The Identification of Nonlinear Systems UsingCt-KtPlane Coordinates

Ming-Fei Chen,Dyi-Cheng Chen,Chung-Heng Yang,Shih-Feng Tseng

doi:10.1155/2014/497872

Abstract

In order to instantaneously distinguish theCt(coefficient of viscous damping) andKt(coefficient of stiffness), which are both functions of time in an M.C.K. nonlinear system, a new identification method is proposed in this paper. The graphs of theCt-Ktare analyzed and the dynamic behavior of M.C.K. systems in aCt-Ktcoordinate plane is discussed. This method calculates two adjacent sampling data, the displacement, velocity, and acceleration (which are obtained from the responses of a pulse response experiment) and then distinguishesCtandKtof an instantaneous system. Finally, this method is used to identify the aerostatic bearing dynamic parameters,CandK.

Highlights

In order to control an M.C.K. system, the stiffness and damping must be known
(C(t → t+Δt), K(t → t+Δt)) is solved as the simultaneous solution of (10), so the time-domain displacement response obtained by experiment can be used to solve C(t) and K(t) for an M.C.K. system
This virtual curve must represent the trajectories of a nonlinear system, in order to verify the accuracy of the proposed method

Summary

Introduction

In order to control an M.C.K. system, the stiffness and damping must be known. in an actual M.C.K. system, the stiffness and damping are essentially nonlinear. Huang et al [11] modified the logarithmic-decrement method to avoid disturbance from measured noise, but the second peak is still required to analyze the damping. For real-time control systems, the current method requires improvement. If the system is exactly described by (1), the set of straight lines at successive times, t, must all pass through a single point in the plane, which determines the values of C and K. If the system is nonlinear or departs from the assumptions of (1) in some other way, such as having nonviscous damping, the successive lines do not all pass through a single point. If the variation is reasonably smooth, they still define an envelope curve This curve in the C-K plane gives the time-dependent values of the equivalent linearized C and K. This paper presents an algorithm to map this envelope and illustrates the method with numerical and experimental examples

Theoretical Background and Methodology

Methodology

Inference

Application

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Conclusions