Methods for modeling and control of systems with hysteresis of shape memory alloy actuators

Hysteresis widely exists in smart materials such as shape memory alloys (SMAs), piezoelectrics, magnetorheological (MR) fluids, electrorheological (ER) fluids and so on. It severely affects the applicability of such materials in actuators and sensors. In this thesis, problems of modeling and control of systems with hysteresic SMAs actuators are studied. The approaches are also applicable to control of a wide class of smart actuators. Hysteresis exhibited by SMAs actuators is rate-independent when the input frequency is low, and can be modeled by a classical Preisach model or a KP model. The classical Preisach hysteresis model is a foundation of other hysteresis models. In this thesis, traditional methods are explained in advance to identify and implement the classical Preisach model. Due to the extremely large amount of computation involved in the methods, a new form of the Preisach model, linearly parameterized Preisach model, is introduced, and then an effective method to implement the model is presented. The KP model is a more effective operator to describe the Preisach class of hysteresis than the Preisach model. The relationship between the two models is revealed to verify the effectiveness of the KP model. Also, a linearly parameterized KP model is proposed. For both of the Preisach hysteresis model and the KP hysteresis model, algorithms of inverse hysteresis operators are developed, and simulations for modeling and inverse compensation are conducted. Since the Preisach model and the KP model can only describe hysteresis which has saturation states and reverse curves with zero initial slopes, a novel hysteresis model is defined to overcome these shortcomings. The newly defined hysteresis model is a low dimensional hysteresis model and can describe hysteresis which has revertible linear parts and reverse curves with non-zero initial slopes. The problems for controlling systems with input hysteresis have been pursued along three different paths: inverse compensation, gradient adaptive control and robust adaptive control for linear and nonlinear systems. Control schemes of open-loop inverse compensation and gradient adaptive inverse compensation for the Preisach hysteresis model are explored to eliminate the effects of the hysteresis when the output of the hysteretic actuator is measurable. Usually hysteresis of smart actuator in systems is not exactly known, but it can be approximately modeled via the linearly parameterized KP model. For a known linear system preceded by an unknown actuator hysteresis, a model reference control scheme combining with an adaptive inverse compensation is designed for tracking control of the systems. While an unknown linear system preceded by an unknown actuator hysteresis, a model reference adaptive control scheme together with an adaptive inverse compensation is developed for tracking control of the system. Simulations for both cases have been performed to illustrate the control methods. Finally, when hysteresis of smart actuator in systems has a non-measurable output and is modeled via the KP model or the newly defined model, a novel robust adaptive control configuration is presented for tracking control of systems. The analysis for the stability and the convergence of the control systems is conducted. Simulations are performed to verify the effectiveness of the novel control method

Hysteresis and economics - taking the economic past into account

The goal of this article is to discuss the rationale underlying the application of hysteresis to economic models. In particular, we explain why many aspects of real economic systems are hysteretic is plausible. The aim is to be explicit about the difficulties encountered when trying to incorporate hysteretic effects into models that can be validated and then used as possible tools for macroeconomic control. The growing appreciation of the ways that memory effects influence the functioning of economic systems is a significant advance in economic thought and, by removing distortions that result from oversimplifying specifications of input-output relations in economics, has the potential to narrow the gap between economic modeling and economic reality

Functional Integration Approach to Hysteresis

A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate envelope construction applied to g(x), inspired by the overdamped dynamics of systems evolving in multistable free energy landscapes. Second, the average hysteresis response of an ensemble of such systems is expressed as a functional integral over the space G of all admissible generating functions, under the assumption that an appropriate measure m has been introduced in G. The consequences of the formulation are analyzed in detail in the case where the measure m is generated by a continuous, Markovian stochastic process. The calculation of the hysteresis properties of the ensemble is reduced to the solution of the level-crossing problem for the stochastic process. In particular, it is shown that, when the process is translationally invariant (homogeneous), the ensuing hysteresis properties can be exactly described by the Preisach model of hysteresis, and the associated Preisach distribution is expressed in closed analytic form in terms of the drift and diffusion parameters of the Markovian process. Possible applications of the formulation are suggested, concerning the interpretation of magnetic hysteresis due to domain wall motion in quenched-in disorder, and the interpretation of critical state models of superconducting hysteresis.Comment: 36 pages, 9 figures, to be published on Phys. Rev.

An estimate of energy dissipation due to soil-moisture hysteresis

Processes of infiltration, transport and outflow in unsaturated soil necessarily involve the dissipation of energy through various processes. Accounting for these energetic processes can contribute to modelling hydrological and ecological systems. The well-documented hysteretic relationship between matric potential and moisture content in soil suggests that one such mechanism of energy dissipation is associated with the cycling between wetting and drying processes. Working from a time-series of soil moisture content data (taken in the south-west of Ireland), and making rather straightforward assumptions regarding the hysteretic relationship mentioned, the average rate of energy dissipation was found to be O(10−5)

Hysteresis and Post Walrasian Economics

Macroeconomics, hysteresis The “new consensus” dsge (dynamic stochastic general equilibrium) macroeconomic model has microfoundations provided by a single representative agent. In this model shocks to the economic environment do not have any lasting effects. In reality adjustments at the micro level are made by heterogeneous agents, and the aggregation problem cannot be assumed away. In this paper we show that the discontinuous adjustments made by heterogeneous agents at the micro level mean that shocks have lasting effects, aggregate variables containing a selective, erasable memory of the shocks experienced. This hysteresis framework provides foundations for the post-Walrasian analysis of macroeconomic systems

Topological energy barrier for skyrmion lattice formation in MnSi

We report the direct measurement of the topological skyrmion energy barrier through a hysteresis of the skyrmion lattice in the chiral magnet MnSi. Measurements were made using small-angle neutron scattering with a custom-built resistive coil to allow for high-precision minor hysteresis loops. The experimental data was analyzed using an adapted Preisach model to quantify the energy barrier for skyrmion formation and corroborated by the minimum-energy path analysis based on atomistic spin simulations. We reveal that the skyrmion lattice in MnSi forms from the conical phase progressively in small domains, each of which consisting of hundreds of skyrmions, and with an activation barrier of several eV.Comment: Final accepted versio