A new method for the identification of the parameters of the Dahl model

Postprint (author's final draft

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

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

Stability of time-varying systems in the absence of strict Lyapunov functions

When a non-linear system has a strict Lyapunov function, its stability can be studied using standard tools from Lyapunov stability theory. What happens when the strict condition fails? This paper provides an answer to that question using a formulation that does not make use of the specific structure of the system model. This formulation is then applied to the study of the asymptotic stability of some classes of linear and non-linear time-varying systems.Peer ReviewedPostprint (author's final draft

Advances on LuGre friction model

Postprint (published version

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

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

A unified approach for the identification of SISO/MIMO Wiener and Hammerstein systems

Hammerstein and Wiener models are nonlinear representations of systems composed by the coupling of a static nonlinearity N and a linear system L in the form N-L and L-N respectively. These models can represent real processes which made them popular in the last decades. The problem of identifying the static nonlinearity and linear system is not a trivial task, and has attracted a lot of research interest. It has been studied in the available literature either for Hammerstein or Wiener systems, and either in a discrete-time or continuous-time setting. The objective of this paper is to present a uni ed framework for the identification of these systems that is valid for SISO and MIMO systems, discrete and continuous-time setting, and with the only a priori knowledge that the system is either Wiener or Hammerstein.Preprin

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