Modified Modeling and Internal Model Control Method of Thrust Ripples in PMLSMs for Ultraprecision Air-Bearing Linear Feed Systems

With the aim of attenuating thrust ripples in ultraprecision air-bearing linear feed systems, a simple and effective internal model control (IMC) system is herein presented based on a modified modeling and identification method of permanent magnet linear synchronous motors (PMLSMs). First, flux linkage equations were used to describe the volt–ampere characteristics of PMLSMs and provide a thrust expression in a differential form based on the principle of virtual work. Then, an analytical formula was obtained through derivation based on the condition of field-oriented control. On this basis, an IMC compensator was designed using an inverse model to attenuate nonlinear thrust effects, and an extended Kalman filter (EKF) was adopted to estimate the actual current in an analog linear amplifier. The boundedness of the nonlinear system was analyzed based on the convergence condition; furthermore, the stability of the proposed IMC compensator with EKF could be guaranteed. Then, an accurate model and thrust parameters were obtained using an identification experiment on an air-bearing linear platform driven by a linear analog amplifier. To demonstrate the coupling effect of current on thrust and confirm the effectiveness of the proposed method, both simulations and experiments were performed at a uniform velocity under extra loads of different weights; then, an extended state observer (ESO) was introduced as a comparative method. Finally, the results of the following error indicated that the proposed method demonstrated improved performance in terms of overcoming the influence of nonlinearity and that it results in smooth velocities in steady states.