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:
- 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?
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 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?