Generalization of the frequency theorem in the case of an unbounded observation operator and its application to absolute stability problems

1990 ◽  
Vol 30 (4) ◽  
pp. 535-542
Author(s):  
V. G. Deich
Keyword(s):  
Absolute Stability ◽  
Stability Problems ◽  
Frequency Theorem ◽  
Observation Operator

The Condition for Absolute Stability of an Electroelastic Actuator Control System for Nanomechatronics

2020 ◽  
Vol 10 (10) ◽  
pp. 52-58
Author(s):  
Sergey M. AFONIN ◽  
Keyword(s):  
Control System ◽  
Adaptive Optics ◽  
Absolute Stability ◽  
Deformation Characteristic ◽  
Straight Line Segment ◽  
Control Mechanisms ◽  
Relative Width ◽  
Random Inputs ◽  
Deformation Control ◽  
Actuator Control

An electroelastic actuator for nanomechatronics is used in nanotechnology, adaptive optics, microsurgery, microelectronics, and biomedicine to actuate or control mechanisms, systems based on the electroelastic effect, and to convert electrical signals into mechanical displacements and forces. In nanomechatronic systems, a piezoactuator is used in scanning microscopy, laser systems, in astronomy for precision alignment, for compensation of temperature, gravitational deformations and atmospheric turbulence, focusing, and stabilizing the image. In this study, a condition for absolute stability of an electroelastic actuator control system for nanomechatronics under deterministic and random inputs is obtained. A number of equilibrium positions in an electroelastic actuator mechatronic control system are found, the totality of which is represented by a straight line segment. The electroelastic actuator’s deformation control system dead band relative width is determined for the actuator’s symmetric and asymmetric hysteresis characteristics. Under deterministic inputs and with fulfilling the condition for the derivative of the nonlinear hysteresis actuator deformation characteristic, the set of equilibrium positions of the electroelastic actuator control system for nanomechatronics is absolutely stable. Under random inputs, the system absolute stability with respect to the mathematical expectations of the electroelastic actuator mechatronic control system equilibrium positions has been determined subject to fulfilling the condition on the derivative of the actuator hysteresis characteristic.

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