How to work out First order Plus Dead Time (FOPDT) model for my process on Simulink - see attachment please, I need dead time alpha and time constant tau

Hi all, I have attached a graph from my Simulink. There is step, which is my setpoint, and there is a curve of high order. I want to produce a First order Plus Dead Time (FOPDT) model using the transfer function G = (Kp*exp(-alpha*s))/(tau*s + 1). I already know my Kp = 1, I want to know how to calculate the dead time alpha and the time constant tau. Thank you in advance.

[Birdman]

Well, in the figure the negative overshoot you see does not mean dead time. It means that there is a positive zero in the root locus. But if you want to express that part with a dead time, that is also fine.

Answer 1

[Birdman]

Hi hoomsn,

I tried to extract approximate values from your figure, therefore the values may contain errors but the important thing is to give you the idea about how to implement it. Firstly, to decide dead time, you need to decide the difference between the start of input and output, which is 3.6-1=2.6 seconds difference(approximate value for output start, at least what I can see). Therefore,

alpha=2.6

Secondly, tau is decided by the time where the output settles 63% of its final value, which is in this case approximately 6.3-2.6=2.7 seconds. Therefore,

tau=2.7

You will see an implementation of it in Simulink. Hope this helps. Let me know if it works for you.