Supplementary Note 12. Correction of mass flow

\(\varPsi \left( p_{high},p_{low} \right) \) is the mass flow when the valve is fully open. Actually, the response time (open/close time) cannot be ignored if the system generates high-frequency actions, especially when we employ cheap commercial solenoid valves. The actual mass flow  should be corrected by a time-based open degree factor \(\varGamma(t)\) . According to Equation (5)