Transfer function for nonlinear hydroelectric tank with square root term

[hdp12]

TL;DR

Need help with finding a transfer function and subsequent equations for a hydroelectric tank I am trying to control with a control system.

Hello there, please help if you are able..

So we have a tank with input volumetric flow and output volumetric flow
The system is controlled by the height of water in the tank

h(t) = h_des + (√h(t))*(-A₂*(√2g) / A₁) - h'(t)

I am trying to find a transfer function for this system but I do not know what to do with the square root aspect of the function. There is no viable laplace transform for it and I don't know what to do

I would be extremely grateful if someone with more knowledge in this subject could help me,
Thank you

 

[anorlunda]

Transfer functions are for linear systems. Linearize the square root about a point. Now you can make a transfer function valid for small perturbations around that point.

 

[berkeman]

So we have a tank with input volumetric flow and output volumetric flow
The system is controlled by the height of water in the tank

h(t) = hdes + (√h(t))*(-A2*(√2g) / A1) - h'(t)

How did you come up with this h(t) function? Is it based on your sensor and actuator? It seems a bit complicated to me. Why not use a bang-bang sensor and actuator to control the fluid height in the tank?

 

[berkeman]

How did you come up with this h(t) function? Is it based on your sensor and actuator? It seems a bit complicated to me. Why not use a bang-bang sensor and actuator to control the fluid height in the tank?

Wait, is this a homework question? If so, we need to transfer this thread to the Homework Help forums...