# Review of Fast Computation Methods for Finite-State Predictive Control of Multi-Phase Drives
## 4 Critical Analysis and Discussion
### Trade-Offs in Weighting Factors Tuning  
Weighting factors allow putting more emphasis on different objectives. One criticism often placed on WF use is that their tuning is difficult [98]. This has prompted both the development of WF-free methods [99] and proposals for WF selection [100].  
The first systematic approach to WF tuning in MPS was proposed by [96], introducing a Pareto-front approach for a six-phase IM. This approach was later expanded in [101] using a multi-objective genetic algorithm for predictive torque control of a six-phase IM, though it overlooked \(x\)-\(y\) plane issues. Other techniques, like NSGA-II with TOPSIS, are applied to WF tuning for conventional IM in [102], though they are limited to load conditions. A multi-objective particle swarm optimization is used in [97] to address both \(x\)-\(y\) currents and switching frequency. Some methods also incorporate artificial intelligence, such as the neural network approach in [103] for two WFs in permanent magnet drives, relying on simulation and limited experimental cases.  
Distinct from these, ref. [22] introduces an adaptive cost function for VSD using a six-phase IM, where performance metrics are explicitly linked to WFs. This adaptive approach characterizes the Pareto front with a single equation, enabling straightforward rule-based adaptation without the computational overhead of genetic or swarm algorithms.  
Recent online WF tuning methods for various VSDs are based on the idea of gain-scheduling, treating the WFs as the gains [104]. More complex algorithms have also been proposed. For instance, ref. [105] applies reinforcement learning to tune WFs in PTC for permanent magnet motors. Although innovative, reinforcement learning requires extensive data.  
In [106], the first variable WF method for drives demonstrates the non-linear relationship between performance indicators and speed. The proposal has some limitations: it does not calculate the actual WFs, it uses TOPSIS at every sampling period rather than adapting only when conditions change, it lacks a clear connection between WFs and performance metrics, an it requires tuning of hyperparameters, preventing full automation. Note that the trade-offs considered in most studies concern just electrical variables [107]. Alternatively, ref. [108] optimizes a single WF for each sampling period in PTC of a three-phase IM yet fails to link performance metrics directly to WFs.  
Advances in hardware have significantly influenced this field, particularly with the introduction of new power converter technologies such as silicon carbide (SiC) and gallium nitride (GaN). These converters enable higher switching frequencies, reducing the emphasis on switching penalty terms in cost functions. However, methods employing weighting factors (WFs) can trade off switching frequency to optimize performance [109; 110], whereas in other approaches, the switching frequency remains relatively fixed [74]. In addition to the above, the field still has to face the challenges of concurrent tuning of both loops in the IFOC scheme [111].  
A final remark can be made regarding computation times for each algorithm. The reported values are different from one publication to another. This is to be expected since many factors affect these figures. The capabilities of the hardware, the expertise in coding, and the number of phases are the main ones. Nevertheless there is a clear distinction between recent fast methods and previous ones. Both in the single-vector and multi-vector cases, the computational load reduction of region-based methods is larger that that of previous methods. This is highlighted in Table 2, where the reported computation times are presented.