Topic

# State variable

About: State variable is a research topic. Over the lifetime, 14354 publications have been published within this topic receiving 254707 citations.

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TL;DR: In this paper, the dependence of the friction force on slip history is described by an experimentally motivated constitutive law where the friction forces are dependent on slip rate and state variables.

Abstract: The dependence of the friction force on slip history is described by an experimentally motivated constitutive law where the friction force is dependent on slip rate and state variables The state variables are defined macroscopically by evolution equations for their rates of change in terms of their present values and slip rate Experiments may strongly suggest that one state variable is adequate or prove that one is inadequate Analysis of steady slip governed by a single state variable in a spring and (massless) slider predict oscillations at a critical spring stiffness k = kcrit The critical stiffness kcrit is given by a simple formula and steady slip is stable for k > kcrit and unstable for k < kcrit State variable friction laws may superficially appear as a simple slip rate dependence, slip distance dependence, or time dependent static friction, depending on experiment and testing machinery Truly complicated motion is possible in a spring-slider model if more than one state variable is used Further consequences of state variable friction laws can include creep waves and apparent rate independence for some phenomena

2,700 citations

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TL;DR: In this article, a dynamical theory of low-temperature shear deformation in amorphous solids is proposed based on molecular-dynamics simulations of a two-dimensional, two-component non-crystalline system.

Abstract: We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal behavior typical of metallic glasses and other viscoplastic materials, specifically, reversible elastic deformation at small applied stresses, irreversible plastic deformation at larger stresses, a stress threshold above which unbounded plastic flow occurs, and a strong dependence of the state of the system on the history of past deformations. Microscopic observations suggest that a dynamically complete description of the macroscopic state of this deforming body requires specifying, in addition to stress and strain, certain average features of a population of two-state shear transformation zones. Our introduction of these state variables into the constitutive equations for this system is an extension of earlier models of creep in metallic glasses. In the treatment presented here, we specialize to temperatures far below the glass transition and postulate that irreversible motions are governed by local entropic fluctuations in the volumes of the transformation zones. In most respects, our theory is in good quantitative agreement with the rich variety of phenomena seen in the simulations. {copyright} {ital 1998} {ital The American Physical Society}

1,769 citations

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TL;DR: In this article, it was shown that the design of an observer for a system with M outputs can be reduced to the design for m separate observers for single-output subsystems.

Abstract: Often in control design it is necessary to construct estimates of state variables which are not available by direct measurement. If a system is linear, its state vector can be approximately reconstructed by building an observer which is itself a linear system driven by the available outputs and inputs of the original system. The state vector of an n th order system with m independent outputs can be reconstructed with an observer of order n-m . In this paper it is shown that the design of an observer for a system with M outputs can be reduced to the design of m separate observers for single-output subsystems. This result is a consequence of a special canonical form developed in the paper for multiple-output systems. In the special case of reconstruction of a single linear functional of the unknown state vector, it is shown that a great reduction in observer complexity is often possible. Finally, the application of observers to control design is investigated. It is shown that an observer's estimate of the system state vector can be used in place of the actual state vector in linear or nonlinear feedback designs without loss of stability.

1,611 citations

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TL;DR: In this paper, it is shown that the input/output relations determine only one part of a system, that which is completely observable and completely controllable, and methods are given for calculating irreducible realization of a given impulse-response matrix.

Abstract: There are two different ways of describing uynamicu systems: (i) bymeans of state variables and (ii) by input/output relations. The first method may be regarded as an axiornatization of Newton’s laws of mechanics and is taken to be the basic definition of a system.It is then shown (in the linear case) that the input/output relations determine only one part of a system, that which is completely observable and completely controllable. Using the theory of controllability and observability, methods are given for calculating irreducible realization of a given impulse-response matrix. In particular, an explicit procedure is given to determine the minimal number of state variables necessary to realize a given transfer-function matrix. Difficulties arising from the use of reducible realizations are discussed briefly.

1,605 citations

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TL;DR: In this paper, the authors study the thermodynamics of nonlinear materials with internal state variables whose temporal evolution is governed by ordinary differential equations, and employ a method developed by Coleman and Noll to find the general restrictions which the Clausius-Duhem inequality places on response functions.

Abstract: This is a study of the thermodynamics of nonlinear materials with internal state variables whose temporal evolution is governed by ordinary differential equations. After employing a method developed by Coleman and Noll to find the general restrictions which the Clausius—Duhem inequality places on response functions, we analyze various types of dynamical stability that can be exhibited by solutions of the internal evolution equations. We also discuss integral dissipation inequalities, conditions under which temperatures can be associated with internal states, and the forms taken by response functions when the material is a fluid.

1,582 citations