# Energy-Feedback Load Simulation Algorithm Based on Fuzzy Control
## 2 Load Simulation Small-Signal Modeling  
According to the test requirements and power feature of the DC power supply, only resistive loads are required during testing. Therefore, DC electronic load just has to simulate pure resistance load, not the capacitive load and inductive load. Moreover, only the three basic modes of constant power, constant current, and constant resistance are needed for load simulation [13], which can be respectively completed by making the DC electronic load's input current \(I_{\text{IN}}\), equivalent resistance \(R_{\text{L}}\), and power output \(P_{\text{IN}}\) equal to the set value. The control objects of different load simulation modes are different and are not conducive to the subsequent control algorithm design and control loop compensation. Among them, the current control not only has fast dynamic response but can also realize the limitation of the peak current of each cycle. Therefore, the core idea of control object normalization is to convert the control of different load simulation modes into the tracking of input current \(I_{\text{IN}}\). The normalized calculation formula of the control object is:  
\[\left\{ \begin{array}{l}I_{\text{IN\_Ref}}=\frac{P_{\text{SET}}}{u_{\text{IN} }}(\text{C-P mode})\\ I_{\text{IN\_Ref}}=\frac{u_{\text{IN}}}{R_{\text{SET}}}(\text{C-R mode})\\ I_{\text{IN\_Ref}}=I_{\text{SET}}(\text{C-Imode})\end{array} \right. \tag{1}\]  
where \(I_{\text{IN\_REF}}\) is the reference value of input-current-tracking instruction for high-efficiency feed-type DC electronic load, \(P_{\text{SET}}\) is the set power, \(R_{\text{SET}}\) is the set resistance, \(I_{SET}\) is the set current, and \(u_{\text{IN}}\) is the input voltage. Load simulation boost circuit adopts closed-loop control; thus the dynamic model and transfer function of the boost circuit are needed to design the feedback loop so as to improve the steady-state precision and dynamic performance of the system. Since the load analog circuit contains boost switch tubes and diodes and other nonlinear devices, which are nonlinear systems [14; 15], the state average method is adopted for modeling. Load simulation boost circuit diagram and component parameters are shown in Figure 1; \(i_{\text{L}}\) is the current through the inductor, \(u_{\text{IN}}\) is the input voltage, and \(u_{\text{C}}\) is the voltage at both ends of the capacitor. It is assumed that the boost is in continuous on-off mode when working normally. The on-off voltage drop is ignored when the switch tube is on, which can be regarded as a short-circuit state. Similarly, it can be regarded as a cut-off state when the switch tube is turned off. In addition, the diode D1 conduction voltage drop is only 0.7 V, far less than boost input and output voltage, and thus can be ignored. According to the analysis in Section 2, the boost circuit has two operating modes, and when it operates in the on mode, the matrix equation describing the current circuit state is:  
\[\left[ \begin{array}{c}\frac{\text{d}i_{\text{L}}}{\text{d}t}\\ \frac{\text{d}uc}{\text{d}t}\end{array} \right]=\left[ \begin{array}{cc}0&0\\ 0&\frac{-1}{RC}\end{array} \right]\left[ \begin{array}{c}i_{\text{L}}\\ u_{\text{C}}\end{array} \right]+\left[ \begin{array}{c}\frac{1}{C}\\ 0\end{array} \right]u_{\text{IN}} \tag{2}\]  
where \(t\) is the response time. When the boost circuit operates in off mode, the matrix equation describing the current circuit state is:  
\[\left[ \begin{array}{c}\frac{\text{d}i_{\text{L}}}{\text{d}t}\\ \frac{\text{d}uc}{\text{d}t}\end{array} \right]=\left[ \begin{array}{cc}0& \frac{-1}{T}\\ \frac{1}{C}&\frac{-1}{RC}\end{array} \right]\left[ \begin{array}{c}i_{\text{L}} \\ u_{\text{C}}\end{array} \right]+\left[ \begin{array}{c}\frac{1}{C}\\ 0\end{array} \right]u_{\text{IN}} \tag{3}\]  
Figure 1: Load analog boost circuit diagram.