# Research on Composite Control Strategy of Quasi-Z-Source DC-DC Converter for Fuel Cell Vehicles
## 3 Component Parameters and Controller Design
### Feedforward Compensation Network and Feedback Control Design  
The block diagram of the closed-loop feedback control system is shown in Figure 4. \(G_{uo-d}(s)\) is the transfer function from duty cycle to output voltage. \(G_{PWM}(s)\) is the transfer function of the pulse width modulator and \(G_{FB}(s)\) is the feedback network transfer function. In the prototype, the hall sensor is adopted to measure the output voltage. According to the variable ratio of the hall sensor, \(G_{FB}(s)\)\(=1/200\) is obtained.  
According to Equation (19) and Tables 1 and 2, when the input voltage is 40 V, \(G_{uo-d}(s)\) can be obtained as shown in Equation (25) by using the ss2 tf function in Matlab.  
\[G_{uo-d}(s)=\frac{\widetilde{u}_{\rm o}(s)}{d(s)}\bigg{|}_{\widetilde{\rm inm}= 0}=\frac{9.41\times 10^{-18}\phi+5.56\times 10^{-11}\beta+6.14\times 10^{-7} \beta^{4}+1.83\times 10^{-3}\beta^{4}+1.15\beta^{2}+317\beta+37553}{1\times 10^{-22 }\beta^{7}+8.24\times 10^{-18}\beta+1.04\times 10^{-13}\beta+3.37\times 10^{-10} \beta^{4}+1.95\times 10^{-7}\beta+5.94\times 10^{-4}\beta+6.69\times 10^{-3} \beta+6.2} \tag{25}\]  
The system feedback controller adopts the proportional plus integral controller (PI controller), as shown in Equation (26).  
\[G_{PI}(s)=K_{p}+K_{i}/s \tag{26}\]  
where, \(K_{\rm P}\) and \(K_{\rm i}\) are proportional and integral coefficients, respectively.  
The feedback controller can eliminate the steady-state error of the output voltage and adjust the system dynamic performance. However, when input voltage disturbance occurs, the system does not adjust the duty cycle to maintain the stability of the output voltage until the output voltage fluctuation is fed back to the control end. Due to the \"soft\" output characteristic of the fuel cell, the feedforward compensation network should be adopted for the DC-DC converter of fuel cell vehicles. Therefore, a composite controller is proposed with input voltage feedforward compensation and feedback control. The block diagram of the system is as shown in Figure 5. \(G_{uo-ui}(s)\) is the transfer function from input  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Values** & **Units** \\ \hline Inductors \(L_{1}\), \(L_{2}\) & 800 & uH \\ Capacitors \(C_{1}\), \(C_{2}\), \(C_{3}\), \(C_{4}\), \(C_{5}\) & 680 & uF \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters table of inductors and capacitors.  
Figure 4: Block diagram of feedback control system.  
to output and \(G_{f}(s)\) is the feedforward compensation transfer function. According to Equation (19), the \(G_{uo-ui}(s)\) can be obtained as in Equation (27), when the input voltage is 40 V.  
\[G_{uo-ui}(s)=\frac{\frac{\widetilde{u}_{0}(s)}{u_{i}(s)}}{\widetilde{u}_{i}(s) }\Big{|}_{\tilde{d}=0}=\frac{-1.02\times 10^{-23}\phi+-9.54\times 10^{-29}s^{5}+9.73 \times 10^{-13}s^{4}+1.14\times 10^{-8}s^{3}+3.55s^{-5}+0.021s+62}{1\times 1 0^{-29}s^{7}+8.24\times 10^{-18}s^{9}+1.104\times 10^{-15}s^{3}+3.37\times 10^{- 76}s^{4}+1.95\times 10^{-9}s^{5}+5.94\times 10^{-10}s^{2}+6.69\times 10^{-3}s+6.2} \tag{27}\]  
According to Figure 5, the feedforward compensation transfer function \(G_{f}(s)\) is as in Equation (28).  
\[G_{f}(s)=\frac{G_{uo-ui}(s)}{G_{PWM}(s)G_{uo-d}(s)} \tag{28}\]  
where \(G_{PWM}(s)\) is a proportional element and is equal to 1 in the simulation system.  
According to Equations (25) and (27), the calculation result of Equation (28) is shown in Equation (29). The feedforward compensation network and feedback controller work together to adjust the duty cycle. The feedforward compensation network can reduce the output voltage fluctuation caused by input voltage disturbance, which is beneficial for improving the performance of the DC-DC converter for fuel cell vehicles.  
\[G_{f}(s)=\frac{-1.02\times 10^{-32}s^{6}+-9.54\times 10^{-29}s^{5}+9.73\times 10^{- 13}s^{4}+1.14\times 10^{-8}s^{3}+3.55s^{-5}+0.021s+62}{9.41\times 10^{-16}s^{6}+5.56 \times 10^{-11}s^{5}+6.14\times 10^{-7}s^{4}+1.83\times 10^{-3}s^{3}+1.15s^{2}+3 17s+37553} \tag{29}\]