## 3 Self-Learning Control System of SynRM Based on EI-BELBIC
### Self-Learning Regulation of Amygdala in EI-BELBIC  
In the vector control system of the synchronous reluctance motor, the error of speed \(e\) is defined as the difference between the reference speed \(\omega_{m}\)\({}^{*}\) and the feedback speed \(\omega_{m}\). The sensory input function (_SIF_) of the brain emotion controller is:  
\[\left\{ \begin{array}{l}SI=S_{1}e+S_{2}\int edt\\ SH=S_{th}e\left|\int edt\right|\end{array} \right., \tag{10}\]  
where \(S_{1}\), \(S_{2}\) and \(S_{th}\) are adjustable parameters of the sensory input function. The thalamus separates the maximum \(SI\) of the sensory stimulus signal \(A_{th}\) and transfers it to the amygdala. The following formulas can be obtained:  
\[A_{th}=\max(SI)=Sth, \tag{11}\]  
\[A_{m+1}=A_{th}\cdot V_{m+1}. \tag{12}\]  
After receiving input signals from the thalamus and sensory cortex, the amygdala takes the weighted sum of the two as the output value of the amygdala, which can be obtained as follows:  
\[A=\sum_{i=1}^{m+1}A_{i}=A_{i}+A_{m+1}=SI_{i}\cdot V_{i}+A_{th}\cdot V_{m+1}= \left(S_{1}e_{1}+S_{2}\int edt\right)V_{1}+S_{th}e\left|\int edt\right|V_{2}, \tag{13}\]  
where \(V_{1}\) and \(V_{2}\) are the weights of the amygdala. The amygdala output showed the ability to follow reward and punishment signals quickly. As a kind of positive excitation, the weight increases when the output value is less than the value of the reward or punishment signal but remains the same when the output value is greater than the value of the reward or punishment signal. The adjustment rates of the weights of the amygdala are as follows:  
\[\Delta V_{1}=\alpha\bigg{[}\bigg{(}S_{1}e+S_{2}\int edt\bigg{)}\cdot\max(0, REW-A)\bigg{]}, \tag{14}\]  
\[\Delta V_{2}=\alpha\bigg{[}S_{th}e\bigg{|}\int edt\bigg{|}\cdot\max(0,REW-A) \bigg{]}, \tag{15}\]  
where, \(\alpha\) is the learning rate of the weight of the amygdala, which is a vital parameter in the adjustment process of the amygdala. The emotional cue function (_ECF_) of the brain emotion controller is defined as:  
\[ECF=REW=R_{1}e+R_{2}\int edt+R_{u}u, \tag{16}\]  
where \(u\) is the output of the controller and \(R_{1}\), \(R_{2}\) and \(R_{u}\) are the adjustable parameters of the _ECF_. Figure 7 shows the adjustment curves of amygdala nodes in the EI-BELBIC with sudden loading. After the load changes suddenly, the rate of change of \(V\) and \(V_{th}\) in Figure 7a, c increases relative to the system error, so that \(V\) and \(V_{th}\) in Figure 7b,d begin to adjust automatically to achieve the purpose of automatic adjustment of the controller parameters as the system changes. Figures 8 and 9 show the self-adjusting curve of node parameters in the amygdala in the EI-BELBIC under magnetic field saturation. Figure 8 shows the node regulation curves in the amygdala when the SynRM is unloaded under magnetic saturation. As shown in Figure 8a,c, when the current of the \(d\)-axis increases, \(\Delta V\) and \(\Delta V_{th}\) change faster. When \(i_{d}=15\) A, the adjustment time of \(\Delta V\) and \(\Delta V_{th}\) is 57% less than that when \(i_{d}=5\) A and 25% faster than that when \(i_{d}=10\) A. Correspondingly, when \(i_{d}=15\) A, the stability time of \(V\) and \(V_{th}\) is 25% less than that when \(i_{d}=10\) A, and 57% less than that when \(i_{d}=5\) A, as shown in Figure 8b,d. As can be seen from the data in Figure 8, the amygdala showed rapid adjustment ability when the SynRM entered the magnetic saturation state, and the amygdala's adjustment ability also increased with the deepening of the magnetic saturation degree. Figure 7: Self-adjustment of amygdala parameters under sudden loading: (**a**) \(\Delta V\); (**b**) \(V\); (**c**) \(\Delta V_{th}\); (**d**) \(V_{th}\). Figure 9: Self-adjusting curves of parameters of amygdala under different working conditions: (a) \(\Delta V\); (b) \(V\); (c) \(\Delta V_{th}\); (d) \(V_{th}\). Figure 9 shows the adjustment process of the amygdala when the SynRM is operated under different loads with and without magnetic saturation, respectively.