# Control System: offset issue with a simple valve model

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

The resulting transfer function is: $$G(s)=\dfrac{0.13}{3s+1}$$

It is obvious that they considered the valve as a first order transfer function.The gain $K_p$ was calculated by: $\dfrac{1.6\text{ kg/s}}{15-3\text{ psi}}=1.6/12=0.133$. Time constant = 3 seconds and that's it.

But the problem is: shouldn't a step input of 15 psi output a signal (1-exponential) with a final value of 1.6 kg/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:

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 yellow waveform is the waveform 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?

If necessary, here's the pdf file.