The fractional-order proportional-integral-derivative (FOPID) controller has two more parameters than the integer-order proportional-integral-derivative (PID). Such characteristic makes the controller design more flexible and leads to superior performance. This study proposes a variable coefficient FOPID (VCFOPID) with optimal single step parameters, combining discrete synthesis and variable control parameters. The new algorithm is compared with previous FOPID discrete methods via several examples. Since the energy losses of the single-ended primary-inductor converter (SEPIC) cannot be ignored, the standard models are insufficient and a new model is derived using quantum-behaved particle swarm optimisation. The VCFOPID is applied to the SEPIC and both the effectiveness of the controller and the model are verified experimentally.
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