# UKF-Based State Estimation for Electrolytic Oxygen Generation System of Space Station
## 3 The Dynamic Model of EOGS  
The whole process and principle of EOGS is analyzed above. The mass exchange relationship of the EOGS is simple, but the heat exchange relationship is great intricate, and it also has a complex coupling relationship with ECLS's other systems. The most important thing is that the heat value in the heat exchange process is difficult to measure and calculate accurately. In order to reflect the problem more clearly and intuitively, the functional block diagram of the EOGS in the space station can be simplified as shown in Figure 4, in which two valves are valve_O2 and valve_H2 is a back pressure valve, and the water vapor separator is a membrane separator. In long-term manned missions, the cabin's oxygen partial pressure and total pressure need to be monitored. Therefore, it is necessary to establish the state equation of these two state quantities. State equation of cabin's oxygen partial pressure is written as:  
\[\dot{P_{\rm O_{2}}^{\rm cabin}}=\frac{R_{a}T_{c}}{M_{\rm O_{2}}V_{c}}w_{\rm O_{2 }}^{\rm cabin} \tag{14}\]  
State equation of cabin's total pressure is written as:  
\[\dot{P_{t}^{\rm cabin}}=\frac{R_{a}T_{c}}{M_{air}V_{c}}(w_{\rm O_{2}}^{\rm cabin }+w_{\rm N_{2}}^{\rm cabin}+w_{\rm CO_{2}}^{\rm cabin}) \tag{15}\]  
The core index reflecting the state of the core is the electrolytic efficiency of the core, which can be reflected by the oxygen and hydrogen production. Due to its small volume and complex internal structure, it is impossible to install sensors to measure the oxygen and hydrogen production. However, the electrolytic core's oxygen production and hydrogen production can be used as state variables of the system. The hydrogen and oxygen production volume of the electrolytic core can be obtained through the establishment of the state equation of oxygen production and hydrogen production and the design of the system state observer. The established equations of state for oxygen production and hydrogen production are as follows:  
\[\dot{P_{H_{2}}^{\rm E}}=\frac{R_{a}T_{c}}{M_{H_{2}}(V_{s}+V_{e})}(w_{H_{2}}^{ \rm E}-w_{H_{2}}^{\rm cabin}) \tag{16}\]  
\[\dot{P_{O_{2}}^{\rm E}}=\frac{R_{a}T_{e}}{M_{\rm O_{2}}V_{e}}(w_{\rm O_{2}}^{ \rm E}-w_{\rm O_{2}}^{\rm cabin}) \tag{17}\]  
where \(V_{e}\) = 1.29 m\({}^{3}\);\(V_{s}\) = 0.29 m\({}^{3}\). According to Figure 4, Valve_O2 and Valve_H2 are back pressure valves, and the \(w_{\rm O_{2}}^{\rm cabin}\) and \(w_{H_{2}}^{\rm cabin}\) in Equations (16) and (17) are as follows:  
\[w_{\rm O_{2}}^{\rm cabin}=\sqrt{2\rho_{\rm O_{2}}}C_{d1}A_{e1}\beta_{1}\sqrt{P_ {O_{2}}^{\rm E}-P_{t}^{\rm cabin}} \tag{18}\]  
\[w_{H_{2}}^{\rm cabin}=\sqrt{2\rho_{H_{2}}}C_{d2}A_{e2}\beta_{2}\sqrt{P_{H_{2}}^ {\rm E}} \tag{19}\]  
Figure 4: The simplified workflow sketch of EOGS. where \(C_{d1}=0.01\); \(C_{d2}=0.002\); \(A_{01}=0.08\); \(A_{02}=0.01\)\(\beta_{1}=1\); \(\beta_{2}=1\). According to [PERSON]'s law, the production of oxygen and hydrogen can be obtained as follows:  
\[w_{O_{2}}^{E}=M_{O_{2}}\frac{In_{c}}{2 Fz} \tag{20}\]  
\[w_{H_{2}}^{E}=M_{H_{2}}\frac{In_{c}}{Fz} \tag{21}\]  
where \(n_{c}=24\); \(F=9.65\times 10^{4}/3600\) Ah/mol; \(z=2\). Selecting \(\left[\dot{P}_{O_{2}}^{cabin},\dot{P}_{t}^{cabin},\dot{P}_{H_{2}}^{E},\dot{P}_ {O_{2}}^{E}\right]^{T}\) as the state variables of the system, i.e., \(x=\left[\dot{P}_{O_{2}}^{cabin},\dot{P}_{t}^{cabin},\dot{P}_{H_{2}}^{E},\dot{P }_{O_{2}}^{E}\right]^{T}=\left[x_{1},x_{2},x_{3},x_{4}\right]^{T}\), the state equation of the system can be obtained as follows:  
\[\left\{ \begin{array}{l}\dot{P}_{O_{2}}^{cabin}=\frac{R_{4}T_{c}}{M_{O_{2}}V _{c}}w_{O_{2}}^{cabin}\\ \dot{P}_{t}^{cabin}=\frac{R_{4}T_{c}}{M_{H_{2}}V_{c}}(w_{O_{2}}^{cabin}+w_{N_ {2}}^{cabin}+w_{CO_{2}}^{cabin})\\ \dot{P}_{H_{2}}^{E}=\frac{R_{4}T_{c}}{M_{H_{2}}(V_{c}+V_{c})}(w_{H_{2}}^{E}-w_ {H_{2}}^{cabin})\\ \dot{P}_{O_{2}}^{E}=\frac{R_{4}T_{c}}{M_{O_{2}}V_{c}}(w_{O_{2}}^{E}-w_{O_{2}}^ {cabin})\end{array} \right.