Nonlinear Hysteresis Behavior Research Articles

Novel multirate control strategy for piezoelectric actuators

In this article, a novel control method is proposed for feedforward compensation of hysteresis non-linearity in various frequency ranges. By integrating a multirate hysteresis compensator controller with PID feedback control, a combined controller is developed and experimentally validated for a piezoelectric micro-positioning system. Piezoelectric materials show non-linear hysteresis behaviour when they experience an electrical field. A fundamental study of a piezoelectric actuator (PEA) shows that the hysteresis effect deteriorates the tracking performance of the PEA. This paper presents a non-linear model which quantifies the hysteresis non-linearity generated in PEAs in response to the applied driving voltages. The tracking control method is based on multirate feedforward control. The proposed multirate control method uses an inverse modified Prandtl-Ishlinskii operator to cancel out hysteresis non-linearity. The controller structure has a simple design and can be quickly identified. The control system is capable of achieving suitable tracking control and it is convenient to use and can be quickly applied to practical PEA applications. Experimental results are provided to verify the efficiency of the proposed method.

Study on ECNLP Dynamics Model of Piezoceramic Actuator and Position Tracking Controller

摘要: 针对压电陶瓷驱动器中存在的复杂非线性滞回动力学特性, 首先建立了一种新型机电耦合非线性集总参数(Electromechanical coupling nonlinear lumped-parameter, ECNLP)模型. 该模型不仅能够准确、合理地刻画压电叠堆中的非线性滞回动、静态特性, 而且充分考虑了驱动器中弹性和运动部件的动力学特性. 基于此模型, 利用微分几何的输入输出线性化原理, 实现了该模型的精确线性化变换, 并导出了相应的线性可控规范型子系统. 根据该子系统, 提出了一种基于LQ方法的压电陶瓷驱动器非线性位移跟踪控制系统, 并进一步验证了余下内动态子系统的稳定性. 最后, 通过仿真计算检验了系统的控制效果. 关键词: 压电驱动 / 机电耦合 / 非线性滞回 / 输入输出线性化 / 位移跟踪控制

Solitons and critical breakup fields in lithium niobate type uniaxial ferroelectrics

Ferroelectric materials, such as lithium niobate, show interesting non-linear hysteresis behavior that can be explained by a dynamical system analysis. By using variational principle, a non-linear Klein-Gordon (K-G) equation is derived for lithium niobate type of uniaxial ferroelectrics involving various types of energy, which was not considered previously to construct the Hamiltonian. This leads to soliton solutions under different conditions of soliton velocity. The critical value of the (dimensional) effective electric field has been estimated to be 54–58 kV/cm for lithium niobate depending on the impurity content in these type inhomogeneous ferroelectrics. Beyond this critical field, there is no existence of solitons. This critical field is related to a break-up mechanism of Landau-Ginzburg two-well potential to a single well, as the driving force is increased.

Dynamical hysteresis in communications: a Volterra functional approach

A formalism to characterise nonlinear dynamical hysteresis is described for multi-channel input-output physical systems that can have multi-valued solutions. The formalism presented is based on an extension to the Volterra functional representation of nonlinear dynamical input-output processes, an extension that overcomes the single-valued limitation of both the Taylor and Volterra series expansions. One important attribute of the formalism is that the coefficients can be physically significant and another is that the response function values can be determined directly from noisy data thereby offering potential insight into the underlying physics of the observed phenomena. The estimated response function values are the empirical coefficients required by a phenomenological theory of the system and can be used to predict likely behaviour, and to design and precisely control improved systems. The response function values that characterise the multi-channel nonlinear and dynamical hysteresis behaviour are estimated using the simultaneous moment equation method. The coefficients that characterise the hysteretic behaviour are obtained by solving a tractable system of simultaneous moment equations that are generated by operating on a suitably truncated Volterra functional expansion. These simultaneous moment equations enable the unknown constant coefficient values to be determined from noisy multi-channel input-output data. In order to demonstrate the attributes of the formalism under controlled conditions, a numerical example is presented which illustrates how to accurately estimate the coefficients of multi-channel nonlinear dynamical hysteresis phenomena corrupted by additive noise. The problems of time-dependent coefficients and the analysis of real data are to be considered elsewhere.

MultiRate Predictive Control of Piezoelectric actuators

Piezoelectric materials show nonlinear hysteresis behaviour when they are under high electrical field and mechanical load. Fundamental study of PEA depicts that the Hysteresis effect deteriorate the tracking performance of The PEA. This paper proposes a nonlinear model which quantifies the Hysteresis nonlinearity generated in Piezoactuators in response to applied driving voltages. A novel perfect tracking control method based on multirate feedforward control is proposed which uses the nonlinear model to compensate mentioned limiting factors in PEA. In this study a multirate control method based on modified Prandtle-Ishlinskii operator as nonlinear model is implemented. It compensates rate dependant hysteresis nonlinearity in PEA. The controller structure has a simple design and can be quickly identified. The control system is capable to achieve suitable tracking control and it is convenient to use and can be quickly applied to the practical PEA applications. Experimental results are provided to verify the efficiency of the proposed method.

Dynamical systems analysis for polarization in ferroelectrics

The nonlinear hysteresis behavior in ferroelectric materials, such as lithium tantalate and lithium niobate, may be explained by dynamical systems analysis. In a previous work, the polarization “domain wall width” was studied in terms of only spatial variation and eventually critical values of polarization were determined to derive the stability zone in the context of Landau-Ginzburg free energy functional. In the present work, the temporal dynamics of the domains themselves are considered by taking the time variation through Euler-Lagrange dynamical equation of motion, which gives rise to a Duffing oscillator differential equation as a governing equation. From this nonlinear Duffing oscillator equation, three cases are studied theoretically: First, with no electric field with and without any damping; secondly, taking the external field as static with damping; and finally, taking an oscillatory electric field with damping. After giving perturbation at the coercive field, the eigenvalues deduced through a Jacobian transformation of the perturbed matrix show interesting cases of stability and instability of polarization for different values of electric field. The possibility of chaos at high oscillatory electric field is also briefly explored merely as a limiting case in terms of the Lyapunov exponents spectrum in our particular ferroelectric system.

An approach to the Klein–Gordon equation for a dynamic study in ferroelectricmaterials

Ferroelectric materials such as lithium niobate and lithium tantalate show a non-linearhysteresis behaviour, which may be explained by dynamical system analysis. The behaviourof these ferroelectrics is usually explained by domains and domain wall movements. So, thespatial variation of the domain wall was studied previously in order to see its effecton the domain wall width in the context of the Landau–Ginzburg functional.In the present work, both temporal and spatial variations of polarization areconsidered, and by using the Euler–Lagrange dynamical equation of motion, aKlein–Gordon equation is derived by taking the ferroelectrics as a Hamiltoniansystem. An interaction has been considered between the nearest neighbour domains,which are stacked sideways in a parallel array with uniform polarization. Thisinteraction term is associated with the spatial term and when this interaction isassumed to be zero, the spatial term vanishes, giving rise to a Duffing oscillatordifferential equation, which can be also studied by a dynamic system analysis.

A Meso-Electro-Mechanical Model for PMN-PT-BT Ceramics Behavior

A three-dimensional, meso-electro-mechanical model has been formulated for description of PMN-PT-BT ceramics. Unlike the experimentally fit models and phenomenological models which are based on state variables and/or empirical relationships, this fully coupled, computational mesomechanics model for polycrystalline PMN-PT-BT ceramics is developed based on considerations of constitutive behavior of single crystals. Specifically, domain wall nucleation and evolution rate equations are proposed in this work to describe the nonlinear hysteresis behavior of these ceramics near the phase transition temperature with maximum permittivity. Comparisons of hysteresis loops under different temperature conditions between testing results and the present simulation show good agreement. Effects of compressive stresses on relationships of strain versus electric field are also discussed.

Simulation of magnetic component models in electric circuits including dynamic thermal effects

It is essential in the simulation of power electronics applications to model magnetic components accurately. In addition to modeling the nonlinear hysteresis behavior, eddy currents and winding losses must be included to provide a realistic model. In practice the losses in magnetic components give rise to significant temperature increases which can lead to major changes in the component behavior. In this paper a model of magnetic components is presented which integrates a nonlinear model of hysteresis, electro-magnetic windings and thermal behavior in a single model for use in circuit simulation of power electronics systems. Measurements and simulations are presented which demonstrate the accuracy of the approach for the electrical, magnetic and thermal domains across a variety of operating conditions, including static thermal conditions and dynamic self heating.

A 2D finite element procedure for magnetic field analysis taking into account a vector Preisach model

The main purpose of this paper is to incorporate a refined hysteresis model, viz. a vector Preisach model, in 2D magnetic field computations. To this end the governing Maxwell equations are rewritten in a suitable way, which allows to take into account the proper magnetic material parameters and, moreover, to pass to a variational formulation. The variational problem is solved numerically by a FE approximation, using a quadratic mesh, followed by the time discretisation based upon a modified Cranck Nicholson algorithm. The latter includes a suitable iteration procedure to deal with the nonlinear hysteresis behaviour. Finally, the effectiveness of the presented mathematical tool has been confirmed by several numerical experiments.

Hysteresis Behaviour and Specific Damping Capacity of Negative Poisson's Ratio Foams

Previously open cell polyurethane foams have been made to be re-entrant, in that their cell ribs are inwardly bent, which results in the foam exhibiting a negative Poisson's ratio(1). Untransformed control and transformed negative Poisson’s ratio foams were cyclically loaded at various levels of pre-strain to determine their hysteresis behaviour, and from this, to elucidate their specific damping characteristics. Both untransformed and transformed foams exhibited non-linear hysteresis behaviour at high cyclic strains, regardless of their initial levels of pre-strain. The specific damping capacity of the transformed foam with extreme compressive pre-strain was higher than that of the untransformed foam. This effect was attributed to the rubbing of the inwardly buckled cell ribs of the transformed foam. The specific damping capacity varied with both the level of pre-strain and with the amplitude of cyclic strain about that level.

Modeling hysteresis in piezoceramic actuators

A major deficiency of piezoceramic actuators is that their open-loop control accuracy is seriously limited by hysteresis. This paper discusses the adaptation of the Preisach model to describe the nonlinear hysteresis behavior of these actuators. The adapted model is used to predict the response of a piezoceramic actuator to a sinusoidal input and a triangular input. The predictions are compared with experimental measurements on a stacked piezoceramic actuator. The model reproduces the hysteresis loop of the actuator to within 3% over the entire working range of 0–15 μm. This opens the possibility of incorporating the model into a control loop in order to overcome the accuracy problem.

Dynamic and static modeling of the Shuttle Orbiter's Thermal Protection System

Seventy percent of the surface of the Shuttle Orbiter is covered by a Thermal Protection System, consisting of ceramic tiles bonded to the Orbiter's aluminum skin through a felt pad. The structural evaluation of the tile/pad system is complicated by the nonlinear elastic properties of the pad. This paper describes the dynamic and static analysis methods utilized to model this nonlinear behavior. Comparisons between test and analysis are shown. Vibration tests of individual tiles identified tile response which results from the nonlinearity of the pad. These phenomena include a highly distorted response waveform when the tile/pad system is base-driven dinusoidally and resonant frequencies which are dependent on both steady pre-load and amplitude of the base drive input. The dynamic analysis accounts for the nonlinear stiffening, hysteresis and viscous behavior of the pad material. Material characterization tests of the pad revealed a load displacement nonlinearity which is agravated with repeated load cycles. A nonlinear stress analysis procedure was developed and programmed to permit the calculation of stresses at the tile/pad bondline for an arbitrary pad contiguration.