Optimal stabilization of partial movements of the frictional speed controller in case of imprecise fulfillment of the conditional connection

Abstract

This chapter examines the movement of frictional controllers, on which, in addition to passive kinematic connections, an imperfect conditional connection is imposed in the form of a constant angular velocity of the receiving shaft. Differential equations of motion of such speed controllers are obtained, and the question of stability of the controller motion with respect to deviation from the conditional connection is considered. The question of optimal stabilization of the programmed motion of the controller in the vicinity of the manifold determined by the conditional connection is considered. It is shown that the system is controlled by the first approximation. Equations are compiled to determine the coefficients of the Lyapunov function, which solves the problem of optimal stabilization of stationary motions of the speed controller. An explicit form of the control force is obtained, which implements the conditional connection. The question of the influence of the elasticity of the intermediate wheel on the stability of the stationary motion of the regulator is considered and conditions are obtained under which the stability in the first approximation takes place.