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Introduction
In past decades, a variety of electronic throttle (ET) control methods, which have great significance on drivability of automobiles and help reduce fuel emissions, have been proposed. Deur et al.[1] proposed an refined proportional-integral-derivative (PID) control approach for the ET valve considering compensation of friction and limp-home effects. However, the guidance rules of how to choose parameters of the compensator were not given. Based on the aforementioned work, Yuan and Wang[2] put forward a neural network-based PID controller, realizing precision control of the ET valve with adaptive updating of the PID parameters. However, the effect of the torque of the return spring is ignored. Subsequently, Sheng and Bao[3] carried out a fractional-order fuzzy-PID control scheme, wherein optimal control parameters are found through the fruit fly optimization algorithm (FOA). Yet, the gear backlash was ignored in this approach, degrading the control performance. Furthermore, Panzani et al.[4] designed an ET controller including linear part and hybrid feedforward-feedback friction compensator to address the control of ET body for ride-by-wire application in sport motorcycles.
On the basis of the nonlinear control, considering that the angular velocity of ET is not measurable, Pan et al.[5] investigated variable structure control based on a sliding mode observer to estimate the angular velocity. However, it only considered the friction torque caused by Coulomb friction, while the stick-slip friction was ignored. Lately, Hu and colleagues[6],[7] proposed a reduced-order observer-based backstepping controller for ET, where a guideline for selection of control parameters was given through the input-to-state stability (ISS) analysis. Unfortunately, though the disturbance was taken into account to show the ISS property, it was not handled directly in the controller design. Therefore, the disturbance would result in the performance deterioration. Recently, Li et al.[8] proposed an extended state observer (ESO)-based backstepping sliding mode control (SMC) approach for the ET valve. Especially, an ESO was designed based on the ET nonlinear model to estimate the throttle opening angle change and uncertainty of ET simultaneously and then the backstepping sliding mode controller was developed to improve the control performance. However, this method only considered the throttle opening angle error while ignoring the throttle opening change error in the feedback signals. Subsequently, Li et al.[9] put forward...