## 1 Introduction
In the Papers [25; 26], a hypothesis verified by numerical simulations is introduced, namely that more efficient control systems are also characterised by a higher value of the FD [27; 28] of the controlled signal. Taking into account these elements, the article starts from the PMSM control based on the DTC strategy, and shows the improvement in the control system performance in the case of constant reference flux by using PI-type fractional controllers, the optimisation of the controller parameters realized using a computational intelligence algorithm [29], particularly the Equilibrium Optimizer Algorithm (EOA)-type algorithm [30; 31], the synthesis of a speed, torque and flux observer, and, in terms of the control system performance, the comparison between these control systems which uses both the usual performance indicators and the FD of the PMSM speed signal. In the case of a variable reference flux, the speed controller provides the reference for the torque controller, while a Sliding Mode Control (SMC) controller [32; 33] is used to provide the flux reference in both the integer-order and fractional-order (FO) SMC variants [34]. The use of FO control algorithms, starting with PI and continuing with SMC, are presented in [35; 36; 37; 38; 39; 40] and are applied to the control of generators, the control of DC-AC converters in microgrids and induction motors. Also, in [10], fractional calculus is used to improve the controller and realize an observer using a reference model. The main drawback is the high sensitivity to disturbances and model description. In these articles, numerical simulations are presented, but without real-time results. In [41], both numerical simulations and real-time implementation for the application of fractional-order control algorithms to PMSM control, using FOC control strategy, are presented. It can be stated that the key elements discussed in this article are the DTC control strategy, and a PMSM observer for flux, load torque and rotor speed, together with the implementation of fractional calculus, to obtain an SMC or PI fractional-order controller. Roughly speaking, by using fractional calculus, more sophisticated PI and SMC type algorithms can be obtained, which will provide better specific performance of the control system for PMSM (response time, overshoot, settling error, torque, etc.). This is based on the very definition of the fractional integro-differential equations used to obtain the above control laws, so that in addition to the tuning parameters of these control laws in the integer (non-fractional) case, additional parameters appear on the FOs of the elements of the tuning laws. It is clear that the presence of additional design parameters will lead to better results; in particular, finding the optimal values of these parameters is carried out using a computational intelligence algorithm of the EOA type. The logic chain for achieving superior performance for the PMSM control system based on the DTC strategy proposed in this article can be clearly seen, together with the relative advantages and disadvantages, especially in terms of the cost of the physical controller in which the algorithms are implemented. In fact, in most of the works presented in the literature, the comparison with the PI control law (a benchmark controller), both through numerical simulations and real-time implementation, is mainly used to obtain control laws that guarantee superior performance. Obviously, the existence of verified results on the performance of different control algorithms gives the control system designer a range of options, and a global techno-economic selection criterion should be used to select the control law.