**EDIT:forgot to show plant
As the question says my pole-zero map for a closed loop system with negative unity feedback appears to indicate that I should expect an critically damped response but when I subject my system to a unit step it is oscillatory. Can anyone offer an explanation or point me in the direction of releveant literature? Thanks
I have a model plant, G, with a time delay (dead time)** of -1 seconds which is defined as:
G = (2*exp(-1*s))/(3*s+1);
**Just as a side note, taking away the dead time has the same final result.
I have the following Ziegler-nichols tuning parameters:
Kp = 1.8;
Ti = 3;
I have made the following PI controller for the plant:
controller = pidstd(Kp,Ti)
I have calculated the open and closed loop system as follows:
gol = controller*G;
gcl = feedback(gol,1);
The PZ map for the closed loop system is:
Based on the PZ map where there is a pole-zero cancellation at -0.333, leaving a single real pole at -1.2 and a damping of 1, I am expecting a critically damped reponse with no oscillations.
However when I plot a step response I get the following: