[Objective] To enhance the control accuracy of the nonlinear flux observer (NFO)-based sensorless control system for permanent magnet synchronous linear motor (PMSLM)

the influence of the inherent end effects in the PMSLM on the motor model parameters is considered and the NFO is redesigned accordingly in this paper. Furthermore

to improve the disturbance rejection capability of the traditional extended state observer (ESO) in PMSLM sensorless control system

a position calculation method employing a variable gain ESO with phase-locked loop (VGESO-PLL) is proposed. [Methods] Firstly

considering the voltage deviation caused by the inherent end effects of the PMSLM during motor operation

a modification to the existing mathematical model was implemented and then the NFO was redesigned. Then

by investigating the impact of ESO bandwidth on position estimation performance

an improved VGESO control method was proposed. This method incorporated a bandwidth variation law driven by the derivative of the estimated speed into the traditional ESO

enabling dynamic adjustment of ESO bandwidth and to enhance the speed observation accuracy under transient conditions. Finally

the characteristic equation of the VGESO was solved by adopting Euler discretization method

and the allowable bandwidth range of the VGESO was determined using the Jury criterion. [Results] Experimental results showed that under operating condition at sudden acceleration from 0.1 m/s to 0.3 m/s

the maximum speed estimation error of the VGESO-PLL was reduced by 8.05% compared to the traditional PLL. Although the maximum speed estimation error was identical to that of ESO-PLL

its speed estimation error exhibited a smaller fluctuation range than ESO-PLL. And under operating condition at sudden deceleration from 0.3 m/s to 0.1 m/s

the maximum speed estimation error of the VGESO-PLL was reduced by 73.1% compared to the traditional PLL and by 37.7% compared to the ESO-PLL. [Conclusion] The restructured NFO in this paper can reflect the influence of the PMSLM end effects. And the proposed VGESO-PLL position calculation method can effectively enhance the speed observation accuracy of the PMSLM under sudden speed change conditions

thereby enhancing the disturbance rejection capability of the VGESO.