Proprietary algorithm developed by MathWorks.
From the "Algorithms" section here : 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 first frequency at which the open-loop gain is unity), the faster the controller responds to changes in the reference or disturbances in the loop.
Adequate robustness — The loop design has enough phase margin and gain margin to allow for modeling errors or variations in system dynamics.
The MathWorks algorithm for tuning PID controllers helps you meet these objectives by automatically tuning the PID gains to balance performance (response time) and robustness (stability margins).
By default, the algorithm chooses a crossover frequency (loop bandwidth) based upon the plant dynamics, and designs for a target phase margin of 60°. If you specify the crossover frequency using wc or the phase margin using pidtuneOptions, the algorithm computes PID gains that best meet those targets.
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