I am posting a control system problem here because of this post reference.
The blue line is output and the pink line is input which was applied during specific time intervals. This dataset has been obtained from a machine that has an existing manually tuned the PID controller.
I want to make an LQI or more perfectly tuned PID controller using bode plots. However, to do that, I will have to identify the transfer function or corresponding state space model.
What is the detailed procedure to obtain the transfer function from the above data set (because this data has been obtained from a machine which already has a manually tuned PID controller controlling it)? The manually tuned values are $K_p=2.2, K_i=0.01, K_d=2$.
I used a system identification application and obtained a state space model with a $75 \%$ fit. I tried implementing a PID controller for it and it required large $K_p, K_d, K_i$ values for the required design parameters.
The gain values used were
These cannot be implemented on a system since it has comparatively very low $K_p, K_i, K_d$ values (manually tuned).