How can I make a transfer function of a centrifugal pump?

Hello,

I've been looking for a mathematical expression for a transfer function of a dredge pump (centrifugal pump), but I can't find anything usefull (I think). 

I want to use this transfer function in a Simulink model for an automatic controller of the pump (see the attached file for a complete picture of the controller). 

Is it correct that the Q-h characteristics define the transfer function of a dredge pump? I've found that you can calculate these curves with the use of the mechanical energy balance theory, but I'm not sure if this is the good direction to look at for a transfer function to be used in Simulink for a dredge pump. The Q-h curves are available for the given pump.

Is it correct to state that the input of the dredge pump equals rpm (angular velocity and torque) and the output equals pressure?

• For the hydromotor I already found a transfer function using a mathematical expression:

Pin = Q * delta p (flow times pressure difference over the motor)

Pout = T*w (Torque times angular velocity)

As the flow depends of the angular velocity and the displacement, the transfer function for the flow will be (V equals the displacement of the hydromotor)

Q = V * w = V * (d phi/dt) = V*s*t (after Laplace transform)

Transfer function = Output/Input = phi / Q = 1/(s*Vs)

I did the same for the Torque and pressure relationship of the hydromotor:

delta p = T/Vs 

Transfer function = output/input = Vs.

Thus, my total transfer function will be: 1/s*vs * Vs = 1/s..

Could someone help me with this?