# What does this "inverse" peak mean? (step function)

I identified my system and now I am trying to tune PI regulator since I think I do not need D.

I came across this graph while Matlabing and I do not know what does it mean.

I am using pidtune() to get my P and I values. (I think computation is all correct, I made model in simulink to confirm). Anyway see my picture and arrow is pointing at what I do not understand. Why is my system going below zero first?

It is supposed to be water flow regulator.

Transfer function: $$\frac{-0.311s + 0.05548}{s^2 + 0.06882s + 0.0007626}$$

Continuous-time PI controller in parallel form: $$K_p + K_i * \frac{1}{s}$$

With $K_p = 0.256$, $K_i = 0.000342$

• Are you absolutely sure your system is starting at the zero state? (including 1st state derivatives and controller integrator) May 18 '14 at 18:57
• Yes there is no point in starting something like water flow controller/system in minus values. May 18 '14 at 21:47
• Is it coming from the -0.311 s in your transfer function?
– Ian
May 18 '14 at 22:13
• I think its because I identified 1st order system as 2nd order system (arx command in Matlab). May 22 '14 at 17:36

What you seem to be concerned about is the well known nonminimum-phase effect of the zero $s_0=0.05548/0.311$ in the right half of the s-plane.

You should first ask yourself whether this lag has a physical interpretation in the context of your system. Many physical systems expose such a dynamics, but here it might also depend on how you carried out the identification.

Then, to properly account for such a lag, if it really exists and is not introduced by the identification process, you should make use of proper techniques. For example, look here.