Review of cost-function design in finite-control-set MPC for PMSM drives

Cost-function design is key to finite-control-set model predictive control (FCS-MPC) of permanent magnet synchronous machine (PMSM) drives. This review classifies the cost-function design and selection from four aspects, i.e., norm choice, mathematical representation, objective combinations, and normalization strategy. It is shown that square-based reference-tracking forms are predominant, current-oriented combinations are most frequently reported, and normalization improves cross-term balance and portability of weighting factor tuning. To illustrate the method-dependent trade-offs, five normalized square-based reference-tracking cost functions, i.e., current, torque-current, flux-current, torque-flux-current, and torque-flux, are implemented and tested on the studied surface-mounted PMSM (SPMSM) under one-step single-vector FCS-MPC. The experimental study includes a representative comparison at 200 rpm and 2 N ⋅ m, a load-torque range, from 0.5 to 2 N ⋅ m at 200 rpm, and a speed range from 100 to 400 rpm at 2 N ⋅ m. The results show that the current design achieves the best phase-current quality with the lowest computational and switching burdens, whereas the torque-flux-current design most effectively suppresses torque and q-axis current ripples at a higher cost of computational burden and average switching frequency. The torque-current design offers a balanced torque regulation and current quality. The flux-current design yields the smallest flux-linkage ripple, and the torque-flux design reduces complexity but degrades current quality. These observations highlight practical trade-offs among torque ripple suppression, flux regulation, current quality, computational burden, and average switching frequency.