###### Abstract  
Modern electric machines are attracting the greatest interest from the research community due to their current increasing number of applications, including electric vehicles and wind power generators. Their use requires the development of complex regulators, where predictive controllers appear as interesting and viable alternatives in recent research works. Although these controllers have an easy formulation and high flexibility to incorporate different control objectives in multidimensional systems, they have limitations that require attention and limit their application: a high computational cost and current harmonic content. This work presents a novel controller that focuses on these limitations, where the additional degree of freedom introduced in the predictive controller through the lead-pursuit guidance law concept is combined with the use of virtual voltage vectors to reduce the harmonic content in a controlled drive. The effectiveness of the proposed controller is explored using a five-phase drive and several figures of merit, such as the root mean square error in current tracking, the total harmonic distortion in the stator currents, and the number of switching commutations per cycle. Different predictive controllers are compared with the proposal in terms of speed regulation, stator current control, and steady-state performance, where the results obtained are analyzed to show the interest, improvements, and limitations of the proposal. e _Applied sciences_  
25 March 20253 of the required calculations and the high computational cost of the controller [6]. This use was recently extended to modern electric devices, such as multiphase drives [7], where the reasons for this interest are the greater complexity and number of variables in the multiphase drive and the intuitive and flexible formulation of the MPC technique. MPC can now be considered a promising control methodology in multiphase drives, where it presents an easy formulation and high flexibility for incorporating different control objectives [8]. However, the application of MPC in multiphase drives faces some limitations that require attention [9; 10; 11]. One limitation is the implementation of the controller. MPC is intensive in computation, and a limit on the sampling frequency is found for any given computing hardware [12]. Many attempts have been reported to decrease this computational load, with most of them based on a reduction in available control vectors [13], the definition of search techniques based on the physical considerations of the system to avoid the usual exhaustive search for finding the control action [14], or the simplification of the combinatorial search [15]. For example, the computational cost of a five-phase drive is reduced using a subset of voltage vectors available in the prediction algorithm in [16] or by eliminating the need for iteration in [17]. But the dependence of MPC on 'uncertainties' in the real system that affect the predictive model (i.e., non-measurable system variables or the discrepancy between actual and estimated or measured values of electrical parameters during normal drive operation) is particularly critical in these lower complexity MPC schemes [18], and the incorporation of more robust controllers, such as deadbeat strategies, is mandatory to achieve satisfactory drive performance [18; 19]. A second important limitation is caused by the absence of an explicit modulation stage due to the fixed-time discretization nature of MPC, which produces not only high-harmonic components but also interharmonics and electrical noise in the drive, particularly for low values of the stator impedance [20]. While harmonics refer to current and voltage waveforms with frequencies that are multiples of the fundamental power frequency and appear due to the power converters used in variable-frequency drives, an important portion of waveform distortion is due to the interharmonics (not integer harmonics) that include subharmonics below the fundamental frequency when predictive controllers are utilized.