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Fractional order nonlinear time delay system parameter estimation method based on Legendre wavelet

A first-order nonlinear and time-delay system technology, applied in the field of system modeling and parameter estimation, can solve problems such as the inability to estimate nonlinear system parameters, and achieve the effects of easy engineering application, avoiding initial state dependence, and small amount of calculation

Pending Publication Date: 2021-10-08
XIAN TECH UNIV
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Problems solved by technology

[0005] The invention provides a method for estimating the parameters of the fractional nonlinear time-delay system based on the Legendre wavelet to solve the problem that the existing integral operation matrix method cannot estimate the parameters of the nonlinear system

Method used

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  • Fractional order nonlinear time delay system parameter estimation method based on Legendre wavelet
  • Fractional order nonlinear time delay system parameter estimation method based on Legendre wavelet
  • Fractional order nonlinear time delay system parameter estimation method based on Legendre wavelet

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Embodiment

[0038] Fractional order nonlinear time-delay systems can be described as

[0039]

[0040] Among them, the model parameters q=1, r=0.5, w=0.5, α 2 = 2, α 1 =1.5, τ=0.7, the system input u(t) is a step signal, and y(t) is the system output.

[0041] Step 1. Establish Legendre wavelet integral operation matrix and time delay operation matrix

[0042] Step 101, establishing a Legendre wavelet integral operation matrix;

[0043] The definition of the Legendre wavelet on the [0, 1] interval is:

[0044]

[0045] where k=1, 2, ..., 9, m = 1 n = 1, 2, 3, ..., 2 k-1 , P m is the Legendre polynomial.

[0046] Define N=512.Legendre wavelet integral operation matrix as

[0047]

[0048] in, is the integral operation matrix of the block impulse function, which is defined as

[0049]

[0050] Among them, T f is the simulation termination time, Γ(α) is the gamma function.

[0051] matrix vector f 1 = 1, f p =p a+1 -2(p-1) a+1 +(p-2) a+1 , p=2, 3...N.

[0052]...

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Abstract

The invention relates to a fractional-order nonlinear time-delay system parameter estimation method based on Legendre wavelets, and the method comprises the following steps: firstly, building an integral operation matrix and a time-delay operation matrix of the Legendre wavelets; and secondly, converting the fractional order nonlinear time-delay differential equation into a Legendre wavelet integral equation, estimating model parameters by using a least square method, and finally identifying a fractional order and a time-delay coefficient through a loop nesting method. When the system is polluted by noise, a wavelet decomposition and reconstruction algorithm can be used for preprocessing the signal, noise in the signal is separated, and the parameter estimation precision is improved. According to the method, a wavelet integral operation matrix method is expanded to a fractional order nonlinear time delay system, and the problems of initial state dependence and identification result randomness existing in algebraic equation solving of a traditional integral operation method are solved.

Description

technical field [0001] The invention belongs to the technical field of system modeling and parameter estimation, and mainly relates to a fractional nonlinear time-delay system parameter estimation method based on Legendre wavelet. Background technique [0002] Fractional calculus is an extension of integer order calculus to non-integer orders. Compared with integer-order calculus, fractional-order calculus has global correlation and memory, and it is more accurate to use fractional-order calculus to establish complex system models with historical dependence or distributed parameters. At present, fractional order models have been widely used in many fields such as electromagnetism, physics, biomedicine, and elastic mechanics. [0003] In actual engineering, many physical systems have time-delay characteristics, such as memristors, heat exchange processes, biological cell culture, and polymer material synthesis. With the deepening of researchers' research on fractional time-...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/20G06F17/14G06F17/11
CPCG06F30/20G06F17/148G06F17/11
Inventor 王春阳王子硕梁书宁王增
Owner XIAN TECH UNIV