Research on Error Characteristics Analysis and Error Compensation Methods for High-Precision Angular Measurement Turntables

Angular displacement sensor plays an indispensable role in high-precision angular measurement and position feedback. With the development of sensing technology, some traditional incremental measurement methods have been unable to meet the requirements such as anti-interference ability, lossless of power-off data information and other factors that are susceptible to environment and mechanical system changes. Therefore, this paper has proposed a method based on combined measurement for absolute measurement of time-grating angular displacement sensor, which is mainly assembling two time-grating sensors that use different pole pair in a co-prime relationship on the axis. By this method, it can build high-precision and high-resolution sensor that meets vernier-subdivision principle in the form of a combination of sensor and fine sensor. The sensor model and simulation experiment results are introduced by Inventor 2016 and ANSYS Maxwell 16.0, respectively. Then, the absolute position measurement method is validated by analyzing the initial phase of the induced electromotive force of the simulation experiment results with the mathematical method. Experiment results show the absolute measurement method is feasible.

The paper presents an original method for the compensation of the frequency dependent systematic error of the time-division multiplier (TDM). The method is based on two identical multipliers working at different conversion frequencies. Full compensation of the error can be achieved using simple calculation taking into account only the values of the output signals of the multipliers and the ratio of the conversion frequencies. It has been shown theoretically, by computer simulation that error of the method is less than +50/spl times/10/sup -6/ in the input signal frequency range up to one tenth of the lower conversion frequency. For the practical realization of the method there is no need to use two complete TDMs, but some simplifications are possible. Applying these simplifications a prototype watt-converter based on this method has been developed and results of measurements show that precision of +/-50/spl times/10/sup -6/ is achieved in the input frequency range from 50 Hz to 10 kHz if the lower conversion frequency is only 100 kHz.

Error analysis and compensation method of displacement measurements based on reflection projection imaging

A large FOV infrared multiple spectrum camera, which contains advance infrared focal plane, acquires large FOV & high resolution multiple spectrum image toward area below the flight vehicle. It takes images on a whole day and nearly a whole whether condition. The multiple spectrum camera system configuration was proposed. Its angular measurement, three coordinate passive location key technology and solution were described in detail. The angular measure electro-circuit & clock synchronization should be finely designed. When the system had been integrated, angular error calibration and compensation, multi-sensor installation attitude calibration were proposed to improve angular measure accuracy and location accuracy. Flight tests shows that image mosaicking accuracy is 10″ which means the technic is effective.

Calibration tests are of great importance to ensure rate-sensing accuracy of GyroWheel, an innovative attitude determination and control device. In the process of calibration tests, turntable errors are inevitable, which hinder the calibration accuracy and rate-sensing capability. Hence, error analysis for GyroWheel calibration tests is conducted, and the relationship between the calibration accuracy and the orientation error is established based on analytical derivation and numerical simulations. Subsequently, an error model of the turntable system is derived using rigid body kinematics, by which the relationship between the orientation error and turntable errors is described. According to sensitivity analysis and manufacturing capability, an error allocation method is proposed to determine the accuracy requirement of the test turntable, and the effectiveness of the proposed method is verified by repeated simulation tests. Based on the presented analysis and proposed method in this paper, the effects of various turntable errors on the calibration accuracy can be obtained quantitatively, and a theoretical basis for the determination of the turntable accuracy is provided, which are of great significance to guide the calibration tests and improve the calibration accuracy of GyroWheel.

In the context of modern power systems, the availability of accurate knowledge of line parameters is a requirement to improve any monitoring and control applications. This knowledge is not easy to obtain even in the presence of a monitoring infrastructure of last generation based on Phasor Measurement Units (PMUs). To address this challenge, the paper proposes a method for improving line parameters estimation through the simultaneous estimation of the systematic measurement errors from the instrument transformers. The problem is faced starting from an appropriate modelling of the system, which includes the uncertainties associated with instrument transformers and PMUs. Moreover, the designed algorithm exploits the available constraint equations derived from the network model. The validity of the proposed approach is tested on a portion of the IEEE 14 bus system and confirmed by the presented results.

As the feedback link of a numerical control system, the measurement accuracy of absolute angular displacement measurements directly affects the control performance of a numerical control system. In previous research, angular displacement measurements based on dual image sensors can achieve higher measurement performance. However, the elimination of harmonic error by the dual image sensor is still limited. For this reason, this paper proposes an image-type angular displacement measurement method based on self-correction error compensation of three image sensors. First, the mathematical model of harmonic error is established, and the shortcomings of using dual image sensors to compensate the error are analyzed. Then, a high precision angular displacement measurement method based on three image sensors is proposed. Finally, the self-correction error compensation method of three image sensors is applied to the angular displacement measurement system, and the measurement performance is verified. The experimental results show that a measurement accuracy of 1.76'' can be achieved on the circular grating with a diameter of 96 mm. In contrast, the dual image sensor can only achieve a measurement accuracy of 2.88''. It is concluded that the odd number of image sensors can achieve higher measurement accuracy than the even number. This research lays a foundation for the realization of high precision image angular displacement measurement.

The disturbance rejection problem of aerial vehicles is a widely concerned issue. For attitude dynamics, we propose a method for directly designing a geometric observer (GOB) based on the special orthogonal group SO(3), thus reducing the impact of model mismatch and being unrestricted by the aircraft attitude. Considering the type of measurement available, we have developed two GOBs: GOB-I, which uses both attitude and angular velocity measurements, and GOB-II, which uses only attitude measurement. The stability of GOB is theoretically proved, with the GOB-I exhibiting almost global asymptotic stability and the GOB-II demonstrating local asymptotic stability. We have compared the estimation performance of our proposed GOB with four other disturbance observers (DOBs) for five types of disturbances. The simulation results show that, in the small attitude scenarios, our proposed GOB-I observer performs comparably with the compensation function observer (CFO) and the nonlinear disturbance observer (NDOB) that use both attitude and angular velocity measurements, while the GOB-II performs comparably with the extended state observer (ESO) that uses only attitude measurements. In the agile attitude scenarios, our proposed GOB-I observer significantly outperforms CFO and NDOB, and GOB-II also performs much better than ESO. Compared with the reduced-order observer, which uses only angular velocity measurement, the GOB-I can handle more complex disturbances and provides compensation for sensor errors. Flight experiments conducted with a lifting-wing quadcopter demonstrate the efficiency of our method in resisting unknown payload in hover flight and model uncertainty in agile maneuver.

Geometrical error compensation of machines with significant random errors

Boltzmann machines show attractive features in traditional neural network tasks. We tested the robustness of the Boltzmann machine in a non-linear mapping task. The system's errors were classified into several categories and the distribution of errors between the categories was studied. Using simulations, it is demonstrated that limitation of the temperature parameter causes the distribution of the network's errors to be unique and different from its usual error distribution. The phenomenon receives a mathematical explanation rooted in the statistical mechanics basics of the Boltzmann machine. This has applications in designing and evaluating mapping tasks for the Boltzmann machines and can help speed up system convergence, which is known to be a major deficit of the Boltzmann machine.

This paper studied the primary sources, evolution rules, and influence mechanisms of the damping anisotropy of the whole-angle hemispherical resonator gyroscope from the perspective of the fabrication process and analyzed the influence of temperature change on the damping anisotropy. An error identification and compensation method is proposed to suppress the effect of the damping anisotropy error on the gyroscope's bias error. According to the energy controller's output, this method involves applying the recursive least squares method to identify the damping anisotropy error and the damping axis angle in real time. Subsequently, a compensation signal is synthesized based on the identification results and applied to the angular rate control loop to compensate for the damping asymmetry error online. The experimental results show that the peak-to-peak value of the angular rate output harmonic error of the gyroscope is reduced from 0.023°/s to 0.005°/s after the error compensation, which is an improvement of about 5 times. In addition, the peak-to-peak value of the gyroscope angular dependent bias error decreases from 0.7072° to 0.08268°, which improves by 8.55 times, and the linearity of the angular measurements is also significantly improved. This methodology can be widely applied to gyroscopes operating in whole-angle mode, which is essential for fundamentally reducing the bias errors of the gyroscope induced by damping asymmetry.

Since the advantages of high precision, large dynamic range in angular velocity measurement, Fiber Optic Gyroscopes (FOGs) are recently proposed to be used as angle measuring instrument. However, in dynamic testing condition like sway, the outputs of FOGs contain inevitable angular velocity measurement error, harming angle measuring accuracy. Therefore, FOGs must be calibrated before using. In this paper, we first propose a high-precision and non-contact angle measurement method with dual-Laser Doppler Vibrometers (d-LDVs) to calibrate the angle measurement error of FOGs in sway condition. Firstly, we verify the accuracy and dynamic range of this proposed angle measurement method by using a high-precision rotary table as an angle benchmark. Experimental results indicate that this method can reach the dynamic angle measurement with the range of ±10°, and the maximum angle measurement error is less than 0.0088°. Secondly, in order to calibrate the angle measuring error of FOGs, we establish an angle calibration system for FOGs based on d-LDVs under sway condition. Experimental result shows that the dynamic angle measurement error of the FOG caused by dynamic environment is less than 0.015°. Because of the zero drift of angular velocity, integral angle of the FOG shows angle drift, and the maximum angle drift is 0.06° (during 30s).

A CPLD-based Photoelectric encoder that measures angle and angular velocity was designed aiming at precise requirements on angle and angular velocity measures in photo-electric servo system. Based on the work principle of photoelectric encoder, a segmented velocity-measure algorithm based on different measure time intervals was presented, and the concrete process in the environment of Isplever Project Navigator was detailed described. Finally, DSP processor TMS320F2812 and CPLD chip LC4512V-75T176 were used for verification. The result showed that this circuit has the features of realization-simple, high measure precision and reliability as well as good commonality. It will lay a solid foundation for the realization of photoelectric servo system’s digital control.

To enhance the accuracy, an efficient methodology was developed and described for systematic geometric error correction and their compensation in five-axis machine tools. The methodology is capable of compensating the overall effect of all position-dependent and position-independent errors which contribute to volumetric workspace. It was implemented on a five-axis grinding machine for error compensation and for the check of its effectiveness. Error compensation algorithm was designed, and a routine was written in Matlab software. The developed technique and software are based on an error table which interprets the function of axis through cubic spline technique and synthesis modeling of a machine tool. Recursive compensation methodology was used to remove the machine errors from the actual tool path and inverse technique was implemented to find the corrected positions of prismatic and rotary joints. Moreover, it can convert the corrected tool paths into practical compensated NC codes. The generated, corrected and modified NC codes directly fed to the controller of a five-axis machine tool. Validation of the technique was preceded by repeated experimentation of measurement and through machining of typical standard workpieces with some additional specific features. Experimental results exhibit effective compensation and remarkable improvement in the parametric and volumetric-workspace accuracy of the five-axis machine tool.

An efficient error compensation system for CNC multi-axis machines