Design of a precise subdivision system for gratings using a modified CORDIC algorithm

Abstract

The authors have proposed a robust linearisation method for determining the angles of sinusoidal signals generated by gratings. This scheme solves the problem of non-linear subdivision by compensating sinusoidal signal. The conventional coordinate rotation digital computer (CORDIC) algorithm is optimised by double-rotation iteration, and the calculation accuracy of arcsine and arccosine functions is improved. A pipeline preprocessing circuit based on the CORDIC is designed for the signal compensation and digital subdivision. The two processes are implemented on a field-programmable gate array chip, which exhibits a wide input range and good dynamic response. A theoretical analysis using stable signals from a function generator verifies that the subdivision system achieves the ideal subdivision effect. The subdivision system is further applied to an anglemeasuring device for a 16,384-line circular grating. The results of subdivision exhibit good linearity for the grating moiré signal. Compared to the angular measurement by a laser interferometer within the three grating lines, the angle-measurement accuracy of ±0.000138° (0.5″) and the relative error is ±0.63% over a travel angle of three grating lines. Notably, the measurement error of the subdivision system is only half of that in a similar commercial product (MicroE system). 2 Architecture of the grating subdivision system The grating sensor generates four sinusoidal signals with a phase difference of 90°, and the period is equal to the grating pitch. The

CORDIC-Based Computation of Arcsine and Arccosine Functions on FPGA

“…Implementation A and [11] use the same setup with 25-bit word length, 12 iterations and an Altera Cyclone EP4CE115F29C7 FPGA. It can be observed that both obtain similar throughput and error.…”

“…This compensation requires a real multiplication, which largely increases the resources needed to implement the algorithm. Alternatively, the double iteration CORDIC algorithm [9]- [11], [14], [15] is based on computing two microrotations by each CORDIC angle in the same direction. This allows to compensate the gain of the microrotations using bit-wise shifts and additions.…”

Research on Particle Swarm Compensation Method for Subdivision Error Optimization of Photoelectric Encoder Based on Parallel Iteration

“…From the above expression, we can conclude that the subdivision angle can be calculated by the arctangent function [18] formula:…”

Improving the subdivision accuracy of photoelectric encoder using particle swarm optimization algorithm

“…The lookup table for the actual calculated angles θm and errors Δθ can be constructed from the obtained waveform parameters and waveform equations, thereby realizing compensation for the sinusoidal errors. When constructing the angle error lookup table, the first step is to identify the angle errors accurately through the lookup table address (Zhu et al 2019). The lookup table constructed in this study is shown in Table 4.…”