With the development of optoelectronic information technology, high-performance optical systems require an increasingly higher surface accuracy of optical mirrors. The fast tool servo (FTS) based on the piezoelectric actuator is widely used in the compensation machining of high-precision optical mirrors. However, with the low natural frequency of mechanical structures, hysteresis of the piezoelectric actuators, and phase delay of the control systems, conventional FTS systems face problems such as a low working frequency and a large tracking error. This study presents a method for the design of a high-performance FTS system. First, a flexure hinge servo turret with a high natural frequency was designed through multi-objective optimization and finite element simulations. Subsequently, a composite control algorithm was proposed, targeting the problems of hysteresis and phase delay. The modified Prandtl–Ishlinskii inverse hysteresis model was used to overcome the hysteresis effect and a zero-phase error tracker was designed to reduce the phase error. The experimental results reveal that the tracking error of the designed FTS system was <10% in the full frequency range (0–1000 Hz).

The accuracy of traditional measuring machines is affected by the measuring range and sensitive geometric errors, and it is not possible to combine large caliber and high-precision measurements. This study proposes a differential geometric error-weighting method for designing a high-precision, large-diameter measuring machine. The machine utilized a zero-Abbe arm structure and applied the rigid body theory and small-angle hypothesis to model geometric errors. Weights were calculated for 23 geometric errors, identifying eight sensitive ones. A picometer-precision laser interferometer (quDIS) with a theoretical positioning accuracy of 0.2 nm/mm and standard flat rulers are used to ensure highly accurate positioning of the Y-axis/Z-axis of the measuring platform and reduce the straightness of both axes by approximately 75%, with radial and axial runout of the rotary table under 100 nm. The development and design method of the high-precision measuring machine proposed in this study is applicable to large-diameter high-precision flexible measurement, and the accurate control of measuring machine movement accuracy is realized by calculating the geometric error weights.

On-machine measurement is a highly effective approach for enhancing machining accuracy and efficiency. A critical factor influencing the accuracy of on-machine measurements is the straightness error of the linear guideway. However, this error is significantly affected by environmental factors such as temperature, vibration, and gravity deformation. To improve the measurement accuracy of machine tools, this study investigates the impacts of these factors on straightness errors and proposes an innovative separation and compensation model for linear guideway straightness. A thermo-mechanical coupling simulation is employed to establish a model that quantifies the influence of thermal errors on straightness. The results demonstrate that thermal gradients cause the straightness error to bend to varying degrees, depending on the temperature distribution. Furthermore, a vibration error model is developed, revealing that the vibration period is approximately twice the ball diameter. Notably, vibration errors can be effectively mitigated using a band-stop filter to eliminate the corresponding frequency components. The study also addresses the effect of gravity deformation, comparing the deformation under different support conditions, highlighting the significance of precise support positioning. Through experimental validation of the straightness error separation and compensation model, it is shown that the straightness error of a conventional linear guideway can be reduced by 95%, and the compensated straightness error is less than 0.2 μm. This novel approach not only improves the accuracy of on-machine measurement but also provides valuable insights for optimizing machine tool performance under dynamic operating conditions.