A new method for evaluating the describing function of hysteresis-type nonlinearities

Ku, Y.H.; Chen, C.F.

doi:10.1016/0016-0032(62)91097-9

Cited by 8 publications

(4 citation statements)

References 2 publications

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“…Using the Gauss elimination method, the obtained simplified equation is 19. The produced graphical phase portrait [10] plot is given below in Figure 11.…”

Section: Resultsmentioning

confidence: 99%

“…Some terms are not dependent on the joint acceleration and velocity. So, the torque can be expressed as shown in Equation (19).…”

Section: = Cos ∅ Sin ∅mentioning

confidence: 99%

“…The method of linearization, Lyapunov stability and Popov criteria for stability analysis of nonlinear systems have been mentioned [18]. Information on the describing function [19] related to nonlinear system behavioral analysis using a simulation approach has been discussed as the most interesting field to involve in the lower limb system behavioral analysis in the research work of this paper. Formalization of the limit cycle prediction depending on the nonlinear element by describing function is presented with great importance in the field of the system's nature prediction [20].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb

et al. 2020

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System performance and efficiency depends on the stability criteria. The lower limb prosthetic model design requires some prerequisites such as hardware design functionality and compatibility of the building block materials. Effective implementation of mathematical model simulation symmetry towards the achievement of hardware design is the focus of the present work. Different postures of lower limb have been considered in this paper to be analyzed for artificial system design of lower limb movement. The generated polynomial equations of the sitting and standing positions of the normal limb are represented with overall system transfer function. The behavioral analysis of the lower limb model shows the nonlinear nature. The Euler-Lagrange method is utilized to describe the nonlinearity in the field of forward dynamics of the artificial system. The stability factor through phase portrait analysis is checked with respect to nonlinear system characteristics of the lower limb. The asymptotic stability has been achieved utilizing the most applicable Lyapunov method for nonlinear systems. The stability checking of the proposed artificial lower extremity is the newer approach needed to take decisions on output implementation in the system design.

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“…Using the Gauss elimination method, the obtained simplified equation is 19. The produced graphical phase portrait [10] plot is given below in Figure 11.…”

Section: Resultsmentioning

confidence: 99%

“…Some terms are not dependent on the joint acceleration and velocity. So, the torque can be expressed as shown in Equation (19).…”

Section: = Cos ∅ Sin ∅mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb

et al. 2020

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“…Kul and Chen [8] proposed a method which can be used for obtaining the describing functions of hysteretic type nonlinearities. Their method is based on circular geometry shapes.…”

Section: Introductionmentioning

confidence: 99%

Identification of Weakly Nonlinear Systems Using Describing Function Inversion

2010

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In this paper describing functions inversion is used and the restoring force of a nonlinear element in a MDOF system is characterized. The describing functions can be obtained using linearized frequency response functions (FRFs). The response of the system to harmonic excitation forces at distinct frequencies close to the resonant frequency results in linearized FRFs. The nonlinear system can be approximated at each excitation frequency by an equivalent linear system. This approximation leads to calculation of the first-order describing functions. By having the experimental describing functions calculated and the system's responses corresponding to the nonlinear element (measured or interpolated), nonlinear parameter identification can be performed. Two numerical and experimental case studies are provided to show the applicability of this method.

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Identification of Nonlinear Systems from Steady-state Frequency Response

Lin

Lee

1983

Journal of the Franklin Institute

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A new method for evaluating the describing function of hysteresis-type nonlinearities

Cited by 8 publications

References 2 publications

Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb

Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb

Identification of Weakly Nonlinear Systems Using Describing Function Inversion

Identification of Nonlinear Systems from Steady-state Frequency Response

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