SYSTEM

Abstract

The main indicators of the rocket stabilization system include the margin of safety and accuracy, as well as the requirement for the power of the executive device. The margin of stability can be quantified as the distance of the operating point in the space of the coefficients of the law of control to the boundary of the region of stability and as a margin for the amplitude and phase of the frequency response. In this work, it is defined on the plane of the roots of a characteristic polynomial as the distance from the imaginary axis of the complex plane to the nearest root. To estimate the accuracy of stabilization, the reduced static error of the yaw angle is chosen. Power requirements for the actuator are defined as the operation of the equivalent steering in the transient process of constant disturbance compensation. In a competitive environment, there is a need to improve the methodology for establishing the dependence of these indicators on the parameters of the missile and the law of control. The object of the study is the system of stabilization of the plane rotational motion of the rocket, the subject of the study is the accuracy, margin of safety and the work of the executive device on the transient process of disturbance compensation depending on the control circuit parameters. The aim is to develop an algorithm for establishing the dependence of these indicators on the presence in the law of regulation of terms proportional to the angle and angular velocity of the equivalent steering gear. A linear stationary model of the plane rotational motion of a rocket in the vicinity of a certain point of the trajectory with taking into account the inertia of the executive device is adopted. For the case when only two of the four coordinates of the state vector are taken into account in the law of control, the restriction from above of the stability margin from the parameters of the actuator and the range of roots of the characteristic polynomial on a straight, parallel imaginary axis of the complex plane are set. For the variant in which all coordinates of the state vector are taken into account in the law of control, the algorithm of optimization of a margin of stability and a static error of stabilization is developed. The estimation of the power requirement of the executive device is obtained using the model of the equivalent steering body in the form of an oscillating link, the parameters of which are stiffness, damping coefficient and moment of inertia. It is shown that the stabilization error and the power requirement of the executive device without changing the stability margin depend on the location of two given roots on the straight, parallel imaginary axis of the complex plane. By simulation it is established that taking into account in the law of control of an angle and angular speed of an equivalent steering gear of the executive device can give improvement of the chosen indicators of system by 10 - 20%. The materials of the work supplement the methodological basis of the missile stabilization system design.