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Article Abstract
A three-degrees-of-freedom measurement system based on the Faraday effect is proposed for simultaneously measuring two-dimensional straightness errors and their position. Thanks to the Faraday effect of the Faraday rotator, the direction of a linearly polarized beam can be changed by 90° when the linearly polarized beam passes through the same Faraday rotator back and forth twice. A novel optical configuration is designed that can integrate the interferometry and position-sensitive detection technology ingeniously and put their advantages together. The measurement principle is described in detail. The influence of angle error of the semitransparent mirror on straightness measurement is discussed. To verify the feasibility of the proposed system, the experimental setup for measuring three degrees of freedom was constructed, and a series of experiments were carried out.
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Article Synopsis
- This paper introduces a hybrid model predictive control (HMPC) method designed for hybrid systems using a mixed logical dynamical (MLD) framework, focusing on precise setpoint tracking and disturbance robustness.
- The HMPC algorithm includes a three degrees-of-freedom (3DoF) tuning technique and anticipates setpoints and disturbances to improve control performance and reduce effort, while incorporating slack variables to maintain feasibility.
- The effectiveness of the HMPC method is showcased through three case studies: production-inventory systems, behavioral interventions for physical activity, and epidemic/pandemic management, demonstrating its adaptability to complex dynamics and uncertainty.