Метод расчета дробных интегралов с динамической коррекцией ошибки для микропроцессорных систем управления

Abstract

Целью работы является разработка численного метода расчета дробного интеграла заданного порядка с минимизированной ошибкой при ограниченных объемах памяти данных и быстродействия для микропроцессорных систем управления. Уменьшение статической и динамической погрешности в десятки раз обеспечивается аппроксимацией старших коэффициентов разложения дробного интеграла вряд геометрической прогрессией и динамической компенсацией возникающей на первом этапе ошибки с помощью адаптивного корректирующего модуляThe purpose of the work is to develop a numerical method for calculating a fractional integral with a minimized error with limited data memory. Control systems with a fractional astaticism for many technical objects provide the best dynamic and static indicators. Controller in such systems include one or more units that perform the operation of fractional integration and/or differentiation of the input signal. To implement such control systems based on single-chip microprocessors, it is necessary to solve the problem of calculating a fractional integral by numerical methods, taking into ac-count the limited arrays of data and processor speed. The proposed solution is based on a combination of two methods. First, the calculation of the fractional integral, carried out by approximating the higher expansion coefficients in a series by a geometric progression, allows the use of memory volumes corresponding to the capabilities of the selected processor. Secondly, the dynamic compensation of the error arising at the first stage is car -ried out using an adaptive correction module. Despite the complication of the algorithm, this method of calculation reduces the errortenfold in both transient and steady-state processes, the properties of thesynthesized calculation block correspond exactly to the properties of a fractional integral of a given order at frequencies from 0 to the maximum necessary in the control system. Dynamic error compensation reduces the required memory capacity for storing arrays of coefficients and input history and requires significantly less processor time to calculate the controller signal. As a result, a quantization period of tens of microseconds can be obtained, which makes it possible to implement fractional integral-differentiating controllers based on widely used modern processors and apply fractional-integral number methods to synthesize high-speed automatic control systems, such aselectric drives with asynchronous motors, engines with series excitation.