Research on Sinusoidal Error Compensation of Moiré Signal Using Particle Swarm Optimization

Abstract

In this paper, the sinusoidal error compensation method based on particle swarm optimization (PSO) is researched to reduce the subdivision precision loss caused by sinusoidal error in a grating moiré signal. On the basis of the principle of arctangent subdivision of a grating moiré signal, the subdivision error caused by sinusoidal error is quantitatively analysed. In view of the sinusoidal error compensation method, the signal compensation method involves complex calculations and occupies many resources; therefore, a sinusoidal error angle compensation method is proposed. The principle of the sinusoidal error angle compensation method based on the PSO algorithm is explained in detail. Aiming at the large calculation amount of the PSO algorithm, the appropriate PSO parameters are selected experimentally, and the complexity of the PSO algorithm is minimized while ensuring the fitting accuracy. The parameters of the signal waveform equation are solved using the PSO algorithm on the field-programmable gate array (FPGA) platform. According to the parameters solved, a lookup table for sinusoidal error compensation is designed. The grating system platform is built to verify the effect of the compensation scheme on the FPGA platform. The results show that the compensation method can effectively reduce the sinusoidal error component in the signal, and the subdivision error is reduced from 0.95'' to 0.56'' in the time domain. Consequently, the zero-order, first-order, second-order and third-order components are considerably suppressed. The compensation scheme can realize the sinusoidal error compensation of the grating moiré signal and effectively improve the measurement accuracy of the grating encoder.

Economic Operation of the Regional Integrated Energy System Based on Particle Swarm Optimization

“…In the process of material heating up, the motion state of atoms in the material changes constantly. When the temperature reaches high enough, its motion state changes from the previous order to disorder [ 22 , 23 ]. In the process of material cooling, the atoms of the material will slowly reach stability from the active state.…”

Design of a Roll Angle Measuring Sensor

“…As Section II and related research demonstrate, the methods based on moiré fringes are only suitable for roll deformation measurement in a small angle range [13], [22]. Moreover, when the roll angle is close to 0°, 90°, or 180°, no effective moiré fringes can be obtained in the optical field of view, which limits the robustness and measurement range of these methods.…”

Methods for Reducing Subdivision Error within One Signal Period of Single-Field Scanning Absolute Linear Encoder

“…To reduce the optical encoders’ SDE, multiple subdivision algorithms [ 17 , 18 , 19 , 20 ] have been proposed, many commercial integrated circuits [ 21 ] have been developed, and numerous gratings with special shapes [ 22 , 23 , 24 ] and devices with special dimensions [ 25 , 26 ] have been applied. Recently, the error compensation models based on particle swarm optimization have been applied to the optical encoders to compensate the SDE [ 27 , 28 , 29 ]. Although there are many research outcomes, there are few studies on the single-field scanning absolute linear encoder’s SDE.…”