This paper presents an original model reference adaptive fractional-order proportional integral derivative (MRAC-FOPID) controller for the stabilization of the idle speed system in an internal combustion engine under different external load torques. The MRAC-FOPID controller is developed by aligning the changing of FOPID controller’s five parameters with a cost function’s negative gradient direction. Numerical simulations are presented and show that the proposed MRAC-FOPID controller uses 49% more control effort to achieve 72% and 40% more reductions in the relative integral squared error (RISE) and relative integral time absolute error (RITAE), respectively, compared to an optimized model reference adaptive proportional integral derivative (MRAC-PID) controller. Furthermore, the MRAC-FOPID controller is found to have better robustness than other two previously published optimal controllers, with only a 3.07% relative change in RISE when facing variable disturbance. This work also highlights a novel Matlab/Simulink based implementation of the adaptively-varying-order derivative operators, which cannot only be extended to the design of other adaptive fractional-order controllers but may also facilitate hardware realization of the MRAC-FOPID controller in real idle speed systems.
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