CUTTING POWER STABILIZATION SYSTEM WITH A FRACTAL INTEGRAL-DIFFERENTIATION REGULATOR
Journal Title: Електромеханічні і енергозберігаючі системи - Year 2018, Vol 2, Issue 42
Abstract
Purpose. To analyze the possibilities and ways of implementing fractional integral-differential regulators for optimization the dynamic and static parameters of closed loop stabilizing the cutting power systems of machine tools. Methodology. The dependence of the cutting power of machine tool on the cutting depth and feed rate is described by empirical expressions which include power functions of fractional order with coefficients determined by the material of the part and tool. Then, taking into account the compliance of the mechanical system "machine-detail", the mathematical model of the object can be reduced to a fractional-differential equation. To obtain optimized dynamic and static parameters, the use of fractional integral-differentiating regulators for controlling the electric drive in an automated system is considered. Results. Synthesized regulators provide a fractional order of closed-loop astaticism in the range from 1.3 to 1.7. This allows to obtain improved dynamic and static indicators, less sensitivity of the system to changing the parameters of the control object. Originality. To implement such regulators on the basis of modern high-speed processors, a new method for the rapid calculation of the fractional integral is proposed, based on the combination of the modified Riemann-Liouville form for calculating only the first 64-256 terms of the infinite series and replacing the leading terms in the expansion by a geometric progression. The resulting logarithmic amplitude-frequency characteristics confirm the expected bandwidth of the control system and the specified fractional order of astaticism. Practical value. By a new method processors such as Intel Quark, Altera Cyclone V, provide a quantization period of tens of microseconds, which meets the requirements of control systems for metal-cutting machines. It allow developing software for automatic correction of the regulators parameters and contributes to the improvement of the quality and productivity of the machine.
Authors and Affiliations
Victor Busher, Ali Aldairi
Keywords
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- EP ID EP659778
- DOI 10.30929/2072-2052.2018.2.42.30-36
- Views 217
- Downloads 0
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