On PID Controllers for a Complex-Order Fractional Model of an Automotive Injection System

Recent studies have shown that complex-order fractional operators allow for compact modeling with simpler structures and less parameters than models based on integer-order operators and even non-integer real-order operators. This work verifies the usefulness and potential of a complex-order fractional model when used to set parameters of a PID controller regulating the common-rail pressure in the injection system of a compressed natural gas engine. Parameters are derived by a general particle swarm optimization that considers a cost function weighting the performance and robustness measures. Simulation results show the effectiveness of the complex-order fractional model-based PID controller through the response to step references, the rejection of disturbances, the low sensitivity to variations of the injection system parameters.