# Control System: Model a simple flow valve

I was reading a paper about a Controller Design for Temperature Control of Heat Exchanger and I couldn't understand how to model the valve used in the system.

No need to read the paper as I will wrap up the whole issue:

Given:

• capacity of control valve is 1.6kg/sec
• time constant is 3 sec
• valve input is pressure varying from 3 to 15 psi

The resulting transfer function is:

It is obvious that they considered the valve as a first order transfer function.The gain Kp was calculated by: (1.6kg/sec)/(15-3)psi=1.6/12=0.133. Time constant=3 seconds and that's it.

But the problem is: shouldn't a step input of 15psi output a signal (1-exponential) with a final value of 1.6kg/sec. But that transfer function won't actually output that. It still needs some kind of a shift. So Am I missing something? Is the model wrong?

I also simulated the transfer function response with MATLAB SIMULINK along with a suggested alternative that probably solve the offset thing:

The resulting waveform:

zoomed in near time=0seconds:

• The yellow waveform is the input step function
• The blue waveform is the output of the transfer function of the valve according to the paper.
• The red waveform is the waveform of the transfer function with an offset.

• problem with the blue waveform: wrong final value.
• problem with the yellow waveform: starts from a negative value (-0.4 kg/sec)

So what is the correct model?

The paper is a bit sloppy about transfer functions. If $G_V$ is the transfer from function from control pressure to flow, then it needs an offset. Step response should be measured for a step from 3 to 15 psi.