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Rationalization method of irrational fractional order system

A fractional-order system and rational fraction technology, applied in the field of automation, can solve problems such as large fitting error, no mention of system identification and control, and inability to achieve accurate identification and control of irrational fractional-order systems, achieving high identification accuracy, good effect

Pending Publication Date: 2020-11-17
SHENYANG NORMAL UNIV
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Problems solved by technology

However, due to the complexity of the irrational fractional system, there is no mention of how to realize the identification and control of the system
There are also some technologies that mention the method of realizing integer-order approximation for irrational fractional-order models, but because the approximate system is of integer order, there must be a large fitting error
Therefore, the existing technology cannot realize the precise identification and control of irrational fractional order systems

Method used

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  • Rationalization method of irrational fractional order system
  • Rationalization method of irrational fractional order system
  • Rationalization method of irrational fractional order system

Examples

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Embodiment 1

[0070] The control object in this example is IPMC (Ionic Polymer Metal Composite). IPMC is a relatively new type of electro-actuated polymer. It can be seen from the research and analysis of its driving performance that IPMC belongs to the irrational fractional system.

[0071] The corresponding frequency domain response curve of the system is obtained through experiments, as shown in figure 2 shown.

[0072] The transfer function corresponding to this irrational fractional order system is:

[0073]

[0074] According to the frequency domain response curve analysis, the system has an oscillation link and an integral link, and the initial rational fractional model is set as follows:

[0075]

[0076] Among them, a 1 、a 2 、a 3 、a 4 、a 5 、a 6 、a 7 、a 8 and b 1 are parameters to be determined.

[0077] The fitness function that sets the physical meaning as the distance between two curves is as follows:

[0078]

[0079] Among them, G(jω) is the corresponding ...

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Abstract

The invention discloses a rationalization method for an irrational fractional order system, and the method comprises the steps: recognizing a rationalization fractional order model with the same frequency domain and time domain response curve as an original irrational fractional order system based on an optimization algorithm for the frequency domain response of the irrational fractional order system, and explaining the recognition accuracy through the fitting degree; and accurate identification of the irrational fractional order system is realized. According to the method, parameters of the rational fractional order model can be directly identified, coefficients and orders can be accurately identified, and the accurate rational fractional order model is constructed; the method can realizethe rationalization of the irrational fractional order system, has the advantages of high identification precision, good effect and the like, and is convenient for realizing the analysis and controlof the original irrational fractional order system. Moreover, according to the method, a mathematical model of the irrational fractional order system can be directly established on the basis of knownsystem response data, and a foundation is laid for researchers to research the irrational fractional order system in the future.

Description

technical field [0001] The disclosure of the invention relates to the technical field of automation, in particular to a rationalization method for an irrational fractional order system, which is used to realize favorable control of the irrational fractional order system. Background technique [0002] Strictly speaking, the mathematical models of natural phenomena should be described by fractional differential equations. In fractional order systems, there is a common and complex system described by irrational fractional order models, which is called irrational fractional order systems. Diffusion phenomena as well as heat flow are well known systems that can be described by irrational transfer functions. [0003] Some methods based on system frequency domain identification have been proposed in the prior art, such as Levy method and its improved algorithm, optimization algorithm, etc. for parameter identification of rational fractional order systems, which can realize accurat...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/25G06N3/00
CPCG06F30/25G06N3/006
Inventor 陈岚峰薛定宇
Owner SHENYANG NORMAL UNIV
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