## 4 Controller Design  
The sliding mode was first discovered by Russian investigators and has made a significant contribution to the design of multiple system controllers. The first control step [14,15], is the designation of the sliding manifold and then a control rule is established that allows the system state to be attracted to the sliding manifold without deviating from it. The system at MPP must satisfy \(\frac{\partial P_{m}}{\partial V_{m}}=0\), and Equation (23) can be obtained [16].  
\[\frac{\partial P_{m}}{\partial V_{m}}=\frac{\partial\left(I_{m}V_{m}\right)}{ \partial V_{m}}=I_{m}+V_{m}\frac{\partial I_{m}}{\partial V_{m}}\,,\,\text{and }\left(P_{m}=P_{g}\,,I_{m}=I_{L}=i_{{}_{eq}},V_{m}=V_{eq}\right) \tag{23}\]  
In Equation (23), \(P_{m}\) is the input power of the generator after three-phase bridge rectification (Figure 4), \(V_{n}\) and \(I_{m}\) are the input voltage and input current of power generation after rectification. According to Equation (23), the sliding manifold is defined by Equation (24):  
\[\frac{\partial P_{m}}{\partial V_{m}}=\frac{\partial\left(I_{m}V_{m}\right)}{ \partial V_{m}}=I_{m}+V_{m}\frac{\partial I_{m}}{\partial V_{m}}\,,\,\text{and }\left(P_{m}=P_{g}\,,I_{m}=I_{L}=i_{{}_{eq}},V_{m}=V_{eq}\right) \tag{24}\]  
When the system is in a sliding condition, \(S=0\), and the equation is expressed as (25).  
\[\frac{\partial P_{m}}{\partial V_{m}}=\frac{\partial\left(I_{m}V_{m}\right)}{ \partial V_{m}}=I_{m}+V_{m}\frac{\partial I_{m}}{\partial V_{m}}\,,\,\text{and }\left(P_{m}=P_{g}\,,I_{m}=I_{L}=i_{{}_{eq}},V_{m}=V_{eq}\right) \tag{25}\]  
In Figure 6 it can be seen that the duty cycle ratio and operating voltage of the \(S\) operation mode at MPP are correlated with \(U\left(0\leq U\leq 1\right).\) The control switch duty cycle is used to adjust the PWM for MPPT. When the system is in the sliding condition, \(S=0\), expressed by Equation (26), and the equivalent control \(U_{eq}\) of the sliding manifold is expressed by Equation (27) [15].  
According to [PERSON] _et al._[15], the appropriate switchover control law \(U_{{}_{sw}}=\sigma S\) is selected, in considering the controller saturation effect \(\sigma>0\), the control law would be as in Equation (28).  
\[U=\begin{cases}\begin{aligned} & 1,U_{{}_{eq}}+\sigma S\geq 1\\ & U_{{}_{eq}}+\sigma S,\textit{for}0\leq U_{{}_{eq}}+\sigma S<1\\ & 0,U_{{}_{eq}}+\sigma S\leq 0\end{aligned}\end{cases} \tag{28}\]  
According to [PERSON] _et al._ and [PERSON] _et al._[14, 15], the controller (28) enables the system to satisfy [PERSON] theory, expressed by Equation (29), and this proves the stability of SMS and MPPT control of the system.  
\[\dot{V}=S\dot{S}<0 \tag{29}\]  
Also, according to [PERSON] _et al._ and [PERSON] _et al._[14, 15], to avoid the control input \(U\) remaining in a saturated state (\(U=0\) or \(1\)) for a long time, or being switched rapidly between two saturation values (which could affect the service life of the switch or cause high frequency switching noise) the value of parameter \(\sigma\) should not be too large, \(\sigma\leq 1\)/ \(R_{{}_{L}}\) is recommended. Therefore, intelligent selection of the value of \(\sigma\) so the controller will be \(0<U<1\) is an important factor affecting performance. This will not only prolong component life and avoid faults, but will also reduce high frequency switching noise affecting converter output power \(P_{{}_{o}}\) and voltage \(V_{{}_{o}}\). Many recent studies have proposed intelligent theories in renewable energy systems to address this question. For example, [PERSON] _et al._[16] used fuzzy theory to deal with the MPPT of the controller in a PV Generation System. In this study extension theory [9, 17] is applied to determine the intelligent selection of parameter \(\sigma\) to reduce the amount of  
Figure 6: Duty cycle and operating voltage of MPPT.  
high frequency switching and high frequency noise in the MPP steady state. A flow chart for such a scheme is shown in Figure 7.