Grating encoder is a sinusoidal encoder based on grating diffraction principle, which is currently utilized in many high-precision displacement systems because of its advantageous characteristics: low cost, simple structure, works in harsh environments, high reliability, and so on. The output signal of grating encoder usually contains noise interference error, amplitude inconsistency error, DC bias error, harmonic error and quadrature phase error. These non-ideal factors are the main reasons for affecting the precision of subdivision.
In the traditional signal subdivision system, it is usually necessary to compensate each kind of error separately, which will consume many hardware and computing resources and cause a significant output latency, especially in the filtering section and normalization section. In this paper, a non-linear Kalman filter-based sin-cos wave subdivision method is proposed. Compared with the traditional filtering methods, non-linear Kalman filter has higher dynamic response and can provide instantaneous phasor estimation. In addition, it can simultaneously achieve filtering, amplitude normalization, decoupling DC bias, harmonic suppression, and phase compensation functions, which significantly reduces the computational burden and facilitates the implementation on low-cost processors.
In this study, a non-linear Kalman filter-based signal segmentation system is implemented on an FPGA platform and verified on a six-degree-of-freedom grating ruler platform. The results show that the single-channel output delay is only 1.8us at a 50MHz clock, which has a very high real-time ability. When the frequency and amplitude of the input signal varies, the non-linear Kalman filter can track instantaneously and has high dynamic characteristics. Experimental results show the effectiveness of this method.
For solving the problem of sub-mirror installation and posture monitoring and compensation, an absolute four-degree-of-freedom (DOF) grating encoder that is able to monitor four degrees of freedom's absolute position and pose in the θx, θy, θz, and z-direction is proposed. In this grating encoder, a grating reflector and three quadrant photodetectors (QPD) are employed and an optical path is configured based on the laser autocollimation principle. A model for the solution of the four-DOF motions from outputs of the three QPDs is established. A calibration method for the identification of the relationships between the absolute positions and QPDs outputs is proposed. A prototype four-DOF grating encoder is constructed for verification of this proposal. Test results demonstrated that the method proposed in this research can achieve absolute position distinguishing with a sub-arcsecond and sub-micrometer accuracy in rotation angles and z-direction, respectively.
KEYWORDS: Field programmable gate arrays, Computer programming, Signal processing, Data conversion, Optical filters, Filtering (signal processing), Digital signal processing, Interfaces, Diffraction gratings, Logic
Compared with the four-phase optical structure, the grating encoder based on two-phase optical structure reduces the number of optical devices used in the system and makes the system more compact. Due to the high requirements for realtime and parallel processing of algorithm solution, the powerful parallel computing ability of Field Programmable Gate Array (FPGA) and customized hardware acceleration algorithm are needed to improve the real-time performance. In the previous research, the displacement signal generated by the grating encoder can be input into the FPGA through analog to digital converter (ADC) sampling, and then complete self-designed filter filtering, phase correction and displacement solution. In this paper, further, the ADC sampling rate adjustable interface is added to the FPGA, the global signal and the dc offset remove algorithm is added, and the displacement solution results in the form of fixed-point number are output to the host computer through the MicroBlaze (MB) soft core. MB core can realize process control and interface conversion on FPGA, and use a small amount of logic resources to replace the functions of MCU and DSP of traditional embedded measurement system, so as to further improve the integration of the instrument. A series of experiments are carried out on the two-phase FPGA platform. ADC sampling rate is 200ksps, 8-Channel synchronous parallel sampling, FPGA system clock frequency is 200MHz. The linear displacement table is set to drive the measurement grating at different displacement speeds, and the total stroke is set to 10mm. The FPGA real-time displacement solution platform is tested. The experimental results show that FPGA obtains accurate displacement solution results under different speed tests. In the test of 2 mm/s, the maximum cumulative displacement measurement error is 5um, which shows the real-time performance and accurate displacement solution performance of FPGA platform.
KEYWORDS: Field programmable gate arrays, Signal processing, Computer programming, Digital signal processing, Optical filters, Data processing, Filtering (signal processing), Sensors, Phase measurement, Optical design
Six-degree-of-freedom (6-DOF) grating encoders have a wide prospect of application. Aiming at the requirement of real-time detection of 6-DOF grating encoders, this study designs and builds a real-time calculation system platform based on field-programmable gate array (FPGA). We realized a real-time parallel calculation of 16-path displacement signal and 24-path angular displacement signal, respectively. Specifically, the optical interference signals, generated by the translation and rotation of the motion stages, are firstly shaped by the front-end analog circuit. We further sampled the front-end analog circuit into an FPGA through a analog-to-digital convertor (ADC) for the realization of the digital filtering, amplitude normalization, phase correction, and phase-information calculation. Thus, the calculated signals on the 6-DOF motions can be displayed in real time. The established system was evaluated with the experimental parameters in terms of the translation with a 50 μm/s moving speed and an 18 mm stroke and the rotation with a frequency of 0.5 Hz, a step length of 100 micro-rad, and within a reciprocating rotation of 24 s. Finally, a linear-displacement error of <1 nm and an angle displacement error of <0.9 micro-rad were achieved, respectively. Furthermore, the system delay of <15 ms is obtained, exhibiting a high performance for the real-time measurement and high integration in the practical application.
The signal processing of the grating encoder has a great impact on its accuracy and resolution. We proposed a new type of signal processing method for a grating encoder using a two-phase differential algorithm based on the two-phase physical structure. The interference signal could be divided into two phases with 90 degrees phase delay, capable of effectively reducing the number of optical devices and the space occupied by the reading head. Owing to the rapid elimination of the DC component in the measurement signal, the measurement displacement was solved swiftly by the two-phase signal using the algorithm. In the experiment, a 660 nm laser and a 1 µm-period grating were used, and the scale grating was actuated at a speed of 1 µm/s by a linear stage. With a sampling rate of 20 kHz, the system resolution of the grating encoder was enabled to reach 50 pm. Simultaneously, there was a measurement error of ±1 µm at a stroke of 4 mm, and the error within a single cycle was 2 nm. Compared with the four-phase algorithm, our proposed two-phase differential algorithm exhibits a compact physical structure and fast solution without reducing the accuracy and resolution, which will be of great significance to the real-time measurement and miniaturization of grating encoders.
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