Optimization for Software Implementation of Fractional Calculus Numerical Methods in an Embedded System.

In this article, some practical software optimization methods for implementations of fractional order backward difference, sum, and differintegral operator based on Grünwald-Letnikov definition are presented. These numerical algorithms are of great interest in the context of the evaluation of fractional-order differential equations in embedded systems, due to their more convenient form compared to Caputo and Riemann-Liouville definitions or Laplace transforms, based on the discrete convolution operation. A well-known difficulty relates to the non-locality of the operator, implying continually increasing numbers of processed samples, which may reach the limits of available memory or lead to exceeding the desired computation time.

Optimal Digital Implementation of Fractional-Order Models in a Microcontroller.

The growing number of operations in implementations of the non-local fractional differentiation operator is cumbersome for real applications with strict performance and memory storage requirements. This demands use of one of the available approximation methods. In this paper, the analysis of the classic integer- (IO) and fractional-order (FO) models of the brushless DC (BLDC) micromotor mounted on a steel rotating arms, and next, the discretization and efficient implementation of the models in a microcontroller (MCU) is performed.