Dynamic model of NC rotary table in angle measurements with time series

Chen, Ziran; Liu, Xiaokang; Peng, Dongming; Zheng, Yu; Chen, Xihou; Zheng, Fangyan

doi:10.1177/0142331212437992

Cited by 14 publications

(7 citation statements)

References 13 publications

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“…The waveform equation of two signals is shown in formula (5). According to the principle of arctangent subdivision, the constructing tangent function is expressed as:…”

Section: Compensation Principle Of Particle Swarm Optimization For Si...mentioning

confidence: 99%

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

et al. 2020

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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.

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“…The waveform equation of two signals is shown in formula (5). According to the principle of arctangent subdivision, the constructing tangent function is expressed as:…”

Section: Compensation Principle Of Particle Swarm Optimization For Si...mentioning

confidence: 99%

“…phase and subdivision based on amplitude [5]- [7]. In the actual application process, the digital subdivision method based on amplitude has better flexibility and is more widely used [8].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…Subdivision of the grating moiré fringes is the primary method for improving the resolution. This method can be roughly classified into two categories: subdivision based on the phase and subdivision based on the amplitude [5][6][7]. From the perspective of ease of application, the latter category is more flexible, and therefore it is widely used.…”

Section: Introductionmentioning

confidence: 99%

“…shows the comparison between the original signals and the constructed function, as obtained from(5).The signal u(θ) can be divided into eight intervals by the crossover and zero-crossing points of the two moiré signals. The phase width of each interval is π/4, and the amplitude and phase of the signal are linearly related.The number of subdivisions at the current position (m) can be determined using the periodic subdivision number (M) and the calculated phase value.…”

mentioning

confidence: 99%

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

Zhu

Huang

et al. 2019

IET Circuits, Devices & Systems

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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

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“…This means the current measurement noise is dependent on the prior ones, and there is an autocorrelation among them. Increased use of time series data has initiated various research and development efforts in many engineering fields with successful applications (Chen, Liu and Peng, 2013; Liu and Mao, 2011; Su et al, 2013). The GPR model with colored noises has also been proposed in Murray-Smith et al (2001), which considers autoregressive and moving average (ARMA) noises with the assumption of full prior knowledge of the parameters of the noise model.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Gaussian process regression for nonlinear modelling with colored noise

Hong

Huang

Ding

et al. 2018

Transactions of the Institute of Measurement and Control

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Nonlinearity of process systems along with colored noises is common in chemical processes. A multivariate (multiple inputs and multiple outputs) Gaussian process regression (MGPR) modelling approach, which can model multivariate nonlinear processes, is developed in this paper. The developed GPR model considers the Gaussian colored noise, rather than the traditional Gaussian white noise. The colored noise is described by the moving average (MA) model and the autoregressive (AR) model, respectively, with unknown parameters so that a MA-GPR model and an AR-GPR model are developed. These two colored noise based models are further extended to the MGPR model to generate the MA-MGPR model and the AR-MGPR model. The covariance functions of the MA-MGPR model or the AR-MGPR model are formulated with consideration of the autocorrelation of noises. Moreover, all parameters are estimated by using a unidimensional updated particle swarm optimization (PSO) algorithm, simultaneously. Numerical examples as well as a three-level drawing model of Carbon fiber production process are used to demonstrate the effectiveness of the proposed modelling approaches.

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Dynamic model of NC rotary table in angle measurements with time series

Cited by 14 publications

References 13 publications

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

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

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

Multivariate Gaussian process regression for nonlinear modelling with colored noise

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