Abstract: For various kinds of variable step-size adaptive filtering algorithms,this paper presents two novel adaptive inverse control systems based on the variable step-size X-filtered,ε-filtered LMS filtering algorithms and feedback com-pensation,and the control systems have fast convergency speed and good robustness.Variable step-size adaptive filtering algorithm can provide the adaptive inverse control(AIC) system with fast convergency speed and small error,and improve the control accuracy.Feedback compensation can counteract the direct current zero frequency drift of the AIC system.The computer simulation results indicate that the system based on these adaptive algorithms is of fast convergency speed,small error and good ability to cancel noises.