Synthesis and technical realization of control systems with discrete fractional integral-differentiating controllers

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.139892

Keywords:

astatic system, fractional integration, fractional differentiation, algorithm of fast fractional integral calculation

Abstract

Control systems with a fractional order which provide better dynamic and static indicators for many technical objects in comparison with systems with integer order of astaticism were studied. Based on the analysis of frequency characteristics, transient processes and a modified criterion for quality assessment, optimal relationships between parameters of the desired transfer function were obtained. Normalized transition functions of closed systems with the order of astaticism from 1 to 2 were presented with overregulation less than 2...5 % on the basis of which parameters can be chosen and the controller structure determined.

The process of stabilizing cutting power was analyzed for a milling machine as an example of the systems with nonlinear parametric and structural dependences in control and perturbation channels. It was shown that fractional integral-differentiating controllers make it possible to provide the order of astaticism from 1.3 to 1.7 and permissible level of overregulation in a wide range of external perturbing influences.

A method for approximate calculation of fractional integrals based on the approximation of the highest coefficients of expansion in a series of geometric progressions was developed. It provides reduction of the memory capacity required to store the coefficient arrays and the history of the input signal and requires significantly less CPU time to calculate the controller signal. For example, for controllers based on the Intel® Quark ™ SoC X1000 or FPGA Altera Cyclone V, the quantization period is 6...15 μs and several milliseconds for Atmega328. This makes it possible to implement fractional integral-differentiating controllers based on widely used modern processors and apply fractional-integral calculus methods for synthesis of high-speed automatic control systems. The proposed methods can be used in the control of the objects both with fractional and integer orders of differential equations.

Author Biographies

Victor Busher, Odessa National Polytechnic University Shevchenka ave., 1, Odessa, Ukraine, 65044

Doctor of Technical Sciences, Professor

Department of electromechanical systems with computer control

Ali Aldairi, Odessa National Polytechnic University Shevchenka ave., 1, Odessa, Ukraine, 65044

Postgraduate student

Department of electromechanical systems with computer control

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Published

2018-08-31

How to Cite

Busher, V., & Aldairi, A. (2018). Synthesis and technical realization of control systems with discrete fractional integral-differentiating controllers. Eastern-European Journal of Enterprise Technologies, 4(2 (94), 63–71. https://doi.org/10.15587/1729-4061.2018.139892

Issue

Vol. 4 No. 2 (94) (2018): Information technology. Industry control systems

Section

Industry control systems

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Copyright (c) 2018 Victor Busher, Ali Aldairi

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