Nonlinear PI current control of reluctance synchronous machines

Abstract

This paper discusses nonlinear proportional-integral (PI) current control with anti-windup of reluctance synchronous machines (RSMs) for which the flux linkage maps are known. The nonlinear controller design is based on the tuning rule "Magnitude Optimum criterion" [1]. Due to the nonlinear flux linkage, the current dynamics of RSMs are highly nonlinear and, so, the parameters of the PI controllers and the disturbance compensation feedforward control must be adjusted online (e.g., for each sampling instant). The theoretical results are illustrated and validated by simulation and measurement results.

On the optimal feedforward torque control problem of anisotropic synchronous machines: Quadrics, quartics and analytical solutions

“…[12], [17], [24], [27], [35]- [37] for PMSMs or [28], [38] for RSMs). This simplification will not be true in the most general case when the flux linkage is a nonlinear function of the currents [11], [33]. Nevertheless, in the humble opinion of the authors, the presented results are of quite some relevance and have not been discussed in this general framework before: The results of this paper can be considered as a generalization of the results for IPMSM in [16] by including resistance R s and mutual inductance L m into the generic optimization formulation.…”

“…The model of an anisotropic (a) permanent-magnet synchronous machine (PMSM), (b) permanent-magnet assisted or excited reluctance synchronous machine (PMA-RSM or PME-RSM, resp. [6], [23]) or (c) reluctance synchronous machine (RSM [6], [32], [33]) in the (d, q)-reference frame 1 is given by…”

“…(ψ pm , 0) , for PMSM and PME-RSM [6] (0, −ψ pm ) , for PMA-RSM [6], [23] (0, 0) , for RSM [6], [32], [33].…”

“…do not depend on the electrical angular velocity ω k , respectively. As before for MTPC and MTPV, the derivation of the implicit form (33) with its parametrization ( 34) is based on Appendix B.…”

“…I; however, for RSMs, all quadrics simplify due to the missing permanent magnet, i.e. (12), voltage ellipse (17), flux norm (20), MTPC hyperbola (23), MTPV hyperbola (29) and MTPF hyperbola (33) become zero (see also (9), ( 15), ( 21), ( 24), ( 30) and (34)), respectively. Therefore, instead of applying case (i) of Appendix D, case (iii) of Appendix D must be considered for the computation of the intersection points of the respective quadrics (see also Tab.…”