Describing function-based identification of nonlinear transfer functions for nonlinear systems from experimental/simulation data

Nassirharand, Amir; Teh, Sze-Hong

doi:10.1504/ijmic.2016.075270

Cited by 3 publications

(4 citation statements)

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“…And the works to be mentioned after the publications of [6,16,17], are those issued by [3][4][5], in which the mathematical models of nonlinear dynamic systems are given in the form of transfer functions, algebraically structured in skew polynomials, as well as the works of [13][14][15], in which mathematical models of nonlinear dynamic systems set by transfer functions with coefficients which depend on the frequency and amplitude of the input periodic signals, shall be really reduced to the class of cybernetic models since their identification is carried out by iterative numerical methods in powerful software environment MATLAB.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

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The Synthesis of Mathematical Models of Nonlinear Dynamic Systems Using Volterra Integral Equation

Мокін

Mokin

Мокін

et al. 2022

IAPGOS

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The problem of creating mathematical models of nonlinear dynamical systems does not have an unambiguous solution and requires the creation of a separate synthesis method for each such object. To develop a method for synthesizing mathematical models of an extensive class of nonlinear dynamical systems with polynomial nonlinearities. The work uses a method based on the solution of the Volterra integral equation in the ideology set forth in Van Trees H.L., according to which the structure of a nonlinear dynamical object present47s a series connection of the linear part, characterizing the inertial properties of the system, and the nonlinear element, given by static characteristic. The difference of the suggested version of the method from the classical one, proposed in the works of Van Trees H.L., is an expansion of their input and output signals into Fourier series and a representation of the inertial part of these systems by their Bode plots, connected into one structure with input and output signals and non-linearity by Volterra integral equation. The algorithm of the proposed method is disclosed by the example of solving the problem of identifying a nonlinear dynamical system which impulse response of the inertial part satisfies the separability requirement, the order of the polynomial nonlinearity is three, and the model of the input signal has the form of a sinusoid "raised" over the time axis on a priori given constant level. A computational experiment was carried out on the example of nonlinear dynamical systems with the third order of the nonlinear characteristic and the first and second orders of the model of the inertial part of these systems with the specified algorithms of their parametric identification. The suggested method allows to synthesis the mathematical model of a nonlinear dynamical system with the polynomial static characteristic to the case when the input signal has an arbitrary number of harmonics, and the model of the inertial part and the nonlinear polynomial function have an arbitrary order.

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Section: Formulation Of the Problemmentioning

confidence: 99%

“…g t e dt g t e dt (15) In view of the above, the equation ( 14) may be rewritten as , , , ( ), (0 , , , , , ( ), (0), ( )) , , , , , ( ), (0), ( )) , , , , , ( ),…”

Section: Theoretical Researchmentioning

confidence: 99%

The Synthesis of Mathematical Models of Nonlinear Dynamic Systems Using Volterra Integral Equation

Мокін

Mokin

Мокін

et al. 2022

IAPGOS

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“…Construct the stacked output vector Y (p, t) and the stacked information matrix Γ(p, t) using (18)- (19). 4. Compute the innovation vector E(p, t) using (16) and compute r(t) using (17).…”

Section: The M-mi-gsg Algorithmmentioning

confidence: 99%

“…The mathematical models must be obtained first for control problems from input-output data. Many practical processes are multivariable and thus multivariate systems are causing people's attention [4,5,6]. There are many identification methods for identifying multivariate systems.…”

Section: Introductionmentioning

confidence: 99%

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

Ding

Zhu

2018

International Journal of Systems Science

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This paper researches the parameter identification methods of multivariate pseudo-linear moving average systems. A multivariate generalized stochastic gradient (M-GSG) algorithm is presented as a comparison firstly. In order to improve the parameter estimation accuracy, a multivariate multiinnovation generalized stochastic gradient (M-MI-GSG) algorithm and a filtering based multivariate generalized stochastic gradient (F-M-GSG) algorithm are presented by means of the multi-innovation identification theory and the data filtering technique. The simulation results confirm that the proposed algorithms are more effective than the M-GSG algorithm.

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New gradient based identification methods for multivariate pseudo-linear systems using the multi-innovation and the data filtering

Ding

2017

Journal of the Franklin Institute

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Describing function-based identification of nonlinear transfer functions for nonlinear systems from experimental/simulation data

Cited by 3 publications

References 0 publications

The Synthesis of Mathematical Models of Nonlinear Dynamic Systems Using Volterra Integral Equation

The Synthesis of Mathematical Models of Nonlinear Dynamic Systems Using Volterra Integral Equation

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

New gradient based identification methods for multivariate pseudo-linear systems using the multi-innovation and the data filtering

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