# Simulating liquid level in a tank

N

I am trying to simulate liquid level in tank with incoming multiphase flow and out going liquid from the bottom of the vessel. The level is being controlled by the control valve. I need to design a PD controller for this purpose. 31.75/s(s+2.5)(s+0.5)

You can see there is an integrator in the open loop and theortically it shouldn't give any steady state error the close loop function obtained from this openloop with feedback is:

5.286
----------------------------
The step response of the close loop function shows a unbounded system; any comments on it? Should we include 31.75 the numerator of the open l
s^3 + 3 s^2 + 1.25 s + 31.72

loop in the calcualtion of the close loop?

I developed a PD compensator using graphical root locus techniques using the following time doima specification overshoot 10% settling time 10 second. The desired pole from this specification is -2.-+2,76i, which gives from gemoetry the position of the required zero as -1.24. Using this zero does not give the required specification so I used z=-.3 (any comments on it?) I am also perplexed about the calculation of the Kd: from graphical root locus method I have used following formula:

Kd= product of vector length of finite pole to desire pole/(productor of vector length of zero to desired pole * 31.75)

The obtained PD compensator is:
0.2866 s + 0.08599 and coreesponding open loop PD compensator is:

9.09 s + 2.727
--------------------
s^3 + 3 s^2 + 1.25 s

The close loop is obtained as:

1.515 s + 0.4545
-----------------------------
s^3 + 3 s^2 + 10.34 s + 2.727

This gives settling time 3 second overshoot is 16 % but steady state is .167 i.e about 99% steady state error.