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Harmonious Linearization of Hysteresis Characteristic of an Electroelastic Actuator for Nanomechatronics Systems
Abstract
An electroelastic actuator on the piezoelectric or electrostriction effect is applied in nanotechnology, nanobiology, biomechanics and adaptive optics for the precision matching in nanomechatronics systems. For the analysis and calculation of nanomechatronics systems is used the harmonious linearization of the hysteresis characteristic for an electroelastic actuator. The piezo actuator works on the basis of the inverse piezoelectric effect due to its deformation when the electric field strength is applied. To increase the range of movement of the piezo actuator to tens of micrometers, the multilayer piezo actuator is applied. The piezo actuator is used in nanomechatronics systems for nanodisplacement in adaptive optics, nanotechnology, scanning microscopy, nanobiomechanics, multicomponent telescopes. The coefficients of harmonious linearization for the basic loop characteristic are determined by the method of the theory of nonlinear automatic systems. On the characteristic of the piezo actuator deformation from the electric field strength, the initial curve is observed, on which the vertices of the basic hysteresis loops lie. The basic hysteresis loops have a symmetric change in the electric field strength relative to zero, and partial loops have an asymmetric change in the strength relative to zero. The expressions for the hysteresis basic and local loops of piezo actuator are received. The coefficients of harmonious linearization for the basic loop characteristic of the piezo actuator for nanomechatronics systems are obtained. The basic and local loops for hysteresis characteristics of the piezo actuator are proposed. The expression is determined for the generalized frequency transfer function of the nonlinear link with the hysteresis characteristic of the basic hysteresis loop for the piezo actuator.KeywordsHarmonious linearizationHysteresisBasic and partial loopsDeformationElectroelastic actuatorPiezo actuatorNanomechatronics system
... [1][2][3][4][5][6][7][8][9][10][11] The nano piezoengine is used for biomechanics for scanning microscopy, nano manipulator, dosing device, nano pump. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] In articles 1,3,18 the absolute stability of control system under deterministic influences is considered. The sets of equilibrium positions of the systems the piezoengines under deterministic influences are obtained in articles. ...
... 18,23 Structural models and transfer functions of the piezoengines are defined in. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]24,25 In this work the absolute stability of system with the piezoengine under randomly influences is obtained for biomechanics. ...
The sufficient condition of absolute stability system with nano piezoengine by using the derivative of the hysteretic piezoengine deformation is determined for the randomly influences. The set of equilibrium positions of the piezoengine in the control system is stable relative to mathematical expectations, when the condition of absolute stability with the maximum piezo module is met. The statistical linearization method is using for the determination condition of absolute stability control system with the nano piezoengine.
... Preisach hysteresis function a piezo actuator has the form [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] The transfer function of the linear part of the scan system with a piezo actuator for elastic-inertia load 22 ...
For the control system with a piezo actuator in astrophysical research the condition for the existence of self-oscillations is determined. Frequency method for determination self-oscillations in control systems is applied. By using the harmonious linearization of hysteresis and Nyquist stability criterion the condition of the existence of self-oscillations is obtained.
The multi-layer longitudinal piezo engine with parallel and coded control is used for nano biomedical research. The characteristics of the multi-layer longitudinal piezo engine with parallel and coded control are determined for nano biomedical research. The characteristics of the multi-layer longitudinal piezo engine are obtained by applied method of mathematical physics.
In the work is calculated of the piezoactuator for astrophysics. The structural scheme of the piezoactuator is determined for astrophysics. The matrix equation is constructed for the piezoactuator. The mechanical characteristic is determined. The parameters of the piezoactuator are obtained in nano control systems for astrophysics.
An electromagnetoelastic actuator is electromagnetomechanical device, intended for actuation of mechanisms, systems or management, based on the piezoelectric, piezomagnetic, electrostriction, magnetostriction effects, converts electric or magnetic signals into mechanical movement and force. The piezo actuator is used in vibration compensation and absorption systems in aircraft and rotorcraft elements, in nanotechnology research for scanning microscopy, in laser systems and ring gyroscopes. The structural scheme of an electromagnetoelastic actuator for nanotechnology research is constructed by using the equation of electromagnetoelasticity and the linear ordinary second-order differential equation of the actuator under various boundary conditions. An electromagnetoelastic actuator is using in nanotechnology, microelectronics, nanobiology, astronomy, nanophysics for the alignment, the reparation of the gravitation and temperature deformations. The nanomanipulator with the piezo actuator is applied in the matching systems in nanotechnology. In the present work, the problem of building the structural scheme of the electromagnetoelastic actuator is solving in difference from Mason’s electrical equivalent circuit. The transformation of the structural scheme under various boundary conditions of the actuator is considered. The matrix transfer function is calculated from the set of equations for the structural scheme of the electromagnetoelastic actuator in control system. This matrix transfer function for the deformation of the actuator is used in nanotechnology research. The structural schemes and the elastic compliances of the piezo actuators are obtained by voltage or current control. The structural scheme of the magnetostriction actuator is constructed for nanotechnology research. The characteristics of the piezo actuator are determined. The structural scheme of the piezo actuator with the back electromotive force is obtained. The transformation of the elastic compliances of the piezo actuators is considered for the voltage and current control.
For the nano piezoactuator with hysteresis in control system its set of equilibrium positions is the segment of line. By applying Yakubovich criterion for system with the nano piezoactuator the condition absolute stability of system is evaluated.
The structural model of the nano piezoengine is determined for applied biomechanics and biosciences. The structural scheme of the nano piezoengine is obtained. For calculation nano systems the structural model and scheme of the nano piezoengine are used, which reflect the conversion of electrical energy into mechanical energy of the control object. The matrix equation is constructed for the nano piezoengine in applied biomechanics and biosciences.
This work determines the coded control of a sectional electroelastic engine at the elastic–inertial load for nanomechatronics systems. The expressions of the mechanical and adjustment characteristics of a sectional electroelastic engine are obtained using the equations of the electroelasticity and the mechanical load. A sectional electroelastic engine is applied for coded control of nanodisplacement as a digital-to-analog converter. The transfer function and the transient characteristics of a sectional electroelastic engine at elastic–inertial load are received for nanomechatronics systems.
A electroelastic engine with a longitudinal piezoeffect is widely used in nanotechnology for nanomanipulators, laser systems, nanopumps, and scanning microscopy. For these nanomechatronics systems, the transition between individual positions of the systems in the shortest possible time is relevant. It is relevant to solve the problem of optimizing the nanopositioning control system with a minimum control time. This work determines the optimal control of a multilayer electroelastic engine with a longitudinal piezoeffect and minimal control time for an optimal nanomechatronics system. The expressions of the control function and switching line are obtained with using the Pontryagin maximum principle for the optimal control system of the multilayer electroelastic engine at a longitudinal piezoeffect with an ordinary second-order differential equation of system. In this optimal nanomechatronics system, the control function takes only two values and changes once.
In this work, the parametric structural schematic diagrams of a multilayer electromagnetoelastic actuator and a multilayer piezoactuator for nanomechanics were determined in contrast to the electrical equivalent circuits of a piezotransmitter and piezoreceiver, the vibration piezomotor. The decision matrix equation of the equivalent quadripole of the multilayer electromagnetoelastic actuator was used. The structural-parametric model, the parametric structural schematic diagram, and the matrix transfer function of the multilayer electromagnetoelastic actuator for nanomechanics were obtained.
The generalized parametric structural schematic diagram, the generalized structural-parametric model, and the generalized matrix transfer function of an electromagnetoelastic actuator with output parameters displacements are determined by solving the wave equation with the Laplace transform, using the equation of the electromagnetolasticity in the general form, the boundary conditions on the loaded working surfaces of the actuator, and the strains along the coordinate axes. The parametric structural schematic diagram and the transfer functions of the electromagnetoelastic actuator are obtained for the calculation of the control systems for the nanomechanics. The structural-parametric model of the piezoactuator for the transverse, longitudinal, and shift piezoelectric effects are constructed. The dynamic and static characteristics of the piezoactuator with output parameter displacement are obtained.
The field of mechatronics using piezoelectric and electrostrictive materials is growing rapidly with applications in many areas, including MEMS, adaptive optics, and adaptive structures. Piezoelectric Actuators and Ultrasonic Motors provides in-depth coverage of the theoretical background of piezoelectric and electrostrictive actuators, practical materials, device designs, drive/control techniques, typical applications, and future trends in the field. Industry engineers and academic researchers in this field will find Piezoelectric Actuators and Ultrasonic Motors an invaluable source of pertinent scientific information, practical details, and references. In the classroom, this book may be used for graduate level courses on ceramic actuators.
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.
A structural–parametric model of a piezo motor is formulated by solving the wave equation. The influence of geometric and physical parameters and external loads on its static and dynamic characteristics in the control system is studied. Transfer functions are derived for piezo motors used in nanodrives. The parametric structure of the piezo motor is determined and transformed.
We developed a structural-parametric models, obtained solution for the wave equation of electroelastic actuators and constructed their transfer functions. Effects of geometric and physical parameters of electroelastic actuators and external loading on their dynamic characteristics determined. For calculation of automatic control systems for nanometric movements with electroelastic actuators, we obtained the parametric structural schematic diagrams and the transfer functions of piezoactuators. Static and dynamic characteristics of piezoactuators determined.
The transfer functions of multilayer nano- and microdisplacement piezotransducers are obtained under the conditions of longitudinal and transverse piezo-optic effects. The absolute stability conditions are derived for the strain control systems of multilayer nano- and microdisplacement piezotransducers. Some compensating devices ensuring the stability of strain control systems of multilayer piezotransducers are chosen.
The use of nano- and micro-scale piezomotors in precision electromechanical systems is considered. The deformation of the piezoconverter corresponding to its stress state is investigated.
A simple proof of the quadratic criterion for absolute stability is given for the nondegenerate case. A similar result was proved earlier (for both degenerate and nondegenerate cases) by the author (1967) by using completely different methods. The proof given has some similarities with the ideas used by Popov (1959-1961) in the proof of his now widely known frequency-domain criterion of absolute stability. The new frequency-domain criterion of absolute stability is given for the system with the periodic coefficient. One illustrative example is considered.
A generalized structural-parametric model of a multilayered electromagnetoelastic transducer is constructed; the influence
of geometric and physical parameters of the transducer and external load on its static and dynamic characteristics is determined;
transfer functions of the multilayered electromagnetoelastic transducer of nano- and micrometric movements are obtained.
I. Diskussion der bisherigen Erfahrungen ber die Zeitabhngigkeit der Magnetisierung. Hypothese einer formalen Analogie zwischen der Jordanschen Verlustkomponente und dem dielektrischen Nachwirkungsverlust. — II. Grundlegende Versuche, die auf Grund der klassischen Theorie zur Prfung dieser Hypothese mglich sind. — III. Messung der Frequenzabhngigkeit der Permeabilitt. Grenordnungsmige Besttigung der Theorie. — IV. Ausfhrung des Schaltversuchs an einem Band- und an einem Massekern einer FeNi-Legierung. Ungltigkeit des Superpositionsprinzips. — V. Deutung der Versuchsergebnisse.
We construct a generalized structural-parametric model of a multilayer electroelastic solid and determine how the geometric
and physical parameters of the transducer and the external load affect its static and dynamical characteristics. We obtain
the transfer functions of a multilayer electroelastic solid for an electromechanical actuator of nano- and microdisplacements.
The stability conditions for a system controlling the deformation of an electromagnetoelastic transducer under deterministic and random actions are discussed. Manufacturing high-precision electromechanical drives based on electromagnetoelasticity are offering challenges under the scope of nanotechnology, nanobiology, power engineering, microelectronics, and adaptive optics. High precision drives are operated within operating loads ensuring elastic strains of the executive electromagnetoelastic transducer. A system designed for the control of micro and nanoscale strains of an electromagnetoelastic transducer. The absolute stability conditions for a system with hysteresis nonlinearity are analytically described by using Yakubovic's absolute stability criterion. The absolute stability conditions obtained for a system can be used for stability estimation and the calculation of the characteristics of the control system.
The use of the solution to the wave equation to construct a generalized structural parametric model of an electromagnetoelastic transducer to determine the effect of its geometry and physical parameters is discussed. High-precision electromechanical drives are operated under working loads ensuring elastic strains of the executive device. Piezoelectric transducers are characterized by high piezoelectric moduli and they are frequently used to produce nanoscale displacements. The solution of the wave equation supplemented with the corresponding electromagnetoelasticity equation and boundary conditions on the transducer's two working surfaces allows to construct a structural parametric model of an electromagnetoelastic transducer. The transfer functions of a piezoelectric transducer are derived from its generalized structural parametric model and are obtained as the ratio of the Laplace transform of the transducer face displacement to the Laplace transform of the input electric parameter.
Absolute stability conditions for the control system of deformation of an electromagnetoelastic converter for nano- and micrometric
movements under deterministic and random impacts are obtained.
A study was conducted to prepare a structural parametric model of a pie piezoelectric nanodisplacement transducer. The structural parametric model was prepared to investigate the potential application of the piezoelectric transducer in the equipment of nanotechnology, microbiology, microelectronics, astronomy, for high-precision superposition, compensation, and wavefront correction. It was found that the piezoelectric transducer operates on the basis of the inverse piezoelectric effect, in which a displacement is due to the deformation of the piezoelectric element, caused by the application of an external electric voltage. The wave equations also needed to solved, to construct a structural parametric model of the voltage-controlled piezoelectric transducer.
Theory of automatic control systems
- V A Besekersky
- E P Popov