Abstract:

Displacement sensors are widely employed in precision machining and metrology, serving as pivotal components for real-time position detection. In practical applications, displacement sensors typically undertake dynamic measurement tasks, and dynamic error, as a critical metric for assessing dynamic measurement accuracy, directly impacts the stability, precision, and robustness of the measurement system. In recent years, scholarly attention has increasingly focused on dynamic errors.

Both domestic and international scholars have conducted a series of in-depth studies on methods to mitigate dynamic errors. Currently, strategies for suppressing dynamic errors primarily involve control methodologies such as adaptive control, model predictive control, and fuzzy control, as well as compensation methods like harmonic compensation, genetic algorithms, and posterior error fitting algorithms. Among these, compensation methods have been widely applied due to their simplicity and efficiency. However, conventional compensation methods encounter challenges related to real-time performance. These methodologies necessitate data collection, transmission, and processing before implementation, causing delays at each stage. Consequently, delayed compensation actions hinder real-time effectiveness, resulting in suboptimal compensation outcomes. To address the real-time challenges associated with compensation, predictive technology, commonly utilized in servo control, is employed. Although predictive technology finds extensive application in various fields, its integration into displacement sensors remains limited.

The time-grating displacement sensor, as a novel variant, has witnessed extensive adoption. While extensive research has advanced the static measurement accuracy of time-grating displacement sensors, limited attention has been given to dynamic measurement accuracy. This paper proposes a real-time compensation method for the measured values of time-grating displacement sensors by predicting dynamic errors. The approach is analyzed in conjunction with the time-grating angular displacement sensor. A dynamic error mathematical model is built based on the characteristics of the time-grating angular displacement sensor, and the unscented Kalman filtering algorithm is applied to construct a dynamic error prediction model. Utilizing this model, the dynamic error of the time-grating displacement sensor at the next moment is predicted and employed as a real-time compensation value for the subsequent measurement. The proposed method’s feasibility and effectiveness are verified through simulation software and a constructed time grid servo motor testing platform. Under constant motor speeds of 5 revolutions per minute (r/min), 50 r/min, and 200 r/min, as well as uniform accelerations of 12 000 revolutions per minute squared (r/min2), and variable accelerations ranging from low to high (1 000 r/min2, 5 000 r/min2, and 12 000 r/min2), the dynamic error of the sensor is reduced by approximately 54.89%, 67.37%, 80.13%, 59.29%, and 47.09%, respectively. Real-time compensation for dynamic errors through prediction significantly enhances the dynamic measurement accuracy of sensors, exhibiting superior compensation effects at higher speeds. In comparison to traditional harmonic compensation methods, this approach demonstrates superior compensation efficacy and higher real-time performance in variable speed conditions.