Search

We show how to combine in a natural way (i.e., without any test nor switch) the conservative and non-conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different classes of schemes: the residual distribution one (Abgrall in Commun Appl Math Comput 2(3): 341-368, 2020), and the active flux formulations (Eyman and Roe in 49th AIAA Aerospace Science Meeting, 2011; Eyman in active flux. PhD thesis, University of Michigan, 2013; Helzel et al. in J Sci Comput 80(3): 35-61, 2019; Barsukow in J Sci Comput 86(1): paper No. 3, 34, 2021; Roe in J Sci Comput 73: 1094-1114, 2017). The solution is globally continuous, and as in the active flux method, described by a combination of point values and average values. Unlike the "classical" active flux methods, the meaning of the point-wise and cell average degrees of freedom is different, and hence follow different forms of PDEs; it is a conservative version of the cell average, and a possibly non-conservative one for the points. This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem. We also develop a method to perform non-linear stability. We illustrate the behaviour on several benchmarks, some quite challenging., Competing Interests: There is no conflict of interest with anything., (© The Author(s) 2022.)

This paper deals with a current sensor fault reconstruction algorithm for the torque closed-loop drive system of an interior PMSM. First, sensor faults are equated to actuator ones by a new introduced state variable. Then, in αβ coordinates, based on the motor model with active flux linkage, a current observer is constructed with a specific sliding mode equivalent control methodology to eliminate the effects of unknown disturbances, and the phase current sensor faults are reconstructed by means of an adaptive method. Finally, an αβ axis current fault processing module is designed based on the reconstructed value. The feasibility and effectiveness of the proposed method are verified by simulation and experimental tests on the RT-LAB platform.