## 3 Finite Control Set MPC in 5 PIM Drives  
Different predictive stator current control strategies can be applied to the 5 pIM drive, which differ mainly in the system variables that are regulated and in the way control actions are applied. The finite control set MPC structure (FCS-MPC) selects the optimal control action that commands the 5p2L-VSI. An outer speed/torque PI-based controller, which is usually based on the conventional field-oriented control (FOC) strategy, needs to be added to provide current references to the FCS-MPC algorithm. These references are given in a rotating reference frame, called \(dq\), for better regulation, where the reference of the \(q\)-current stator (\(i_{sq}\)*) is the output of a PI regulator, while the reference of the \(d\)-current (\(i_{sq}\)*) is set to its nominal value. Once the objective currents are defined, the FCS MPC selects one switching state from the 32 possibilities to follow those references. This selection is made by minimizing a cost function that compares the current references with a prediction made based on a mathematical model of the system: the prediction model. The basis of the predictive controller is then the optimal selection of the switching state of the power converter using a predictive model of the controlled system (a five-phase induction drive in our case).  
An alternative way of implementing an MPC algorithm is the variable sampling time lead-pursuit controller or VSTLPC technique in what follows. The basis of this technique is the optimal selection of both the switching state of the power converter and its time of application between all possibilities without the necessity of a cost function. VSTLPC begins finding the optimal switching state from some measurements (rotor speed and stator currents) and applying the lead-pursuit concept: Hitting a moving target requires some anticipation, since it takes some time for the control action to produce an effect on the system, and during such time, the target changes its position. In this way, the controller points to an advanced stator current reference, and the switching vector that produces the trajectory of the stator currents to the reference is selected.  
This work combines VSTLPC and the VVV concepts in the current control of the 5 pIM drive to reduce harmonic distortion in machine currents and to improve the efficiency of the system (see Figure 4). Then, the outer speed loop is maintained while the control action is implemented using VSTLPC and considering different sets of VVV.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value/Description** \\ \hline Rated current (A\({}_{\text{rms}}\)) & 2.5 \\ Pairs of poles & 3 \\ Conductor & Copper \\ Diameter (mm) & 0.7 \\ Number of slots & 30 \\ Number of turns & 165 \\ Type of windings & Single layer \\ Winding pitch & 5 slots (full pitch) \\ Stator resistance, \(R_{s}\) & 12.85 \(\Omega\) \\ Rotor resistance, \(R_{r}\) & 4.80 \(\Omega\) \\ Stator leakage inductance, \(L_{ls}\) & 79.93 mH \\ Rotor leakage inductance, \(L_{lr}\) & 79.93 mH \\ Mutual inductance, \(L_{m}\) & 681.7 mH \\ Rotational inertia, \(J_{m}\) & 0.02 kg-m\({}^{2}\) \\ \hline \end{tabular}
\end{table}
Table 1: Induction machine used in our study.