Robust speed control of hybrid electric vehicle using fractional order fuzzy PD and PI controllers in cascade control loop

Abstract

In this paper, a novel scheme is proposed for speed control of highly nonlinear hybrid electric vehicle (HEV) having an electronic throttle control system (ETCS) in the cascade control loop. Fractional order fuzzy PD (FOFPD) and fractional order fuzzy PI (FOFPI) nonlinear controllers are developed and used as primary and secondary controllers, respectively in the cascade control loop. These controllers are variable gain fuzzy controllers having an adaptive nature. Their corresponding integral counterpart, fuzzy PD and fuzzy PI controllers are realized by keeping integer order differentiator and integrator in FOFPD and FOFPI controllers. Further, fractional order PD (FOPD) and fractional order PI (FOPI) controllers are implemented by using non-integer order operators in conventional PD and PI controllers. Extensive simulations have been carried out using National Instruments software LabVIEW™ and its add-on tools such as control design and simulation toolkit to perform a comparative study for FOFPD, FPD, FOPD and PD as primary controller and FOFPI, FPI, FOPI and PI as secondary controller for setpoint tracking of speed of HEV. Multi objective genetic algorithm is used to optimize the gains of primary and secondary controllers for minimization of integral of absolute error (IAE), maximum overshoot and settling time. Performances of tuned controllers are further evaluated for tracking of speed profile, disturbance rejection and model uncertainty. It has been observed that combination of FOFPD and FOFPI controllers outperformed rest of the controllers in servo, regulatory and uncertain environment and demonstrate very robust behavior for speed control of HEV.