Maximum Nonlinearity Error Research Articles

An Auto-Balancing Capacitance-to-Pulse-Width Converter for Capacitive Sensors

A novel auto-balancing capacitance-to-pulse-width converter (CPC) that uses sinusoidal excitation, and operates in a closed-loop configuration, is presented in this paper. Unlike most of the existing CPCs, the proposed interface circuit is compatible with both single-element and differential capacitive sensors. In addition, it provides a pulse-width modulated (PWM) signal which can easily be digitized using a counter. From this PWM signal, a ratio output is derived when a single-element sensor is interfaced, and a ratiometric output is obtained for a differential sensor. The final digital output is independent of the nominal capacitance of the sensor and has a linear characteristic irrespective of the sensor characteristic being linear or inverse. The CPC is designed such that the PWM output depends on the change in the sensor capacitance alone. It is insensitive to parasitic capacitance and has very low sensitivity to the non-idealities of the components and ICs used. The effects due to some of the non-idealities are automatically corrected by the negative feedback based auto-balancing employed. The effect of component mismatch is significantly reduced by a one-time correction mechanism. These benefits are achieved without the use of any complex or expensive analog building blocks. The prototype exhibits a maximum non-linearity error of less than 0.7%, a resolution of 13.02 effective number of bits (ENOB), a signal-to-noise ratio (SNR) of 80.12 dB, and a rise time of 5 ms. Thus, the proposed simple, yet effective, low-power, low cost, auto-balancing CPC can be used to interface a wide range of existing and new capacitive sensors to digital systems.

A Closed-Loop Capacitance-to-Frequency Converter for Single-Element and Differential Capacitive Sensors

A novel closed-loop switched-capacitor (SC) capacitance-to-frequency converter (CFC) is presented in this article. The proposed CFC is capable of measuring from either a single-element or a differential capacitive sensor (DCS), providing ratio and ratiometric outputs, respectively. Most of the existing autobalancing schemes for capacitive sensors use the closed-loop approach but require precise sinusoidal ac excitation and provide an analog output that is sensitive to parasitic capacitances. Also, the use of voltage-controlled resistors (VCRs) in many of these schemes limits the linearity and accuracy of their output. The SC-CFC presented in this article employs a simple dc reference for excitation and gives a digital output that is insensitive to parasitic capacitances, by virtue of design. Additionally, the output is linear, irrespective of the sensor characteristic, and independent of the nominal value of the sensor. This feature, along with its compatibility with single-element and DCSs, facilitates its ease of integration with a wide range of capacitive sensors. The CFC has a one-time correction mechanism that significantly reduces the impact of component mismatch. The prototype of the proposed scheme exhibits a maximum nonlinearity error (NLE) of 0.24%, a resolution of 12.59 effective number of bits (ENOB), and a rise time of 6 ms. In addition, the proffered design is fit for integrated circuit (IC) fabrication as it employs an SC approach.

Double-actuator position-feedback mechanism for adjustable sensitivity in electrostatic-capacitive MEMS force sensors

This paper presents a novel double-actuator position-feedback mechanism for micro electro-mechanical electrostatic-capacitive force sensors. Compared to a single-actuator position-feedback operation, the innovative use of two independent electrostatic actuators allows to obtain electrically adjustable force sensitivity and measurement range independently from the working position and the stiffness of the internal mechanical movable structure of the device. Additionally, the proposed configuration allows to electrically set and keep fixed the working position of the force probe tip thanks to the position-feedback loop, thus ideally offering an infinite input mechanical impedance, irrespectively from the force measurement range and sensitivity adjusted to the desired values. The proposed mechanism has been experimentally validated on an electrostatic-capacitive MEMS device that includes a capacitive position sensor and a pair of electrostatic actuators, employing the gravity force to provide accurate and repeatable values for the external applied force. The obtained experimental results are in good agreement with both theoretical predictions and parametric numerical analyses. The proposed mechanism allows to adjust the sensitivity in the range from 2.34 up to 8.43 V/μN with a corresponding force measurement range, defined at a maximum nonlinearity error of 1% referred to the full scale, from [-217, 226] down to [-20.5, 21.4] nN, respectively. The measurement repeatability, which sets the resolution of the MEMS force sensor, has been estimated at one standard deviation σ resulting in 345 pN.

A heavy load miniature six-component force sensing mechanism with hybrid branches

The heavy-load force sensing mechanisms with small size and wide range have always been a challenge. To tackle this challenge, we propose a parallel six-component force sensing mechanism with sensitive measuring branches and high load-bearing branches based on the design idea of hybrid branch. Based on the virtual work principle and the geometric compatibility condition, the stiffness model and force mapping relationship of the mechanism are deduced, which provide the theoretical basis for the mechanism. Further, the comparison between the numerical calculation and the simulation values of the force sensing mechanism shows that the mathematical model is in good agreement with the finite element model. Finally, a calibration testing platform is built to analyze the measuring performances of the force sensing mechanism. By using the least square method to analyze the experimental data, the calibration matrix is obtained and the maximum nonlinear error is 1.65%.

An 8-Tap CMOS Lock-In Pixel Image Sensor for Short-Pulse Time-of-Flight Measurements.

An 8-tap CMOS lock-in pixel image sensor that has seven carrier-capturing and a draining time window was developed for short-pulse time-of-flight (TOF) measurements. The proposed pixel for the short-pulse TOF measurements has seven consecutive time-gating windows, each of which has the width of 6 ns, which is advantageous for high-resolution range imaging, particularly for relatively longer distances (>5 m) and under high ambient light operations. In order to enhance the depth resolution, a technique for the depth-adaptive time-gating-number assignment (DATA) for the short-pulse TOF measurement is proposed. A prototype of the 8-tap CMOS lock-in pixel image sensor is implemented with a 1POLY 4METAL 0.11-μm CIS process. The maximum non-linearity error of 1.56%FS for the range of 1–6.4 m and the depth resolution of 6.4 mm was obtained at 6.2 m using the DATA technique.

Design and Testing of the Space Floating Potential Detector

A space floating potential detector (FPD) is an instrument being developed to study the charging of spacecraft structures. It measures the floating potential that arises as the spacecraft interacts with the low Earth orbit (LEO) plasma as well as the Earth’s magnetic field. The FPD belongs to the active potential control system and consists of three functional modules. Leakage current-eliminating and zero-clearing techniques are used in the detector design to ensure the measurement of the floating potential over the long term within the range from −150 to 0 V and at a voltage resolution of less than 1 V. In order to investigate the performance of the FPD, a typical LEO space plasma environment is simulated in the laboratory. The calibrations of the FPD show that the output voltage is basically linear with the input bias voltage, and the maximum nonlinear error is less than 0.9%.

Resolution Enhancement in Directly Interfaced System for Inductive Sensors

In this paper, a resolution enhancement method for direct interfacing of inductive sensors, without employing analog-to-digital converter and/or external driver circuit, is presented. In order to achieve better resolution with minimum relative error and current consumption factors, different schemes are implemented which vary in terms of: 1) step-input voltage provision methodology, i.e., through microcontroller ( $\mu \text{C}$ ) pin or through external supply; 2) number of switches used; and 3) method of voltage detection, i.e., either using capture module or employing built-in comparator only. The maximum achievable resolution limits are explored by reducing the lower reference voltage ( $\text{V}_{\mathrm {Ref L}}$ ) in case of detection through built-in analog comparator and/or reducing the series resistance. The one-point calibration technique is used to determine the accuracy. The experiments are performed at 16-MHz clock frequency in the inductance range of: 1) 10–100 $\mu \text{H}$ and 2) 100–1000 $\mu \text{H}$ . The results show that in the limits of a maximum current sourcing/sinking capacity of a typical $\mu \text{C}$ , i.e., 40 mA, the proposed methodology enhances the resolution to $4~\mu \text{H}$ with a relative error of 1.2 in the percentage of full-scale span (%FSS). The maximum nonlinearity error in %FSS for inductance range 10–100 $\mu \text{H}$ and 100–1000 $\mu \text{H}$ is 1.1% and <0.4%, respectively.

A novel torque sensor based on the angle of magnetization vector

Torque is an important parameter of a mechanical power system, which reflects transmission efficiency, transmission reliability, and operating conditions of equipment. Torque monitoring is very important for real-time control and fault diagnosis of mechanical equipment. A torque measurement method based on the theory of magnetic effect is proposed for multipoint torque monitoring in shafting. A model of the deflection angle of the magnetization vector and torque is established based on the theory of magnetic equivalent. A non-contact signal extraction circuit based on hall sensor is designed, a torque loading experimental device is set up, and the torque calibration experiment is completed. The experimental results show that the sensitivity of the torque measurement system is 17.7 mV/Nm, and the maximum nonlinear error is 0.77% full scale. The deflection angle of the magnetization vector has a good linear relation with the torque, which can be measured indirectly by the deflection angle. This method has the advantages of a simple device, strong anti-interference ability, and non-contact measurement. Because it is not necessary to do special treatment to the elastic shaft, it is convenient to form a non-contact torque sensing node, which can realize real-time monitoring of multipoint torque of shafting.

Automatic calibration system for micro-displacement devices

With the advanced development of micro-displacement technology, the correlated applications of piezo transducers (PTs) have been widely implemented in the precision industry. The calibration of significant parameters of PTs, including nonlinearity and error due to hysteresis, must be determined and verified before their employment. Hence, the development of an automatic calibration system which can ensure quality and detect any decline or damage before the utilization of the PT is the primary goal.A self-developed system based on the international specification of ASTM-E2309 for the automatic calibration of PTs is constructed in this study. The system bears the feature of a common optical path and a resolution of sub-mm order. The testing results illustrated that the repeatability of the proposed Fabry–Pérot interferometer is within 15 nm. In accordance with the experimental arrangement of synchronic measurement, the comparison results between the self-developed and the commercial interferometer indicate that the differences of the maximum nonlinearity and maximum hysteresis error are less than 1%. By the presented correct method, the maximum nonlinearity error can be minimized to 0.5% and the maximum hysteresis error will be reduced to 1.1%.

Novel non-contact torque measurement using the magnetomechanical effect

With the recent developments in science and technology, torque measurements have been widely used in many fields. However, present torque measurement methods have limitations for long-term applications. Therefore, a new method of non-contact torque measurement based on the magnetomachanical effect is reported that may be used in reducing fatigue for long-term measurements. The theory of the changes in magnetization with torque are analyzed to construct a model. Hence, an experiment platform was constructed that includes an excitation coils, shaft, and Gauss meter. The relationship between the magnetic induction and the torque was measured using this apparatus. The results show that the experimental measurements are in agreement with mathematical models obtained using magnetomechanical concepts. The results also show that the maximum nonlinearity error of the system is 0.6% and the maximum repetitive error is 3.125%. Additionally, this proposed method meets the requirements for long-term torque measurements and may also be used for the non-contact characterization of the torque of watercraft and airplanes.

Research on static decoupling algorithm for piezoelectric six axis force/torque sensor based on LSSVR fusion algorithm

Abstract Six axis force/torque sensors with characteristics of high precision, high reliability, and high dynamic, have become one of the major bottlenecks restricting the development of the robot. Aiming at the existing decoupling problem of piezoelectric six axis force/torque sensor with four point support structure, this paper presents the research and application on static decoupling method. Firstly, initial experimental data for decoupling of piezoelectric six axis force/torque sensor is obtained by making a calibration experiment. And then, experimental data are analyzed according to evaluate indicator. The linear decoupling algorithm based on the least square (LS) method is performed. Fusion decoupling algorithm based on Least Square Support Vector Machine Regression (LSSVR) is adopted to optimize multi-dimensional nonlinear characteristics of sensor output. The mapping relation between input and output of the sensor is identified. After LSSVM fusion algorithm decoupling, the maximum nonlinear error and cross coupling error are 0.89%, and 0.1%, respectively. The results show that the decoupling of LSSVR fusion algorithm can reduce the nonlinear error and cross coupling error of the fabricated piezoelectric six axis force/torque sensor. It has important significance to improve the measurement accuracy of robot force feedback with piezoelectric six axis force/torque sensors.

Design and implementation of an intrinsically safe liquid-level sensor using coaxial cable.

Real-time detection of liquid level in complex environments has always been a knotty issue. In this paper, an intrinsically safe liquid-level sensor system for flammable and explosive environments is designed and implemented. The poly vinyl chloride (PVC) coaxial cable is chosen as the sensing element and the measuring mechanism is analyzed. Then, the capacitance-to-voltage conversion circuit is designed and the expected output signal is achieved by adopting parameter optimization. Furthermore, the experimental platform of the liquid-level sensor system is constructed, which involves the entire process of measuring, converting, filtering, processing, visualizing and communicating. Additionally, the system is designed with characteristics of intrinsic safety by limiting the energy of the circuit to avoid or restrain the thermal effects and sparks. Finally, the approach of the piecewise linearization is adopted in order to improve the measuring accuracy by matching the appropriate calibration points. The test results demonstrate that over the measurement range of 1.0 m, the maximum nonlinearity error is 0.8% full-scale span (FSS), the maximum repeatability error is 0.5% FSS, and the maximum hysteresis error is reduced from 0.7% FSS to 0.5% FSS by applying software compensation algorithms.

Reduced-code test method using sub-histograms for pipelined ADCs

The measurement of static test parameters for an analog-todigital converter (ADC) requires a large volume of test data, especially for a high-resolution ADC. This paper proposes a reduced-code test method for pipelined ADCs that does not compromise test accuracy. The proposed method calculates fault information at each stage by using sub-histograms. The simulation results based on 12-bit pipelined ADCs show a maximum integral nonlinearity error of 0.590 LSB with only 3.92% of the codes required for the conventional histogram-based method.

A new crank arm-based load cell for the 3D analysis of the force applied by a cyclist.

This report describes a new crank arm-based force platform designed to evaluate the three-dimensional force applied to the pedals by cyclists in real conditions. The force platform was designed to be fitted on a conventional competition bicycle crankset while data is transmitted wirelessly through a BluetoothTM module and also stored on a SD card. A 3D solid model is created in the SolidWorks (Dassault Systèmes SOLIDWORKS Corp.) to analyze the static and dynamic characteristics of the crank arm by using the finite elements technique. Each crankset arm is used as a load cell based on strain gauges configured as three Wheatstone bridges. The signals are conditioned on a printed circuit board attached directly to the structure. The load cell showed a maximum nonlinearity error between 0.36% and 0.61% and a maximum uncertainty of 2.3% referred to the sensitivity of each channel. A roller trainer equipped with an optical encoder was also developed, allowing the measurement of the wheel's instantaneous velocity.

Analysis and Compensation Strategy of Non-Linear Error in Five-Axis CNC Machining

This paper presents a new strategy of analysis and compensation of non-linear error. Non-linear error is an important source of machining error in multi-axis numerical controlled machining and it is unavoidable. In view of tool positions optimization in five-axis CNC machining of complex surface, this paper presents a strategy for non-linear error compensation in five-axis machining: Firstly, non-linear error caused by the change of tool axis vector is analyzed and the non-linear error model is established, in order to get the maximum non-linear error of interpolation segment; Then, the tool position that meets the machining accuracy is obtained; Finally, Simulation and analysis of the model show that the proposed method is effective and greatly improves the geometric accuracy.

A 7.5 ps single-shot precision integrated time counter with segmented delay line

This paper describes the design and test results of time interval counter featuring the single-shot precision of 7.5 ps root mean square (rms) and measurement range of 1 ms. These parameters have been achieved by combining direct counting method with a two-stage interpolation within a single clock period. Both stages of interpolation are based on the use of tapped delay lines stabilized by delay locked loop mechanism. In the first stage, a coarse resolution is obtained with the aid of high frequency multiphase clock, while in the second stage a sub-gate delay resolution is achieved with the use of differential delay line. To reduce the nonlinearities of conversion and to improve the precision of measurement, a novel segmented delay line is proposed. An important feature of this segmented delay line is partial overlapping of measurement range and resulting enhancement of both resolution and precision of time interval counter. The maximum integral nonlinearity error of the fine-stage interpolators does not exceed 16 ps and 14 ps in START and STOP interpolators, respectively. These errors have been identified by statistical calibration procedure and corrected to achieve single-shot precision better than 7.5 ps (rms). The time counter is integrated in a single ASIC (Application Specific Integrated Circuit) chip using a standard cost-effective 0.35 μm CMOS (Complementary Metal Oxide Semiconductor) process.

A self-decoupled three-axis force sensor for measuring the wheel force

The wheel force transducer is an important device in the automotive testing field which can measure the force or torque applied to the wheel. Because existing wheel force transducers are almost commercial products, they are too expensive and technical information about them has not been made public; this slows down the development of the wheel force transducer to a certain extent. Accordingly a three-axis wheel force transducer is presented in this paper which is self-decoupled without calculating the decoupling matrix in theory. Its elastic body has a spoke structure with eight elastic beams, which means that it is easy to fabricate. This paper first introduces the overall elastic body structure of the proposed wheel force transducer. Then the strain gauge arrangement, the principle of strain measurement, the connection modes of the bridge circuits and the rotation decoupling principle for Fx and Fz are analysed, and the self-decoupled characteristics are depicted in detail. Finally, to verify the validity of the designed wheel force transducer, three kinds of experiment are carried out. In the static experiments the static performance and the self-decoupled characteristics of the wheel force transducer are verified; in the dynamic tests, a vehicle dynamics test system is adopted to verify the accuracy of the wheel force transducer in the dynamic environment; in road tests, the sensor is installed in the vehicle to verify whether the output of the proposed wheel force transducer can reflect the variation in the force applied to the wheel in practical applications. The results shows the following: first, the maximum non-linearity error, the maximum hysteresis error and the maximum repeatability error of the proposed wheel force transducer are 0.9% of the full scale, 1.1% of the full scale and 0.5% of the full scale respectively; second, the static coupling rate is about 0.08%, which means that the designed wheel force transducer is self-decoupled in theory; third, the proposed wheel force transducer can measure Fx, Fz and My effectively in real applications.

A Method to Compensate Thermocouple Sensor Non-Linearity Based on Lagurre Orthogonal Polynomial Basis Functions Neural Network

This paper presents a new method to compensate thermocouple sensor non-linearity based on laguerre orthogonal polynomial basis functions neural network. The mathematical model is established based on laguerre artificial neural network for non-linearity compensation. The principle and training algorithms of laguerre orthogonal polynomial basis functions neural network are introduced. The results show that non-linearity compensation method has the advantages of high precision, good real time and strong robustness, etc. The maximum non-linearity error is 0.17%.

Design and Implementation of a Three Dimensional Wheel force Transducer

Wheel force transducer (WFT) plays a key role in automobile detection technology, and they can measure the force and torque applied in the wheel. However, the most current generation of WFT are commercial products which are expensive and their technical information is not public. Accordingly, a three-dimensional wheel force sensor based on spoke structure with eight elastic beams is presented in this paper. Firstly, the overall structure of the proposed WFT is described, and then the design of the elastic body is introduced briefly. Afterwards, the strain gauge arrangement, the principle of strain measurement and the connection mode of bridge circuit are analyzed in detail. Finally, static calibration and dynamic tests is performed. Experiment results demonstrate the proposed WFT has the characteristic of large scale, good linearity, low hysteresis, high repeatability and weak interdimensional couplings. The maximum nonlinearity error, the maximum hysteresis error and the maximum repeatability error of the proposed WFT is 0.6% F.S, 0.7% F.S and 0.4% F.S separately.

Study on Post-Processing of Five-Axis Cnc Machining

According to the feature of five-axis CNC machine tools’structure, do researches on post-process technique. By means of analysis of the kinetic model of five-axis CNC machine tools, Position and orientation of the tool in the workpiece coordinate system transforms to that of the machine coordinate system. Besides, Because of the rotation，Five-axises maching will produce the non-linear error．This article provides an easy algorithm to find the maximum non-linear error. Finally, an impeller, for example, simulates in the computer and machine by a 5-axis machine tool.