Linearization

An air supply for control equipment can consist of a compressor and an air tank, which, among other things, have the purpose of smoothing pressure fluctuations. In the system shown, the container is provided with two identical valves. The container has a volume of V (m3) and contains W (kg of air). During stationary operation, the pressures are P_i0 = 3 atm, P_u0 = 2 atm, and the mass flow is Gi0 = Gu0 = 10 kg / h. It is assumed that the air can be described as an ideal gas and that the mass flow through the valves can be related to the pressure drop across the valves as follows,

G = k * sqrt (deltaP)

Where k is a common constant for the two valves, and P is the pressure drop across the valve. The density of the air, , can be calculated from the ideal gas equation, = P M / (R T) where R = 0.082 m3 atm / (kmol K) T = 300 K (assumed to be constant) M = 29 kg / kmol (molar mass for air)

b) Determine the transfer functions from pi to p and pi to gu (lowercase letters denote deviation variables). Pu can be considered to be constant.

P, V, W Pi, G; PUG