## 2 Motor Model and Brain Emotional Limbic System Calculation Model  
### SynRM Model  
The principle of reluctance minimization is followed by SynRMs to generate electromagnetic torque. In the \(d-q\) rotating coordinate system, the mathematical model of the SynRM [17] is as follows:  
\[\left\{ \begin{array}{l}u_{d}=R_{s}i_{d}-\omega_{r}L_{q}i_{q}+\frac{4\phi_{d} }{dt}\\ u_{q}=R_{s}i_{q}+\omega_{r}L_{d}i_{d}+\frac{4\psi_{q}}{dt}\end{array} \right., \tag{1}\]  
\[T_{em}=\frac{3}{2}p\cdot(L_{d}-L_{q})\cdot i_{d}\cdot i_{q}, \tag{2}\]  
where \(u_{d}\) and \(u_{q}\) are the voltage of the stators \(d\)-axis and \(q\)-axis; \(R_{s}\) is the phase resistance of the stator; \(L_{d}\) and \(L_{q}\) are the inductance of the \(d\)-axis and \(q\)-axis; \(i_{d}\) and \(i_{q}\) are \(d\)-axis and \(q\)-axis currents; \(\psi_{d}\) and \(\psi_{q}\) are \(d\)-axis flux and \(q\)-axis flux; \(\omega_{r}\) is electric angular velocity; \(T_{em}\) is torque; \(p\) is the number of pole pairs of the motor. The definition of the \(d-q\) axis of the SynRM is shown in Figure 1.  
According to Formula (2), the SynRM has only reluctance torque, determined by the difference in inductance between the \(d\)-axis and \(q\)-axis and the product of current of the \(d\)-axis and \(q\)-axis. When the stator current is low, both \(L_{d}\) and \(L_{q}\) are constant, but with the increase of the stator current, \(L_{d}\) and \(L_{q}\) will gradually decrease and \(L_{d}\) and \(L_{q}\) tend toward a constant value when the stator current increases to a specific value. In the actual operation of the motor, \(L_{d}\) is not only related to \(i_{d}\) but also affected by \(i_{q}\). The Ansoft software is used to obtain the data of experimental prototypes \(L_{d}\) and \(L_{q}\) changing with \(i_{d}\) and \(i_{q}\), then the change curve is obtained as shown in Figure 2.  
In the ideal model of the SynRM, one of the main assumptions is that the magnetomotive force presents a sinusoidal distribution, as does the air-gap flux density. However, in the actual operation of the motor, the air-gap flux density does not present an ideal sinusoidal distribution [18; 19; 20]. The main reason is that the rotor core is affected by magnetic saturation and its magnetization curve is nonlinear. The finite element simulation of the two-dimensional transient field of the SynRM under different currents is carried out by Ansys 2021 R1, and the flux density diagrams are shown in Figure 3. It can be seen from the figure that the magnetic saturation degree of the motor is different under different currents (\(i_{1}<i_{2}<i_{3}\)). Thus, a variable air gap can be assumed as a function of the excitation current. The more significant the magnetic saturation is, the more critical the air gap is. The air gap can be regarded as an iron core with a coil and an air gap. Thus, the relationship between current and magnetic field can be found by using Ampere's Law, which is satisfied even in the case of magnetic saturation. The literature [21] proposed the concept of equivalent excitation current \(l_{m}\), which is defined as:  
Figure 1: Definition of the \(d-q\) coordinate axis of the SynRM. Figure 2: Variation of \(d-q\) axial inductance under magnetic saturation: (**a**) \(L_{d}\) surface over the \(i_{d}-i_{q}\) plan; (**b**) \(L_{q}\) surface over the \(i_{d}-i_{q}\) plan. \[I_{m}=\sqrt{i_{d}^{2}+k^{2}i_{q}^{2}}, \tag{3}\]  
where \(k\) is defined as a coefficient related to the inductance values of the \(q\)-axis and \(d\)-axis and \(k^{2}=L_{q}/L_{d}\). It can be seen from Figure 2 that the ratio of saturated inductance to unsaturated inductance of the \(d\)-axis is approximately equal to that of saturated inductance to unsaturated inductance of the \(q\)-axis.