Controling mirror movement with piezoelectric stage

[yoavmer]

I am moving a small glued mirror (~10 gram) attached to a piezoelectric stage:
http://www.physikinstrumente.com/product-detail-page/s-330-300700.html
The mirror moves back and forth for a few milliseconds using a PID control loop, the range is about 2mrad.

I want to increase the angular amplitude and maximal speed of that movement, for that I want to tweak the PID coefficients.
1) Can someone tell me using control theory how to calibrate them?
2) The entire system resonant frequency is about 2kHz, should I stay away from it or try to use it?

 

[Illmatic1]

1) The best way to calibrate the PID coefficients is to use a process known as tuning. Tuning involves tweaking the PID coefficients until you achieve the desired behavior. Depending on the type of control system being used, there are several different methods for tuning the PID coefficients. Some common methods include Ziegler-Nichols, the Tyreus-Luyben, and the Cohen-Coon methods. Each of these methods has its advantages and disadvantages, so it is important to research which one is best for your particular application before implementing it.2) It is usually best to stay away from the system's resonant frequency when tuning a PID controller. This is because the controller can become unstable if it is tuned too close to the resonant frequency, leading to oscillations and poor performance. If the system needs to operate close to the resonant frequency, then some additional damping may be required to ensure that the controller remains stable.