# Complementary Cooperation of Dual Power Circuits to Drive Active Magnetic Bearings
## 4 Simulations  
In this section, intensive simulations, via MATLAB/Simulink, for PWM-TPs to track the desired output are undertaken to verify the feasibility and efficacy of DC\({}^{2}\). The Simulink model of DC\({}^{2}\) is depicted in Figure 8. The corresponding environmental setup for the simulations undertaken later is listed in Table 1. The reference signal to track, i.e., the desired output, is a step-wise function while the applied voltage to drive the AMB coil, \(V_{P}\), is set as 40 VDC. \(i_{AMB}^{ref}\) is the desired current applied to the AMB coils while \(u_{AMB}^{ref}\) is the corresponding voltage command. The constant resistance with respect to \(u_{AMB}^{ref}\) over \(i_{AMB}^{ref}\), i.e., \(R_{iu}\) in Figure 5, is set as 1 \(\Omega\). On the other hand, \(i_{AMB}\) is the actual current at the AMB coils, and \(\hat{u}_{AMB}\) is the converted voltage with respect to the measured current by the equipped current sensor (CS) upon \(i_{AMB}\). The constant resistance for \(i_{AMB}\) converted to \(\hat{u}_{AMB}\) is set as 1 \(\Omega\). In addition, a switch is applied to determine the timing of change between these two modes, i.e., DDM and ADM. As long as the error between \(i_{AMB}\) and \(i_{AMB}^{ref}\) is over 0.03 A, then DC\({}^{2}\) is controlled by PWM-TP under DDM. On the contrary, as the error between \(i_{AMB}\) and \(i_{AMB}^{ref}\) is less than or equal to 0.03 A, then DC\({}^{2}\) is controlled by PWM-TP under ADM. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameters** & **Value** \\ \hline Solver Type & Variable-step \\ Numerical Method & ode23t \\ Supply Voltage to AMB & 40 VDC \\ PWM Switching Frequency & 22 kHz \\ Threshold to Switch Operation Mode & 0.03 V \\ Threshold of Multiplexer & 3.005 V \\ Gate-source threshold voltage of MOSFET & 3 V \\ Drain-source on Resistance of MOSFET & 0.028 \(\Omega\) \\ Channel Modulation of MOSFET & 0.01 V\({}^{-1}\) \\ Gate-source voltage for R\_DS (on) & 10 V \\ Drain current for R\_DS (on) & 75 A \\ Transresistance of Current Sensor & 1 \(\Omega\) \\ P Gain of PWM-TP under DDM & 300 \\ I Gain of PWM-TP under DDM & 1000 \\ P Gain of PWM-TP under ADM & 90 \\ I Gain of PWM-TP under ADM & 300 \\ Resistance of AMB coil & 0.9 \(\Omega\) \\ Inductance of AMB coil & 13 mH \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Environmental setup of simulations. Figure 8: Simulink model of DC\({}^{2}\) (dual cooperative drive circuit). The desired output, i.e., \(i_{AMB}^{ref}\) shown in Figure 8, to be tracked is nothing but a sequence of step-wise signal whose quantity in ampare is limited by [0, 1.5 A]. The time duration of each step is set as 5 ms. The output currents and the tracking errors with respect to output current by two-state Power Amplifier (PA), i.e., DDM, three-state PA, DC\({}^{2}\) and ADM, are shown in Figure 9. Unfortunately, the peak-to-peak amplitudes of current ripples under DDM are up to 30 mA. Since the current ripples are too severe so that the regulation performance of AMB upon the position deviation of rotor is much downgraded, the other operation mode, namely ADM, has to be joined to reduce the aforesaid current ripples. It is noted that, under ADM, _M_**#2** is ensured to operate in saturation region. As _M_**#2** operates in its saturation region, the higher the gate-source voltage, \(V_{GS}\), the steeper the slope of the curve of \(i_{D}\) versus \(V_{DS}\). Therefore, under ADM, once \(V_{DS}\) of _M_**#2** is altered during a very short time interval which is taken by the on-off action of _M_**#1**, the lower \(i_{D}\) is induced, the minor current ripple would be carried by the resulted output current. From the simulation results under ADM, when \(i_{AMB}\) is 1.5 A, the amplitude of current ripples is about 7.2 mA. Moreover, the amplitude of current ripples is down to 2.1 mA as \(i_{AMB}\) is reduced to 0.01 A. On the other hand, it can be observed that steady-state errors are within [\(-\)10 mA, \(+\)5 mA] under DDM.