Absolute Stability of Control System with Electro Magneto Elastic Actuator for Nano Science and Nano Biomedicine Research

Affiliation: National Research University of Electronic Technology MIET, Moscow, Russia * Corresponding author: Afonin SM. National Research University of Electronic Technology MIET, Moscow, Russia Email: eduems@mail.ru Citation: Afonin SM. Absolute stability of control system with electro magneto elastic actuator for Nano science and Nano biomedicine research (2019) Nanomaterial Chem Technol 1: 19-22. Received: Sep 10, 2019 Accepted: Sep 19, 2019 Published: Sep 27, 2019 Copyright: © 2019 Afonin SM. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

The condition of the absolute stability on the derivative for control system of the deformation of the electro magneto elastic actuator is calculated. The problems of using criteria absolute stability of the control system with electro magneto elastic actuator for Nano science and Nano biomedicine research are discussed. The stationary set of the control system of the deformation of the electro magneto elastic actuator is determined.

Aim
The aim of this work is to calculate the condition of the absolute stability on the derivative for control system of the deformation of the electro magneto elastic actuator in automatic nanomanipulators for nanoscience and nanobiomedicine research.

Method
The frequency methods for Lyapunov stable control system are used to determine the condition of the absolute stability of control system with electro magneto elastic actuator in automatic nanomanipulators for nanoscience and nanobiomedicine research [2,3].

Results
We determined the expression for the sufficient absolute stability condition of the control system with the hysteresis nonlinearity of the electro magneto elastic actuator using the Yakubovich absolute stability criterion with the condition on the derivative, which is the development of the Popov absolute stability criterion [2,3].
For the Lyapunov stable control system and the Yalubovich absolute stability criterion for the systems with the single hysteresis nonlinearity provides the simplest and pictorial representation of results of the investigation of the stability of the strain control system with the electro magneto elastic actuator.
We use the transfer function of the linear part of the system   ij Wp and the hysteresis function of the relative deformation j S of the electro magneto elastic actuator for description of the system.
We have the description of the hysteresis nonlinearity of the actuator in the form [17] Citation: Afonin SM. Absolute stability of control system with electro magneto elastic actuator for Nano science and Nano biomedicine research (2019) Nanomaterial Chem Technol 1: The set bounded by the points of intersection of the ordinate axis with the hysteresis loop at the maximum admissible field strength in the piezoactuator.
We receive the stationary set for the deformation of the piezoactuator on Figure 1 for the stable linear part of the control system. Therefore, we draw the straight line L with the equation Let us consider butterfly type characteristic of the deformation of the electro magneto elastic actuator for Nano science research. For the actuator with the electrostrictive effect the deformation characteristic on butterfly wings is observed for unipolar change of the electric field strength on Figure 2.
The particular cycle is the hysteresis loop. For butterfly type characteristic deformation of actuator in the control system the coordinate origin is moved to new zero with top dash on Figure 2. For hysteresis loop on butterfly type characteristic we have stationary set N of the system marked segment of straight line L in Figure 2. For the magnetostrictive actuator the deformation characteristic has the butterfly type.  : : : : where the ratios of the tangents of the inclination angle of the tangent line to the hysteresis nonlinearity of the piezoactuator for longitudinal, transverse and shift piezoeffects are proportional to the ratios of the piezomodules. We have the expression for the sufficient absolute stability condition of the system with the hysteresis nonlinearity of the electro magneto elastic actuator using the Yakubovich absolute Citation: Afonin SM. Absolute stability of control system with electro magneto elastic actuator for Nano science and Nano biomedicine research (2019) Nanomaterial Chem Technol 1: 19- 22 13 stability criterion with the condition on the derivative. The Yalubovich criterion is the development of the Popov absolute stability criterion [2].
For the Lyapunov stabile control system the Yalubovich absolute stability criterion for the system with the single hysteresis nonlinearity provides the simplest and pictorial representation of results of the investigation of the stability control system [2,3]. Therefore, the sufficient absolute stability condition of For the absolute stability criterion for the system with electro magneto elastic actuator on the plane of the logarithmic amplitude frequency characteristic and the phase frequency characteristic we have The corrected logarithmic amplitude frequency characteristic is below the boundary curve in the form     ω 20lg 1 / cosφ 9 L  For the piezoactuator from PZT the value of the maximum tangent of the inclination angle of the tangent line to hysteresis nonlinearity is about 1 nm/V for longitudinal piezoeffect and about 0.6 nm/V for transverse piezoeffect.

Summary
We used the frequency methods for Lyapunov stable control system to calculate the condition the absolute stability of the control system with electro magneto elastic actuator in automatic nanomanipulators.

Conclusions
We received the stationary set of the control system of the deformation of the electro magneto elastic actuator. We determined condition of the absolute stability on the derivative for the control system with the electro magneto elastic actuator in automatic nanomanipulators for nanoscience and nanobiomedicine research.