A fractional-order fuzzy PID controller has been extensively
studied by Das et al. [20,22,23] which is a combination of fractional
fuzzy PD and fuzzy PI controllers. On this basis, we designed an
AFFFOPID controller for PSHURS and its structure is shown in
Fig. 1. In Fig. 1, the error between x and xc and its FO differential
are the input of FLC. {Ke, Kd} are the input scaling factors (SFs)
and {KPI, KPD} are the output SFs. And in order to improve the regulation
rate of controller, error tracking element of guide vane
opening has been added into the proposed AFFFOPID method. Furthermore,
the integer order rate of the error at the input to the FLC
is replaced by its fractional differential order l. Also, the FLC output
is fractionally integrated with integral order k which can be
tuned to meet the specifications of designer. For Fig. 1, the control
law of this controller is given by formulas (1) and (2).