Red blood cell reproduction model-based fractional-order PD controller design method
A technology of red blood cells and design methods, applied to controllers with specific characteristics, electric controllers, etc., can solve problems such as lack of practical application background, fractional calculus has no clear physical meaning, and fractional calculus develops slowly.
Inactive Publication Date: 2018-08-14
NANJING UNIV OF POSTS & TELECOMM
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The history of fractional calculus can be traced back to 1695. Since fractional calculus had no clear physical meaning and lack of practical application background at that time, the development of fractional calculus has been relatively slow.
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[0028] The present invention will be further described below in conjunction with the accompanying drawings.
[0029] The system principle diagram of the fractional-order PD controller design method based on the red blood cell reproduction model proposed by the present invention is as follows figure 1 shown. The design method of fractional order PD controller based on red blood cell reproduction model includes the following steps:
[0030] Step 1: Perform fractional conversion processing on the original model.
[0031] The integer-order red blood cell reproduction model is as follows:
[0032]
[0033] Among them, N(t) represents the number of red blood cells at time t, δ represents the death probability of red blood cells, γ and ρ represent the production rates of red blood cells per unit time, both of which are positive numbers, and τ represents the amount required to produce a red blood cell time.
[0034] Caputo fractional calculus is as follows:
[0035]
[0036...
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The invention discloses a red blood cell reproduction model-based fractional-order PD controller design method. The method includes the following steps that: an original integer-order red blood cell reproduction model is transformed into a fractional-order red blood cell reproduction model through using a fractional-order theory, and the stability feature and balance point information of the fractional-order red blood cell reproduction model are obtained through analysis; a fractional-order PD controller is designed according to the fractional-order red blood cell reproduction model; and system delay is selected as a bifurcation parameter, and stability analysis and bifurcation analysis are performed on the feature equation of a linearized controlled system model, so that appropriate controller parameters are selected, and the stability domain and bifurcation of the system can be controlled. According to the red blood cell reproduction model-based fractional order PD controller designmethod of the invention, on the basis of a time lag perspective, the influence of time lag on the dynamic behavior of the fractional-order red blood cell reproduction model is fully considered, the activity law and regulation mechanism of red blood cells in the model can be better described; the fractional-order PD controller can better improve the feedback performance of the control system and make the stable area of the system more maneuverable.
Description
technical field [0001] The invention belongs to the technical field of controllers, and relates to a design method of a fractional-order PD controller based on a red blood cell reproduction model. Background technique [0002] Wazewska-Czyzewska and Lasota proposed a red blood cell reproduction model as early as 1976. Over the years, the research enthusiasm for this model has continued unabated, and the research results on the stability and bifurcation of the integer order tend to be saturated. The study of fractional order has become a hot spot in recent years. The history of fractional calculus can be traced back to 1695. Since fractional calculus had no clear physical meaning and lack of practical application background at that time, the development of fractional calculus has been relatively slow. It was not until 1983, after Mandelbort proposed the fractal theory, that the application research of fractional calculus attracted widespread attention from scholars at home a...
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IPC IPC(8): G05B11/42
CPCG05B11/42
Inventor 孙青山肖敏
Owner NANJING UNIV OF POSTS & TELECOMM