A Design Method of VSS Observer for Continuous-Time Systems with Output Uncertainties

Research output: Contribution to journalArticle

Abstract

VSS observers are considered for continuous-time systems, in which the nominal plant model is linear, but there exist bounded plant and output uncertainties. We first present a design method of a VSS observer based on use of some extensions of a conventional approach that uses an algebraic Lyapunov equation. It is then shown that such a method cannot be successfully applied to the system with any linear part, if we desire to use a unique solution to the algebraic Lyapunov equation. Namely, this method is only applicable to a restricted class of systems. In order to develop a VSS observer applicable to a wider class of systems, we next propose a design method based on use of an algebraic Riccati equation, associated with a linear filtering problem. A relationship between the two design methods is also discussed. Simulation results show that the proposed method is effective for designing a VSS observer for a second-order nonlinear system with band limited output noise, as the output uncertainty.

Original languageEnglish
Pages (from-to)416-424
Number of pages9
JournalJSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing
Volume40
Issue number3
Publication statusPublished - Sep 1997
Externally publishedYes

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Continuous time systems
Riccati equations
Nonlinear systems
Uncertainty

Keywords

  • Algebraic Lyapunov Equation
  • Algebraic Riccati Equation
  • Nonlinear Observer
  • Nonlinear Systems
  • Output Uncertainties
  • Robust Estimation
  • Variable Structure Systems (VSS)
  • VSS Observer

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • Mechanical Engineering
  • Engineering(all)

Cite this

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title = "A Design Method of VSS Observer for Continuous-Time Systems with Output Uncertainties",
abstract = "VSS observers are considered for continuous-time systems, in which the nominal plant model is linear, but there exist bounded plant and output uncertainties. We first present a design method of a VSS observer based on use of some extensions of a conventional approach that uses an algebraic Lyapunov equation. It is then shown that such a method cannot be successfully applied to the system with any linear part, if we desire to use a unique solution to the algebraic Lyapunov equation. Namely, this method is only applicable to a restricted class of systems. In order to develop a VSS observer applicable to a wider class of systems, we next propose a design method based on use of an algebraic Riccati equation, associated with a linear filtering problem. A relationship between the two design methods is also discussed. Simulation results show that the proposed method is effective for designing a VSS observer for a second-order nonlinear system with band limited output noise, as the output uncertainty.",
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AB - VSS observers are considered for continuous-time systems, in which the nominal plant model is linear, but there exist bounded plant and output uncertainties. We first present a design method of a VSS observer based on use of some extensions of a conventional approach that uses an algebraic Lyapunov equation. It is then shown that such a method cannot be successfully applied to the system with any linear part, if we desire to use a unique solution to the algebraic Lyapunov equation. Namely, this method is only applicable to a restricted class of systems. In order to develop a VSS observer applicable to a wider class of systems, we next propose a design method based on use of an algebraic Riccati equation, associated with a linear filtering problem. A relationship between the two design methods is also discussed. Simulation results show that the proposed method is effective for designing a VSS observer for a second-order nonlinear system with band limited output noise, as the output uncertainty.

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