In the context of electro-magnetic suspension(EMS)control systems,the effective extraction of gap and gap differential signals stands as a pivotal challenge,directly influencing the system's control performance.To enhance the quality of sensor signal extraction,an enhanced non-linear tracking differentiator(TD)has been ingeniously devised to address the intricacies of control functions,convoluted parameter configurations,and the issue of chattering in the output.Primarily,a novel tracking differentiator has been conceived by introducing the inverse square root function and the terminal attractor function.Subsequently,the stability theory has been employed to validate the convergence of the improved tracking differentiator.Furthermore,the frequency domain characteristics have been scrutinized through a sweep frequency test,elucidating the parameter tuning principles of the tracking differentiator.Conclusively,a series of closed-loop control system simulations and physical verifications have been executed. The results conclusively demonstrate the pronounced advantages of the improved square root unit tracking differentiator (ISRU-TD)in terms of steady-state error reduction.The steady-state error of the output position signal has been reduced by a noteworthy 92.58%,in comparison to ATD,by 18.18%when compared to Fhan-TD,and by 3.7%in comparison to HSTD. Furthermore,ISRU-TD substantially reduces the adjustment time of the output position signal,exhibiting reductions of 38.68%compared to ATD,61.99%compared to Fhan-TD,and 58.06%compared to HSTD.This underscores its exceptional capability in signal tracking and noise suppression.