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Equilibrium space and a pseudo linearization of nonlinear systems.

Ryotaro Sakata1,2, Tatsuya Oshima1, Shin Kawai1

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This study introduces equilibrium space to model systems with infinite equilibrium points. A novel pseudo linearization method accurately represents nonlinear systems and their stability, outperforming existing techniques for discrete-time modeling.

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • System Modeling

Background:

  • Traditional methods struggle with systems possessing infinite equilibrium points.
  • Lyapunov's linearization method is a cornerstone for stability analysis.

Purpose of the Study:

  • To extend the concept of equilibrium points to equilibrium space.
  • To develop a pseudo linearization technique for nonlinear systems.
  • To accurately derive discrete-time models from nonlinear continuous-time systems.

Main Methods:

  • Extension of equilibrium point concept to equilibrium space.
  • Application of Lyapunov's linearization method in the context of equilibrium space.
  • Development and application of a novel pseudo linearization method.
  • Derivation of a discrete-time model for a control moment gyroscope system.

Main Results:

  • The proposed pseudo linearization accurately represents the equilibrium state and stability of the original nonlinear system.
  • The derived discrete-time model shows improved accuracy compared to forward-difference and conventional pseudo linearization methods.
  • Effective modeling is achieved even with large sampling intervals.

Conclusions:

  • The equilibrium space concept and pseudo linearization offer a robust approach for analyzing and modeling complex nonlinear systems.
  • This method provides a more accurate discrete-time representation, crucial for control system design.
  • The technique demonstrates significant advantages over existing methods, particularly for systems with extensive equilibrium points.