Problem with PID tuning
Please note the following:
As you know, the PI controller is responsible in modifying the steady state response. That is improving the steady state values and settling time. You are simply adding a pole at the origin.

On the other hand, the PD controller will help you in improving the transient response. That is overshoot, rise time and peak time.

Now it is important to remember that adding a PI controller will 'usually' increase the order of the system which will cause a change in the previous steady state value.

Similarly, adding PD controllers will change the transfer function of your original system due to exposing the system to a zero. This means that the root locus 'if plotted' will be different.

Therefore; there will always be a compromise -trade off-. The best you can do is add margins of errors or inequality ranges for accepted values for both steady state and transient parameters.

Long story short, adding any controller to the system to improve the steady state will effect the transient and vice verse.