I am posting a control system problem here because of this post reference.

Question: I have input and output datasets. These are graphically shown below.

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 $K_p=2.2, K_i=0.01, K_d=2$.

My attempt

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).

I am posting a control system problem here because of this post reference.

Question: I have input and output datasets. These are graphically shown below.

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 $K_p=2.2, K_i=0.01, K_d=2$.

My attempt

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).

I am posting a control system problem here because of this post reference: https://meta.stackexchange.com/questions/207787/is-there-a-control-theory-site

Question: I have input and output datasets. This can be graphically shown below,

Blueline is output, Pink line is input which was given a specific time. This dataset has been obtained from a machine that has manually tuned the PID controller. I want to make an LQI or more perfectly tuned PID controller using bode plots. But for that, I will have to identify the Transfer function/ StateSpace Model. What would be the detailed procedure to obtain the transfer function from this data set, because this data has been obtained by a machine which already has a manually tuned PID controller? Please guide me about it. The manually tuned values are Kp=2.2, Ki=0.01, Kd=2.

My Try:

I used a system identification app and obtained a State-Space Model with fit % 75. I tried making a PID controller for that and it required large Kp Kd KI values for desired requirements.

and my gain values were

Which cannot be implemented on a system as it has very low Kp KI Kd values(manually tuned).

I am posting a control system problem here because of this post reference.

Question: I have input and output datasets. These are graphically shown below.

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 $K_p=2.2, K_i=0.01, K_d=2$.

My attempt

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).