Results 1  10
of
19
A free energy model for hysteresis in ferroelectric materials
 Journal of Intelligent Material Systems and Structures
"... In this paper, we construct a framework for modeling hysteresis and constitutive nonlinearities in ferroelectric compounds based on energy analysis at mesoscopic scales in combination with stochastic homogenization techniques to construct macroscopic models. In the first step of the development, pre ..."
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Cited by 44 (37 self)
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In this paper, we construct a framework for modeling hysteresis and constitutive nonlinearities in ferroelectric compounds based on energy analysis at mesoscopic scales in combination with stochastic homogenization techniques to construct macroscopic models. In the first step of the development, previous analysis is used to construct Helmholtz and Gibbs energy relations at the lattice level. This provides local polarization relations which can be extrapolated to provide constitutive models for certain homogeneous, single crystal compounds. To incorporate material and field nonhomogeneities, as well as the effects of polycrystallinity, certain parameters in the local models are assumed to be manifestations of underlying distributions having densities which must be identified for a given compound. Two techniques for estimating the unknown densities are presented, and the accuracy of the resulting model is illustrated for both symmetric major loops and biased minor loops through fits and predictions with experimental PZT4 and PZT5H data. i 1
Leeuwen, Adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parametrization
 IEEE Transactions on Automatic Control
"... Abstract—In this paper, we propose a solution to the problem of adaptive control and parameter estimation in systems with unstable target dynamics. Models of uncertainties are allowed to be nonlinearly parameterized, and required to be smooth and monotonic functions of linear functionals of the para ..."
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Cited by 17 (1 self)
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Abstract—In this paper, we propose a solution to the problem of adaptive control and parameter estimation in systems with unstable target dynamics. Models of uncertainties are allowed to be nonlinearly parameterized, and required to be smooth and monotonic functions of linear functionals of the parameters. The mere assumption of existence of nonlinear operator gains for the target dynamics is sufficient to guarantee that system solutions are bounded, reach a neighborhood of the target set, and the mismatches between the modeled uncertainties and their compensator converge to zero. With respect to parameter convergence, a standard persistent excitation condition suffices to ensure that it is exponential. When a weaker, nonlinear version of persistent excitation is satisfied, asymptotic convergence is guaranteed. The spectrum of possible applications ranges from tyreroad slip control to asynchronous message transmission in spiking neural oscillators. Index Terms—Adaptive control, exponential convergence, monotone functions, nonequilibrium dynamics, nonlinear parametrization, (nonlinear) persistent excitation, parameter estimation, unstable. I.
Estimation and Control for Systems with Nonlinearly Parameterized Perturbations
"... A class of systems influenced by nonlinearly parameterized perturbations is considered. An estimation scheme is developed whereby exponentially stable estimates of the unknown parameters can be obtained with an arbitrarily large region of attraction, provided the states are available for measuremen ..."
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Cited by 3 (1 self)
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A class of systems influenced by nonlinearly parameterized perturbations is considered. An estimation scheme is developed whereby exponentially stable estimates of the unknown parameters can be obtained with an arbitrarily large region of attraction, provided the states are available for measurement. The method applies to a class of perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known. Compensation for the perturbations in the system equations is considered for a class of systems which have uniformly globally bounded solutions and for which the origin is globally asymptotically stable when no perturbations are present. Examples with simulations are given in order to illustrate the results.
WeA10.1 A Polynomial Adaptive Estimator for Nonlinearly Parameterized Systems
"... In this paper, we propose a new Polynomial Adaptive EstimatorpAE) algorithm to estimate parameters that occur nonlinearly. The estimator is based on a polynomial nonlinearity in the Lyapunov function which is chosen so as to guarantee stability and parameter convergence in systems with polynomi ..."
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Cited by 2 (1 self)
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In this paper, we propose a new Polynomial Adaptive EstimatorpAE) algorithm to estimate parameters that occur nonlinearly. The estimator is based on a polynomial nonlinearity in the Lyapunov function which is chosen so as to guarantee stability and parameter convergence in systems with polynomial nonlinearity in the unknown parameters. We further extend the PAE algorithm to Discretizedparameter Polynomial Adaptive Estimator(DPAE) to achieve stability in general Lipschitzcontinuous nonlinear functions. We establish the Nonlinear Persistent Excitation (NLPE) condition for parameter convergence using both the PAE and the DPAE. 1 lntmductioa The problem of parameter estimation in a nonlinearly parameterized system can be stated as follows: L = f ( Y, % o o) (1) where f is nonlinear in the unknown parameter BO. The goal is to develop an estimatorB = f (Y, % 6') uf, C = $ y (2) with 6adjusted so that s ̂+ B o, A stability framework has been established for studying estimation and contml of nonlinearly parameterized systems in [1][7]. In [1,2], for example, stability and parameter convergence with suitable NLPE conditions have been established. The problem however is that the NLF'E condition is quite restrictive, and requires a certain property to be satis0 ed by all possible subsets in the parameter space and is rather dim cult to check. One of the reasons for this is that the unknown parameter is estimated using a quadratic nonlinearity in the Lyapunov function which essentially generates a linear function in the parameter error. For example, for the system in (I), and the estimator in (2), suppose the parameter estimation is chosen as 6 =
A new adaptive control algorithm for systems with multilinear parametrization : nparameters case
 In Taming Heterogeneity and Complexity of Embedded Control: CTSHYCON Workshop on Nonlinear and Hybrid Control
, 2006
"... Abstract — Adaptive control of nonlinearly parametrized (NLP) systems is an unknown field, where few results have been proposed up to now. In this paper, we propose a new adaptive control algorithm for systems with multilinear parametrization, that belong to the class of nonlinear parametrizations. ..."
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Abstract — Adaptive control of nonlinearly parametrized (NLP) systems is an unknown field, where few results have been proposed up to now. In this paper, we propose a new adaptive control algorithm for systems with multilinear parametrization, that belong to the class of nonlinear parametrizations. The proposed controller is a non certainty equivalence one where only the original parameters, without then the need of overparametrization, are adapted. An important feature of the proposed approach is that its convergence properties are not based on projections inside the hypercube to where the parameters are known to lie. Simulations show the efficacy of the approach highlighting this fact, that is, that convergence holds even for the case where the adapted parameters do not belong to the hypercube where the true parameters are known to be. I.
Observer Design and Parameter Estimation for Linear Systems with Nonlinearly Parameterized Perturbations
, 2009
"... We introduce a method of observer design for systems described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. The design is modular, and consists of a modified highgain observer that estimates the states of the sy ..."
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Cited by 1 (0 self)
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We introduce a method of observer design for systems described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. The design is modular, and consists of a modified highgain observer that estimates the states of the system together with the full perturbation, and a parameter estimator. The parameter estimator is constructed by the designer to identify the unknown parameters, by dynamically inverting a nonlinear equation. We apply the method to observer design for a DC motor with friction modeled by the dynamic LuGre friction model, estimating the internal state in the friction model and an unknown parameter representing Coloumb friction.
ModelBased Robust Control Designs for High Performance . . .
"... The increasing employment of smart structures in industrial, automotive, aerospace, and aeronautic processes necessitates the study of materials exhibiting constitutive nonlinearities and hysteresis. The high performance and high speed demands of such processes can often be met by transducers utiliz ..."
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Cited by 1 (1 self)
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The increasing employment of smart structures in industrial, automotive, aerospace, and aeronautic processes necessitates the study of materials exhibiting constitutive nonlinearities and hysteresis. The high performance and high speed demands of such processes can often be met by transducers utilizing piezoceramic, shape memory alloy, or magnetostrictive elements. Here, the focus is placed on magnetostrictive materials. These materials provide several benefits such as the ability to generate large forces and strains and provide precision placement. However, to achieve the full potential of magnetostrictive materials, models and control laws which accommodate the inherent nonlinearities and hysteresis must be employed. Furthermore, it is advantageous to consider material characterization, model development, and control design simultaneously to fully exploit unique sensor and actuator capabilities of these magnetostrictive materials in coupled systems. An emphasis has been placed on the design of models for magnetostrictive transducers and control strategies that are implementable in real time and incorporate realistic operating conditions. To this end,
Nonlinear adaptive parameter estimation algorithms for hysteresis models of magnetostrictive actuators
 Proceedings of the SPIE, Smart Structures and Materials 2002, Volume 4693
, 2002
"... Increased control demands in applications including high speed milling and hybrid motor design have led to the utilization of magnetostrictive transducers operating in hysteretic and nonlinear regimes. To achieve the high performance capabilities of these transducers, models and control laws must ac ..."
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Cited by 1 (1 self)
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Increased control demands in applications including high speed milling and hybrid motor design have led to the utilization of magnetostrictive transducers operating in hysteretic and nonlinear regimes. To achieve the high performance capabilities of these transducers, models and control laws must accommodate the nonlinear dynamics in a manner which is robust and facilitates realtime implementation. This necessitates the development of models and control algorithms which utilize known physics to the degree possible, are low order, and are easily updated to accommodate changing operating conditions such as temperature. We consider here the development of nonlinear adaptive identication for low order, energybased models. We illustrate the techniques in the context of magnetostrictive transducers but they are suÆciently general to be employed for a number of commonly used smart materials. The performance of the identication algorithm is illustrated through numerical examples.
LIBRARIES Parameter Estimation and Control of Nonlinearly Parameterized Systems
, 2005
"... Parameter estimation in nonlinear systems is an important issue in measurement, diagnosis and modeling. The goal is to find a differentiator free online adaptive estimation algorithm which can estimate the internal unknown parameters of dynamic systems using its inputs and outputs. This thesis pro ..."
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Parameter estimation in nonlinear systems is an important issue in measurement, diagnosis and modeling. The goal is to find a differentiator free online adaptive estimation algorithm which can estimate the internal unknown parameters of dynamic systems using its inputs and outputs. This thesis provides new algorithms for adaptive estimation and control of nonlinearly parameterized (NLP) systems. First, a Hierarchical Minmax algorithm is invented to estimate unknown parameters in NLP systems. To relax the strong condition needed for the convergence in Hierarchical Minmax algorithm, a new Polynomial Adaptive Estimator (PAE) is invented and the Nonlinearly Persistent Excitation Condition for NLP systems, which is no more restrictive than LPE for linear systems, is established for the first time. To reduce computation complexity of PAE, a Hierarchical PAE is proposed. Its performance in the presence of noise is evaluated and is shown to lead to bounded errors. A deadzone based adaptive filter is also proposed and is shown to accurately estimate the unknown parameters under some conditions. Based on the adaptive estimation algorithms above, a Continuous Polynomial Adaptive
Nonlinear Adaptive Parameter Estimation Techniques for Magnetic Transducers Operating in Hysteretic Regimes
"... Increased control demands in applications including high speed milling and hybrid motor design have led to the utilization of magnetostrictive transducers operating in hysteretic and nonlinear regimes. To achieve the high performance capabilities of these transducers, models and control laws must ac ..."
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Increased control demands in applications including high speed milling and hybrid motor design have led to the utilization of magnetostrictive transducers operating in hysteretic and nonlinear regimes. To achieve the high performance capabilities of these transducers, models and control laws must accommodate the nonlinear dynamics in a manner which is robust with regard to system inputs and facilitates realtime implementation. This necessitates the development of models and control algorithms which utilize known physics to the degree possible, are loworder, and are easily updated to accommodate changing operating conditions such as temperature. We consider here the development of nonlinear adaptive identification techniques for loworder, energybased hysteresis models having nonlinear parameterizations. We illustrate the techniques in the context of magnetostrictive transducers but they are sufficiently general to be employed for a number of commonly used smart materials including piezoceramics, magnetostrictives and shape memory alloys. The performance of the resulting nonlinear identification algorithms are illustrated through numerical examples. Index Terms: Magnetostrictive materials, hysteresis, constitutive nonlinearities, nonlinear parameterization, adaptive estimation