Passivity analysis and passivation of feedback systems using passivity indices
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Abstract:
Passivity indices are used to measure the excess or shortage of passivity. While most of the work in the literature focuses on stability conditions for interconnected systems using passivity indices, here we focus on passivity and passivation of the feedback interconnection of two input feed-forward output-feedback (IF-OF) passive systems. The conditions are given to determine passivity indices in feedback interconnected systems. The results can be viewed as the extension of the well-known compositional property of passivity. We also consider the passivation problem which can be used to render a non-passive plant passive using a feedback interconnected passive controller. The passivity indices of the passivated system are also determined. The results derived do not require linearity of the systems as it is commonly assumed in the literature.Keywords:
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The paper discusses the preservation of u-average passivity throughout suitable interconnection. The concept of power preserving connection is introduced. It is instrumental to ensure u-average passivity of the interconnected system with respect to new external controls.
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Passivity and dissipativity are energy-like concepts, widely used in control design, that capture the "energy" consumption of a dynamical system and therefore relate closely to the physical world. Passivity indices of a system are measures of its passivity margins and represent shortage and excess of passivity in a system. With the aid of passivity indices, one can measure how passive a system is, or how far from passivity it is. Passivity indices extend all the analysis and design methods based on passivity to nonpassive systems as well. One of the advantages of using passivity is its tight relationship to stability. Another is its compositionality, which, together with its generality, makes it possible to use passivity in a wide range of complex control systems. In the present entry, an overview of dissipativity and passivity is given. Passivity indices of a system and their relation to stability are defined, and methods to find the indices are presented.
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Building from recent results on passivity for a class of hybrid systems, we investigate the properties of negative feedback interconnections of such systems. We establish links between the passivity properties of the individual subsystems and passivity, stability, and asymptotic stability of their interconnection. As a main difference to the continuous time counterpart, it is found that the sum of the two storage functions of two individual hybrid subsystems may not be a storage function for their interconnection. This issue motivates exploring additional sufficient conditions that guarantee that passivity and stability of the interconnected system hold using the individual storage functions. Throughout the paper, an application and examples illustrate the definitions and the results obtained.
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Passivity and dissipativity are energy-like concepts, widely used in control design, that capture the "energy" consumption of a dynamical system and therefore relate closely to the physical world. Passivity indices of a system are measures of its passivity margins and represent shortage and excess of passivity in a system. With the aid of passivity indices, one can measure how passive a system is, or how far from passivity it is. Passivity indices extend all the analysis and design methods based on passivity to nonpassive systems as well. One of the advantages of using passivity is its tight relationship to stability. Another is its compositionality, which, together with its generality, makes it possible to use passivity in a wide range of complex control systems. In the present entry, an overview of dissipativity and passivity is given. Passivity indices of a system and their relation to stability are defined, and methods to find the indices are presented.
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Abstract Descriptions are given of the various phenomena associated with the passivation and reactivation of iron in concentrated nitric acid. Covered are apparent and true passivation potential, apparent and true passivation current density, passivity producing and passivity maintaining current density. Information is given also on equivalent current density in a redox system, the role of nitrous acid in passivation by concentrated nitric acid, the corrosion of passive iron, refractoriness toward activation, rhythms and activity waves.
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