The autonomous displacement and displacement measurement functions of the maglev ruler are performed by the mover core. The magnetic levitation ruler can serve as a viable alternative to the linear measurement system of a coordinate measuring machine. The stability of the four magnetic fields in air gaps and the levitation position of the maglev ruler is one of the key factors for the stability of the thrust force on the power core, and it is also one of the key factors for ensuring the precision of the maglev ruler. There is cross-coupling between the two ends of the mover core of the maglev ruler, resulting in a strongly coupled, nonlinear, multi-input and multi-output system for the levitating system of the maglev ruler. This paper establishes a mathematical model for the levitating system of the maglev ruler and designs a levitating control system for the maglev ruler based on an active disturbance rejection control algorithm to achieve decoupling and disturbance suppression. Through simulation analysis and experimental testing of the levitating system with starting and disturbance, it is proved that the levitating control system of the maglev ruler has good dynamic characteristics, static characteristics, and robustness.

This paper is centered around the autonomous displacement of the maglev ruler system, with the core objective of optimizing the performance of its horizontal control system. The horizontal positioning precision of the maglev ruler’s mover core plays a crucial role in determining the survey accuracy. Moreover, its horizontal system exhibits distinct nonlinear and strongly coupled characteristics. Initially, a mathematical model is meticulously established based on the principles of magnetic circuits and dynamics. By analyzing the relationship between the Ampere force and the coil current, and constructing the dynamic equations, it is clearly demonstrated that this system belongs to a nonlinear and strongly coupled type with two inputs and two outputs. Subsequently, the active disturbance rejection control algorithm is employed to address the decoupling issue, and a novel differential tracker, SYSTD, is designed. SYSTD is constructed using specific elementary functions. Through rigorous theoretical derivation, its favorable stability is verified. The basis for parameter selection is obtained through phase-plane analysis, and a detailed tuning method is provided. Additionally, a sensor-less control technology is proposed, where survey coils are wound along the horizontal control coils to estimate the position of the mover core. The simulation and experimental results indicate that the improved system showcases excellent performance. In the simulation, the positioning accuracy can reach ±5 μm, while, in the experiment, the control accuracy can achieve ±2 μm. It can effectively realize decoupling control and possesses good dynamic, static characteristics, as well as remarkable robustness. This research paves the way for the practical application of the maglev ruler system in fields such as coordinate survey.