## 3 Controller Design and Genetic Algorithm Optimization Approach
### Sliding Mode Control  
Due to the inability of the small-signal model to predict the stability of the converter under large transients, other control approaches need to be considered. SMC has many advantages as a control method. Firstly, SMC provides guaranteed stability and robustness against parameter uncertainties [22]. Secondly, SMC is a nonlinear control method that introduces the sliding mode to compensate for the system's nonlinear characteristics and effectively handles stability issues during large transients. Therefore, adopting SMC is highly beneficial in ensuring the stability and robustness of the system in practical applications. In the DAB, a sliding mode can be introduced to control the output of the bidirectional transformer and full-bridge topology. This paper adopts a super sliding mode-based SMC approach, where the sliding mode is composed of the error between the system output and the desired output, as well as the rate of change of the error. Specifically, based on the system model and desired performance requirements, the required super sliding mode parameters are calculated and applied to the controller. Firstly, the error between the output voltage and the reference voltage is selected as \(x_{1}=V_{\text{err}}={V_{0}}^{*}-{V_{o}}\), along with its integral as the state variable of the sliding surface. To eliminate the steady-state error introduced by the equivalent SMC, the quadratic integral of the aforementioned error is further chosen to eliminate the steady-state error. Therefore, the state variables of SMC are defined as:  
\[x= \begin{bmatrix}x_{1}\\ x_{2}\\ x_{3}\end{bmatrix} ^{T}= \begin{bmatrix}V_{\text{err}}\\ \int_{0}^{t}V_{\text{err}}\ dt\\ \int_{0}^{t}x_{2}\ dt\end{bmatrix}  \tag{14}\]  
The sliding surface represents the instantaneous feedback tracking trajectory of the system, and a linear combination of the weighted values of the state variables is selected as the sliding surface:  
\[S(x,t)=\sum_{i=1}^{3}\alpha_{i}x_{i} \tag{15}\]  
where \(\alpha_{i}\) denotes the weighting coefficients of the sliding surface. Setting the first derivative of the sliding surface to zero ensures that the system state slides quickly on the sliding surface. In SMC, the direction of the control force is determined by the first derivative of the sliding surface, thus setting it to zero eliminates interference from the control force, ensuring that the system state slides quickly along the normal direction of the sliding surface, achieving fast and stable control effects. Using the invariance condition [25]:  
\[\frac{\text{d}S(x,t)}{\text{d}t}=0 \tag{16}\]  
Figure 2: Control block diagram of DAB PI control based on pole placement method: (**a**) DAB feedback control block diagram; (**b**) DAB feedback equivalent PI control block diagram. The equivalent control can be achieved, and based on Equation (15), we have:  
\[i_{2}=C_{\rm o}\frac{\rm d}V_{\rm o}}{\rm d}t+\frac{V_{\rm o}}{R_{\rm o}}=\frac{V _{\rm o}}{R_{\rm o}}+C_{\rm o}\frac{\alpha_{2}}{\alpha_{1}}V_{\rm err}+C_{\rm o }\frac{\alpha_{3}}{\alpha_{1}}\int_{0}^{t}V_{\rm err}\ dt \tag{17}\]  
Secondly, setting the second derivative of the sliding surface to zero ensures that the control force has good robustness and adaptability. In SMC, due to uncertainties and disturbances affecting the system, the first derivative of the sliding surface will vary, thereby affecting the magnitude and direction of the control force. To maintain the stability and robustness of the control force, it is necessary to set the second derivative of the sliding surface to zero, which ensures that the control force has an appropriate adjustment speed and range when regulating on the sliding surface, avoiding excessive or insufficient adjustments that lead to system instability.