# Review of Fast Computation Methods for Finite-State Predictive Control of Multi-Phase Drives
## 3 Fast Computation Strategies
### Simplification of the CF and Search Method  
Another strategy to accelerate the computation of the control signal in FSMPC for MPS focuses on simplifying the optimization problem, achieved through two primary approaches. The first approach simplifies the cost function by reducing the number of terms, including methods that eliminate the need for a weighting factor (WF). The second streamlines the search process by limiting the exploration of the full set of possible control actions, effectively pruning the search tree. It is crucial to highlight that these strategies do not reduce the number of ACSs; instead, they optimize the selection process for efficiency. A method for six-phase PMSM is presented in [26], employing two groups of Virtual Vectors with varying magnitudes. This approach improves torque regulation and eliminates the need for weighting factor tuning in the cost function. Additionally, a one-step lookup table is introduced to exclude unnecessary Voltage Vectors, significantly reducing computation time. Other authors propose a Model-Free Predictive Control (MF-PC) algorithm that eliminates complex operations such as multiplications and parameter estimation, providing enhanced accuracy and robustness to parameter variations while maintaining low computational complexity. Ref. [27] demonstrates that the method can effectively manage load disturbances and parameter mismatches, achieving reduced harmonic distortion andtorque ripple. It highlights the advantages of a parameter-independent control strategy that avoids the computational burden of traditional approaches while maintaining high precision. Ref. [28] introduces the ABC frame for multi-phase systems, which predicts control actions independently for each phase. By avoiding the need for frame transformations and weighting factors, this approach significantly reduces computational burdens. Simulations and experiments demonstrate its effectiveness, achieving comparable performance to traditional methods while improving efficiency, particularly in systems with multiple phases. Regarding WF elimination, it naturally occurs in Virtual Voltage Vector (VVV) approaches, as \(x\)-\(y\) currents do not need to be included in the cost function, and switching becomes more predictable. Other works explicitly perform WF elimination, such as in [29; 30; 31]. Additionally, some approaches focus on the design of parameter-free cost functions, as seen in [32; 33]. Restrained Search Predictive Control (RSPC) is a technique presented in [34] that reduces computational complexity by limiting the number of inverter switching states that can be evaluated in each sampling cycle. Instead of exhaustively analyzing all possible switching combinations, RSPC imposes constraints that select only a subset of switching vectors, thereby reducing the number of phase changes in the inverter. This approach lowers switching losses and improves system efficiency. RSPC focuses on two main restrictions: selecting only those vectors that involve one or no commutations per cycle and preventing any inverter phase from switching in two consecutive cycles. These constraints facilitate real-time implementation, enhance drive efficiency, and reduce the maximum switching frequency, which is especially advantageous in high-power applications and complex multi-phase systems. Improved techniques of RSPC is presented in [35] for multi-phase drives, where the commutations of VSI are minimized, favoring the drive efficiency. On the other hand, ref. [36] presents a computationally efficient multi-step direct predictive torque control (M-DPTC) for surface-mounted permanent magnet synchronous motors (SPMSMs). The method uses a simplified predictive model and a novel optimization approach to reduce computational complexity, achieving logarithmic time growth instead of exponential. By utilizing lookup tables and addition operations, the algorithm avoids exhaustive computations, enabling real-time implementation within short sample periods.