Design and High Accuracy Numerical Implementation of Fractional Order PI Controller for a PMSM Speed System

In this paper, a systematic design and high accuracy implementation of fractional order proportional integral (FOPI) controller is proposed for a permanent magnet synchronous motor (PMSM) speed system, and the numerical implementation performance of the fractional order operator is evaluated with comprehensive investigation using different implementation methods. Three commonly used numerical implementation methods of fractional operators are investigated and compared in this paper. Futhermore, for the impulse response invariant method, the effects of different discretization orders on the system control performance are compared. The simulation results show that the high accuracy numerical implementation method of the designed high-order FOPI controller has improved performance over normal accuracy fractional order operation implementation.

Short note: empirical findings for spatial and temporal discretization orders for the Taylor – Green vortex

Purpose The purpose of this paper is to shed some light into the equivalency of grid size and spatial and temporal orders of accuracy for turbulent flows. Design/methodology/approach This paper compared several finite difference schemes on various meshes and various orders of accuracy for the canonical Taylor–Green vortex testcase. Findings A remarkable empirical result observed is that the accuracy of eighth-order schemes on grids of size 2 h was equivalent to second-order schemes on grids of size h. This was the case when going from 1003 to 2003 as well as from 2003 to 4003. In all these cases, kinetic energy, vorticity and numerical dissipation were compared in detail. Research limitations/implications The results obtained were carried out using finite difference solvers. It remains to be seen if similar behaviors are also observed for other numerical schemes. Originality/value These (surprising) findings should be of interest to the larger community.