The single axis linear displacement measurement system of CMM is composed of grating ruler, servo motor and linear motion mechanism. Although the measuring accuracy of grating ruler is high, the accuracy of servo motor and linear motion mechanism is low. Therefore, the complex structure limits the measurement accuracy of the linear displacement measurement system. This paper introduces a novel linear displacement measurement system named magnetic levitation ruler. According to the working principle of grating ruler and the characteristics of magnetic levitation technology, the magnetic circuit design and structural design of magnetic levitation ruler are completed in this paper. The mover core of the magnetic levitation ruler is in the stable working magnetic field provided by the stator yoke. The horizontal control coil wound on the mover core can obtain more stable ampere force to improve the control accuracy of the mover core displacement. Therefore, the mover core can be moved in step mode, and the length of each step is fixed. Each step is the minimum scale of the magnetic levitation ruler. Therefore, the mover core can implement displacement measurement while moving in a linear motion. This paper analyzes the working principle of levitation, horizontal motion, and displacement measurement of magnetic levitation ruler, and determines the structural materials and parameters of magnetic levitation ruler with the help of finite element analysis software. The simulation results show that the levitation force of the magnetic levitation ruler is proportional to the current passing through the levitation coils, and the thrust of the horizontal control coil is less disturbed by the magnetic field. Compared with the linear displacement measurement system with rotational servo motor or permanent magnet synchronous linear motor as the core, the magnetic levitation ruler has stable magnetic field, strong controllability, high integration, and is easier to achieve high-precision control.

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.

The autonomous displacement and displacement measurement functions of the maglev ruler are performed by the mover core. The stability of the four magnetic field 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 ADRC 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.