Typical PID tuning objectives include:
Closed-loop stability — The closed-loop system output remains bounded for bounded input.
Adequate performance — The closed-loop system tracks reference changes and suppresses disturbances as rapidly as possible. The larger the loop bandwidth (the frequency of unity open-loop gain), the faster the controller responds to changes in the reference or disturbances in the loop.
Adequate robustness — The loop design has enough gain margin and phase margin to allow for modeling errors or variations in system dynamics.
MathWorks® algorithm for tuning PID controllers meets these objectives by tuning the PID gains to achieve a good balance between performance and robustness. The algorithm designs an initial controller by choosing a bandwidth to achieve that balance, based upon the open-loop frequency response of your linearized model. When you interactively change the response time, bandwidth, transient response, or phase margin using the PID Tuner interface, the algorithm computes new PID gains.