Absolute Stability of Control System for Deformation of Electromagnetoelastic Actuator Under Random Impacts in Nanoresearch

Abstract

The electromagnetoelastic actuator on the piezoelectric, piezomagnetic, electrostriction and magnetostriction effects is used in nanoresearch, nanotechnology, nanobiology and adaptive optics. The piezo-actuator is applied in nanotechnology and nanomechanics. The Yakubovich absolute stability criterion of the control system with the condition on the derivative for the hysteresis nonlinearity of the electromagnetoelastic actuator is used. This criterion with the condition on the derivative is development of the Popov absolute stability criterion. The stationary set of the control system for the electromagnetoelastic actuator with the hysteresis deformation is the segment of the straight line. This segment has the points of the intersection of the hysteresis partial loops and the straight line. The absolute stability conditions on the derivative for the control systems with the piezo-actuator at the longitudinal, transverse and shift piezo-effect are received. The condition of the absolute stability on the derivative for the control system for the deformation of the electromagnetoelastic actuator under random impacts in nanoresearch is obtained. For the Lyapunov stable control system this Yakubovich absolute stability criterion has the simplest representation of the result of the investigation of the absolute stability.