A Servo Control Algorithm Based on an Explicit Model Predictive Control and Extended State Observer with a Differential Compensator

Positioning servo systems utilizing permanent magnet synchronous linear motors (PMSLMs) are conventionally governed by cascaded P-PI controllers, which, despite their simplicity and robustness, suffer from limited tracking and anti-disturbance performance due to their single-degree-of-freedom (1-DOF) structure. This paper introduces a novel two-degree-of-freedom (2-DOF) control algorithm that integrates explicit model predictive control (EMPC) with a differential-compensated extended state observer (DCESO). The EMPC framework leverages position and velocity as state variables, eliminating the need for integral terms and thereby enhancing dynamic response. By employing an offline optimization approach, a control law is explicitly formulated to handle system constraints while minimizing online computational overhead. Additionally, a velocity feedforward term derived from the MPC framework is incorporated to further reduce tracking errors. To bolster disturbance rejection, the proposed DCESO introduces a differential compensator that mitigates the low-pass effects inherent in traditional ESOs, thereby improving estimation dynamics. Experimental results demonstrate that the proposed method significantly outperforms the conventional P-PI controller, increasing the position loop bandwidth from 147 Hz to 208 Hz and markedly enhancing anti-disturbance performance. The algorithm’s low online computational demand makes it highly suitable for industrial applications.