  This study proposes a one-shot data-driven tuning method for a
fractional-order proportional-integral-derivative (FOPID) controller. The
proposed method tunes the FOPID controller in the model-reference control
formulation. A loss function is defined to evaluate the match between a given
reference model and the closed-loop response while explicitly considering the
closed-loop stability. A loss function value is based on the fictitious
reference signal computed using the input/output data. Model matching is
achieved via loss function minimization. The proposed method is simple and
practical: it needs only one-shot input/output data of a plant (no plant model
required), considers the bounded-input bounded-output stability of the
closed-loop system from a bounded reference input to a bounded output, and
automatically determines the appropriate parameter value via optimization.
Numerical simulations show that the proposed approach facilitates good control
performance, and destabilization can be avoided even if perfect model matching
is unachievable.
