## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **M2 (3.0 kW)** & **M3 (4.0 kW)** & **M4 (5.5 kW)** & **M5 (7.5 kW)** & **M6 (11 kW)** & **M7 (15 kW)** \\ \hline Electrical Active & 3.5 & 4.7 & 6.4 & 8.6 & 12.4 & 16.6 \\ Power (KW) & 400 & 400 & 400 & 400 & 400 & 400 \\ Line Current (Arms) & 6.2 & 7.9 & 10.6 & 13.9 & 20.5 & 27.6 \\ Frequency (Hz) & 50 & 50 & 50 & 50 & 50 & 50 \\ Power Factor & 0.82 & 0.85 & 0.87 & 0.89 & 0.87 & 0.87 \\ Poles Pairs & 1 & 1 & 1 & 1 & 1 & 1 \\ Efficiency & 0.857 & 0.860 & 0.861 & 0.875 & 0.890 & 0.902 \\ Mechanical Power (kW) & 3.0 & 4.0 & 5.5 & 7.5 & 11.0 & 15.0 \\ Torque (N.m) & 9.86 & 13.24 & 18.45 & 25.04 & 36.32 & 49.36 \\ Shaft RPM & 2905 & 2885 & 2846 & 2860 & 2892 & 2902 \\ Slip (\%) & 3.17 & 3.83 & 5.13 & 4.67 & 3.60 & 3.27 \\ F (Friction Factor) (N.m.s) & \(2.43\times 10^{-4}\) & \(3.29\times 10^{-4}\) & \(4.65\times 10^{-4}\) & \(6.27\times 10^{-4}\) & \(9.01\times 10^{-4}\) & \(1.20\times 10^{-3}\) \\ J (Moment of Inertia) & 0.0041 & 0.0061 & 0.014 & 0.016 & 0.038 & 0.048 \\ (kg.m\({}^{2}\)) & & & & & & \\ Motor Type & Squirrel-cage & Squirrel-cage & Squirrel-cage & Squirrel-cage & Squirrel-cage \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Electric three-phase induction motors M2, M3, M4, M5, M6, and M7, measured and calculated parameters to be inserted in Matlab’s “Simulink” model. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \begin{tabular}{c} **Drum** \\ **Operating** \\ **Speed (rev/min)** \\ \end{tabular} & \begin{tabular}{c} **Speed** \\ **Variation** \\ \end{tabular} & \begin{tabular}{c} **Gearbox** \\ **Ratio** \\ \end{tabular} & \begin{tabular}{c} **Motor Shaft** \\ **Efficiency** \\ \end{tabular} & \begin{tabular}{c} **Differential** \\ **Operating** \\ **Speed (rev/min)** \\ \end{tabular} & \begin{tabular}{c} **F (Friction** \\ **Scroll Speed** \\ **(rev/min)** \\ \end{tabular} & \begin{tabular}{c} **J (Moment** \\ **Factor)** \\ **(N-m-s)** \\ \end{tabular} & \begin{tabular}{c} **Additional** \\ **(kg.m\({}^{2}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Motar Sheft** \\ **Torque When** \\ **Loaded (N-m)** \\ \end{tabular} \\ \hline \multirow{3}{*}{4916} &
\begin{tabular}{c} Pulley with \\ two toothed \\ drive belts \\ \end{tabular} & 1.7365 & 0.97 & 2831 & 12 & 0.009714 & 2.341 & 1.8025 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Horizontal centrifuge “Baby-1” measured and calculated parameters subsequently inserted in Matlab’s “simulink” model. as measured for the IM, being a form of on/off control in the family of feedback control systems [22; 23]. Moreover, the vector control algorithm allows for the enhanced dynamic behavior of the IM, allowing designers to optimally size the IM rather than oversize it to guarantee the desired transient behavior (i.e., a shorter time to reach the operational speed of the horizontal centrifuge). In addition, a smaller IM normally also delivers a larger fraction of its nominal power; thus, its operating point can offer a better overall efficiency [23]. Being interested in steady-state conditions, the horizontal centrifuge relation between rotational speed and loading torque needs to be carefully characterized. From Table 3, the horizontal centrifuge parameters are known, and, therefore, the mechanical system to be solved involves a general mechanical balance equation in order to calculate how the centrifuge speed depends on the applied torque. In addition, the gearbox ratio needs to be varied from \(-45\%\) to \(+45\%\) with reference to its nominal 1.7365 value. The Simulink block that made this calculation possible is shown in Figure 1; Torque_in and epsilon_gear are the inputs while n_motor is the output. The decanter and induction motor are considered as an unicum and, for each single component, its friction factor (Fm) and its moment of inertia (Jm) are considered. The efficiency of the gearbox is eta_gear. The additional torque when the centrifuge is running loaded is considered through the LoadTorque input.