## 2 Materials and Methods
In this case, the mechanical characteristics at the same voltages and misalignment angles are identical, and the graphs of the mechanical characteristics are superimposed on each other [17]. All the characteristics were obtained at the minimum residual resistance in the common rotor circuit (\(Ra=0.3\) Ohm). Based on the characteristics presented in Figure 4b-d, the values of the supply voltages changed to within 75-100% of the nominal value, while the equalizing moments reached up to (\(M_{\text{n}}=1.0\div 2.5\)) from the nominal moments, and the angular positions of individual rotors changed to within a range of \(0^{\circ}\) to \(90^{\circ}\). As shown by the mechanical characteristics in Figure 4b,c, the motors receiving the maximum voltage (in our case, \(U_{123}=U_{\text{n}}\) and \(K_{\text{L123}}=1.0\)) create the maximum torque, while motors with lower supply voltages create moments inversely proportional to the square of the voltage. In Figures 4d and 4c, the mechanical characteristics are similar but differ at the same full voltages for the first and third motors. In addition, the value of the supply voltage of the second motor is reduced by 25% and differs in the angular positions of the rotors of the second motor (\(20^{\circ}\) and \(45^{\circ}\)). In this case, the equalizing moments reach up to (\(M_{\rm n}=1.0\div 1.5\)). The results of this study reveal that the differences in angular positions should not exceed \(90^{\circ}\), while the value of the supply voltage should be changed to no lower than \(0.75\) of the nominal value. With such changes in parameters, the MAED system with TVCs operates stably. Equalizing moments are also formed due to differences in drive moments. Based on the obtained expressions of the moments, the following is true with the in-phase rotation of three machines, that is, with \(U_{1}=U_{2}=U_{3}=U_{1\rm n}\) and \(\phi_{1}=\phi_{2}=\phi_{3}\):  
\[U=I_{11}Z_{1}-I_{21}jx_{0}\]0  
In this case, all three machines operate on rheostatic characteristics with tripled additional resistance values \(3 Ra\), and the equalizing moments are equal to zero. \[U=I_{11}Z_{1}-I_{21}jx_{0}\]1 _Cont._  
\[U=I_{11}Z_{1}-I_{21}jx_{0}\]2 Mechanical characteristics of a three-motor electric drive carding machine (CM) at different mismatch angles and levels of total rotor resistance. (**a**) For different values of \(Ra\) corresponding to critical slip: blue \(S^{\prime}\)m = 0 (without additional resistance \(Ra=0\)); orange line \(S^{\prime}\)m = 0.212; green line \(S^{\prime}\)m = 0.347; red line \(S^{\prime}\)m = 0.645. (**b**) \(M_{1}\) is the moment of the first engine, dotted blue line, M\({}_{2}\) is the moment of the second engine, solid green line \(\varphi_{1}=\varphi_{2}=30^{\circ}\), \(\varphi_{3}=90^{\circ}\) is the moment of the second engine, dotted orange line, \(M_{1}=M_{2}\) are equal moments of the first and second engines (\(\varphi_{1}=\varphi_{2}=30^{\circ}\), \(\varphi_{3}=90^{\circ}\)), \(M_{3}\) is the moment of the third engine, dotted red line (\(\varphi_{1}=90^{\circ}\), \(\varphi_{2}=30^{\circ}\), \(\varphi_{3}=0^{\circ}\)). (**c**) \(M_{1}\) moment of the first engine, \(M_{2}=M_{3}\) moments of the second, third engines (\(\varphi_{1}=90^{\circ}\), \(\varphi_{2}=\varphi_{3}=0^{\circ}\), \(S^{\prime}\)m = 0.645), \(M_{1}\) moment of the first engine, \(M_{2}=M_{3}\) moments of the second, third engines (\(S^{\prime}\)m = 0.347, \(\varphi_{1}=90^{\circ}\), \(\varphi_{2}=\varphi_{3}=0^{\circ}\)), \(M_{1}\) moment of the first engine, black dotted line \(M_{2}=M_{3}\) moments of the second and third engines, orange dotted line (\(S^{\prime}\)m = 0.202, \(\varphi_{1}=90^{\circ}\), \(\varphi_{2}=\varphi_{3}=0^{\circ}\)). (**d**) \(M_{1}\) moment of the first engine, blue dotted line, \(M_{2}=M_{3}\) moments of the second, third engines, red dotted line (\(\varphi_{1}=90^{\circ}\), \(\varphi_{2}=\varphi_{3}=0^{\circ}\)). \(M^{\star}=M_{\rm n}/M_{\rm nom}\)—relative moments of engines (n = 1, 2, 3).