# Complementary Cooperation of Dual Power Circuits to Drive Active Magnetic Bearings
## 4 Simulations
In comparison, the steady-state errors are, all the time, within the range [0, \(+\)8 mA] under ADM. This range is about half of that under DDM. Besides, it is obvious that there are a few spikes induced at three-state PA while no any spikes at DC\({}^{2}\). Since DDM and ADM possess their own particular merits, DDM and ADM are combined together to constitute the proposed DC\({}^{2}\). As a matter of fact, taking advantage of joint DDM and ADM, the tracking of DC\({}^{2}\) can be further reduced to be within [\(-\)1.5 mA, \(+\)2 mA]. To be more explicitly compared, the tracking errors (TEs) by two-state power amplifier (PA), three-state PA and DC\({}^{2}\) are summarized in Table 2. As the applied current to AMB coils, \(i_{AMB}\), is 0.01 A, the tracking error by DC\({}^{2}\) is below 15% while the tracking error by two-state PA is up to 133.6%. As \(i_{AMB}\) is much greater  
Figure 9: Output currents and tracking errors by three-state PA (power amplifier), DDM (digital driving mode), ADM (analog driving mode) and DC\({}^{2}\) (dual cooperative drive circuit). than 0.01 A, the tracking by DC\({}^{2}\) is reduced to 0.3% or below. On the other hand, the comparison, in terms of the peak-to-peak amplitude of current ripple (PPACR), by a two-state PA, three-state PA and DC\({}^{2}\) is concluded by Table 3. During the k\({}^{\text{th}}\) time interval, PPACR is defined as the difference between \(\max\{i_{AMB}(t),\ (k-\ 1)T_{S}<t\leq kT_{S}\}\) and \(\min\{i_{AMB}(t),\ (k-\ 1)T_{S}<t\leq kT_{S}\}\) where \(k\in N\), \(T_{S}\) is the time period and \(i_{AMB}(t)\) the actual current applied to coils at AMB. The current ripples by two-state PA are over 27 mA. Compared with two-state PA, the improvement degree of reducing peak-to-peak amplitude of current ripples by DC\({}^{2}\) is up to 94% as \(i_{AMB}\) is by 0.01 A, i.e., low drive current, under steady-state circumstance. On the contrary, as \(i_{AMB}\) is by 1.5 A, i.e., high drive current, under transient-state circumstance, the improvement degree of reducing the peak-to-peak amplitude of current ripples by DC\({}^{2}\) is about 74%. Besides, the power dissipations at MOSFETs by two-state PA, three-state PA and DC\({}^{2}\) are summarized in Table 4. The power dissipation at MOSFETs is mainly determined by the applied current, on-resistance of MOSFET and the time duration at on-state, i.e., duty cycle. It is noted that the duty cycle under ADM are normally below 20% while it is usually above 75% under DDM. Therefore, though the on-resistance of _M#2_ under ADM is about twice of that under DDM, the power dissipation at _M#2_ under ADM is still lower than that under DDM. To sum up, owing to the mutually complementary cooperation between DDM and ADM, the proposed DC\({}^{2}\) at least has three outstanding advantages such as: (i) the slew rate of output current is high, (ii) the tracking errors can be greatly reduced, and (iii) the current ripples are significantly suppressed. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Two-State PA (DDM)**} & \multicolumn{2}{c}{**Three-State PA**} & \multicolumn{2}{c}{**DC\({}^{2}\)**} \\ \cline{2-7}
**A: Amplitude of \(i_{AMB}\) (A)** & **B: TE** & **C: Error** & **D: TE** & **E: Error** & **F: TE** & **G: Error** \\  & **(mA)** & **C = B/A (\%)** & **(mA)** & **E = D/A