# Random PWM Technique Based Two-State Markov Chain for Permanent Magnet Synchronous Motor Control
## 4 Experimental Results and Analysis
### Experimental Results of the RPWM Based on Two-State Markov Chain  
Figure 12 shows the current harmonic suppression effect of the RPWM based on a two-state Markov chain. By comparing Figure 12 with Figure 11, it can be seen that, compared with the traditional RPWM, the RPWM based on the two-state Markov chain further spreads the harmonic energy concentrated at the carrier frequency and its multiples and further reduces the amplitude of the harmonic energy. In the power spectral density near 10 kHz and 20 kHz, when the modulation index is 0.5, it drops from \(-24.42\) dB/Hz and \(-26.78\) dB/Hz to \(-27.29\) dB/Hz and \(-28.89\) dB/Hz, respectively; when the modulation index is 1.0, it drops from \(-15.62\) dB/Hz and \(-23.90\) dB/Hz to \(-16.10\) dB/Hz and \(-25.63\) dB/Hz. At the same time, the phenomenon of several carrier periods being greater than or less than the expected carrier period appearing in the local current waveform has decreased, and the quality of the current waveform has been improved. Figure 11: Current harmonic suppression effect of the conventional RPWM. In order to further optimize the random number generation results and enhance the spread spectrum effect, this paper conducts rapid optimization of two key spread spectrum parameters, \(r\) and \(p\), based on the immune algorithm. When the peak value of the current harmonic is the minimum value, the optimal parameter combination is obtained. The optimal parameter group is then introduced into the RPWM based on the two-state Markov chain to improve the randomization of the carrier frequency distribution and further suppress the peak value of harmonic energy in order to achieve the optimal EMI suppression effect. As shown in Figure 13, the current harmonic suppression effect based on the parameter optimization of the two-state Markov chain using the immune algorithm is presented. By comparing this method with the previous two RPMMs, it can be found that it performs better in terms of the power spectral density of the phase current and the current quality. The current frequency spectrum distribution is more uniform, the harmonic peaks in the power spectrum are significantly reduced, and the influence of EMI is further decreased. At the same time, from the local amplification waveform of the phase current, it can be seen that the phenomenon of being greater than or less than the expected carrier period for several consecutive carrier periods basically does not occur, and the current quality is maximally improved. Figure 12: Current harmonic suppression effect of the two-state Markov chain. By combining Tables 2 and 3, it can be seen from the power spectral density that compared with the traditional RPWM and the RPWM based on the two-state Markov chain, the two-state Markov chain parameter optimization method based on the immune algorithm has the best current harmonic suppression effect under different modulation indices. Figure 14 presents the EMI suppression effect of the two-state Markov chain parameter optimization method based on the immune algorithm under different rotational speeds and modulation indices. The EMI suppression effect is calculated as follows: the power spectral density amplitudes of the proposed method at 1 time and 2 times carrier frequencies are compared with those of the traditional SVPWM, and the obtained decrease amplitude (percentage quantity) is averaged to obtain the final result. The results show that the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Modulation Strategy** & **10 kHz** & **20 kHz** \\ \hline Conventional SVPWM & \(-19.01\) & \(-17.52\) \\ Conventional RPWM & \(-24.42\) & \(-26.78\) \\ Markov-RPWM & \(-27.29\) & \(-28.89\) \\ Proposed methodology & \(-28.45\) & \(-30.73\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Amplitude of the power spectral density near the main frequency under different modulation strategies when \(M\) is 0.5. (Unit: dB/Hz). Figure 13: Current harmonic suppression effect of the two-state Markov chain parameter optimization based on immune algorithm.