Semilinear Duhem Model for Rate-Independent and Rate-Dependent Hysteresis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57865/1/HysteresisSemilinearDuhemTAC2005.pd

Piecewise Linear Identification for the Rate-Independent and Rate-Dependent Duhem Hysteresis Models

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57843/1/HysteresisIDTACMarch2007.pd

A survey of the hysteretic Duhem model

The Duhem model is a simulacrum of a com- plex and hazy reality: hysteresis. Introduced by Pierre Duhem to provide a mathematical representation of thermodynamical irreversibility, it is used to describe hysteresis in other areas of science and engineering. Our aim is to survey the relationship between the Duhem model as a mathematical representation, and hysteresis as the object of that representation.Peer ReviewedPostprint (author's final draft

Minor loops of the Dahl and LuGre models

PreprintHysteresis is a special type of behavior encountered in physical systems: in a hysteretic system, when the input is periodic and varies slowly, the steady-state part of the output-versus-input graph becomes a loop called hysteresis loop. In the presence of perturbed inputs or noise, this hysteresis loop presents small lobes called minor loops that are located inside a larger curve called major loop. The study of minor loops is being increasingly popular since it leads to a quantification of the loss of energy due to the noise. The aim of the present paper is to give an explicit analytic expression of the minor loops of the LuGre and the Dahl models of dynamic dry friction.Preprin

Causal canonical decomposition of hysteresis systems

Hysteresis is a special type of behavior found in many areas including magnetism, mechanics, bi-ology, economics, etc. One of the characteristics of hysteresis systems is that they are approximatelyrate independent for slow inputs. It is possible to express this characteristic in mathematical languageby decomposing hysteresis operators as the sum of a rate independent component and a nonhystereticcomponent which vanishes in steady state for slow inputs. This decomposition -calledcanonical decom-position- is possible for a class of hysteresis operators for which a continuous input leads to a continuousoutput and a continuous hysteresis loop. The canonical decomposition can be obtained using the conceptofcon uencewhich is an equation that continuous hysteresis operators should verify.On the other hand, hysteresis systems are causal which means that their output depends on the currentand/or previous values of the input but not on the future values of that input. Are the components ofthe canonical decomposition also causal? The answer is en general negative. The lack of causalityof these components means that they cannot be written in the form of differential equations, integro-differential equations, partial differential equations, partial integro-differential equations and many otheruseful structures.This paper proposes a new decomposition of hysteresis operators calledcausal canonical decompositionin which the rate independent component and the nonhysteretic component are both causal. The maintool to obtain the causal canonical decomposition is a new mathematical equation that we calluniformcon uence. Using this equation we show that the causal canonical decomposition is unique. The conceptsintroduced in the paper are applied to the hysteretic scalar semilinear Duhem model as a case study.Peer ReviewedPostprint (author's final draft

Characterization of the hysteresis Duhem model

The Duhem model, widely used in structural, electrical and mechanical engineering, gives an analytical description of a smooth hysteretic behavior. In practice, the Duhem model is mostly used within the following black-box approach: given a set of experimental input-output data, how to tune the model so that its output matches the experimental data. It may happen that a Duhem model presents a good match with the experimental real data for a specific input, but does not necessarily keep signi cant physical properties which are inherent to the real data, independently of the exciting input. This paper presents a characterization of different classes of Duhem models in terms of their consistency with the hysteresis behavior.Postprint (published version

Consistency of the Duhem Model with Hysteresis

The Duhem model, widely used in structural, electrical, and mechanical engineering, gives an analytical description of a smooth hysteretic behavior. In practice, the Duhem model is mostly used within the following black-box approach: given a set of experimental input-output data, how to tune the model so that its output matches the experimental data. It may happen that a Duhem model presents a good match with the experimental real data for a specific input but does not necessarily keep significant physical properties which are inherent to the real data, independent of the exciting input. This paper presents a characterization of different classes of Duhem models in terms of their consistency with the hysteresis behavior

A velocity based active vibration control of hysteretic systems

Hysteresis is a property of systems that do not instantly follow the forces applied to them, but react slowly, or do not return completely to their original state. A velocity based active vibration control, along with a special class of hysteretic models using passive functions are presented in this paper. This hysteretic model is based on a modification of the Bouc–Wen model, where a nonlinear term is replaced by a passive function. The proposed class retains the rate-independence property of the original Bouc–Wen model, and it is able to reproduce several kinds of hysteretic loops that cannot be reproduced with the original Bouc–Wen model. Using this class of hysteretic models, a chattering velocity-based active vibration control scheme is developed to mitigate seismic perturbations on hysteretic base-isolated structures. Our hysteretic model is used because of its simplicity in proving the stability of the closed-loop system; i.e., a controller is designed using the proposed model, and its performance is tested on the original hysteretic system, modeled with Bouc–Wen. Numerical experiments show the robustness and efficiency of the proposed control algorithm.Peer ReviewedPostprint (author's final draft