Nonlinear Error Model Research Articles

Simulation of Motion Nonlinear Error Compensation of CNC Machine Tools With Multi-Axis Linkage

In order to solve the problem of nonlinear error for a dual rotary table five-axis CNC machine tool due to the linkage of rotary and translational axes, the simulation of motion nonlinear error compensation for a multi-axis linkage CNC machine tool is proposed. The adjacent points in the tool position file are selected as the tool position points for building the model, and then the nonlinear error model resolved by the harmonic function is established according to the error distribution in the classical post-processing. The nonlinear error between the two tool position points is quickly predicted by the analytical expression of this model, and the real-time error compensation of the intermediate interpolation points is realized. Finally, MALTLAB simulation analysis is performed on the tool position file of an impeller part machining to verify the effectiveness of the proposed algorithm. The experimental results show that it can be seen from the distribution curve of the nonlinear error that it is about 10% after compensation as before compensation, thus verifying the effectiveness of the nonlinear error compensation mechanism. The correctness of the nonlinear error analysis and compensation method and the effectiveness of post-processing are verified.

Comparação das distribuições Normal, Logística, Laplace e t de Student para o erro experimental na descrição bayesiana do acúmulo de matéria seca de Allium sativum

ABSTRACT: This study assessed distributions associated with Bayesian nonlinear modeling error in the description of total plant dry matteraccumulation (TDMA) of Allium sativumas a function of days after planting (DAP). According to the DIC criterion, Logistic and Gompertzmodels that use student’s t distribution error exhibited the highest DIC with logistic error distribution. In general, the difference of DIC in all the scenarios was not more than 5.The Bayes factor (BF) criterion showed no difference in the Logistic and Gompertzmodel fit when four distributions are used for the errors, where BF values do not exceed 2. Posterior distributions and the usual estimators of Logistic and Gompertz model parameters were similar even forvaried error distribution. In summary, there was no difference in the use of 4 distributions associated with the modeling error of garlic plant growth by the Bayes factor, whereby the results showed that alternating between error distributions significantly changes the number of Markov Chain Monte Carlo (MCMC) iterations.

High-precision identification and compensation of nonlinear error in hemispherical resonator gyro

This paper presents a novel nonlinear error identification and compensation method for the Hemispherical Resonator Gyro (HRG) from the signal processing perspective. Firstly, the paper establishes an HRG nonlinear error model that reveals the quantitative correlation between angle measurement error and the amplitude-gap ratio. Subsequently, a dynamic analysis model for gyro drift is developed using nonlinear motion equations. Based on this, a scalar factor nonlinear identification model encompassing assembly and nonlinear errors is proposed. Nonlinear optimization is then used to identify error parameters accurately. Finally, a joint compensation method is devised to mitigate assembly and nonlinear error issues. Empirical findings provide concrete validation for the precision of the identification and compensation method. The experimental results demonstrate that reductions of 97%, 89%, and 40% after the joint compensation are achieved in the fourth harmonic component, scale factor nonlinearity, and bias instability of the gyro, respectively.

In-field calibration of triaxial accelerometer based on PE-ANGO

Abstract This paper presents a new method for in-field calibration of accelerometers to address the problems of low efficiency and high cost associated with traditional calibration methods. A nonlinear mathematical model of the accelerometer is established, and the cost function is analysed and deduced the cost function. Then, an adaptive Northern Goshawk Optimisation (NGO) algorithm based on prior knowledge enhancement is introduced. A method of collecting multi-position data with a hand-held accelerometer is introduced, and the proposed algorithm is used to in-field calibrate nine parameters of the accelerometer’s nonlinear error model. In addition, simulation is used to compare the results of calibrating the accelerometer using the proposed algorithm and the original algorithm, demonstrating the superiority of the proposed algorithm. Finally, experimental results confirm that the proposed method can rapidly calibrate accelerometer error parameters without relying on complex equipment and with greater accuracy than traditional methods.

Sampled-data output tracking control based on T–S fuzzy model for cancer-tumor-immune systems

This study investigates the tracking control issue for a cancer-tumor immune nonlinear model, which explains the interaction between cancer cells and the immune system in the body. To achieve this, the nonlinear model is first converted into linear sub-models using the Takagi–Sugeno (T–S) fuzzy methodology. The tracking and control of cancer cell proliferation while preserving immune cells is proposed using a sample-data output tracking control technique. Time-dependent discontinuous Lyapunov Krasovskii functional is recommended based on the improved Wirtinger inequality, this may provide additional information about the sawtooth structure of the sampling interval. Less conservative stability criteria are extracted having the form of linear matrix inequalities (LMIs) in consequence of extended reciprocally convex matrix inequality and Wirtinger-based integral inequality. The proposed approach achieves the stabilization of an augmented time delay system that connects with a given fuzzy nonlinear model and tracking error system. Furthermore, the proposed approach reduces the impact of external disturbances under the H∞ norm bound.

A Dose of Reality About Dose-Response Relationships.

Observational research can be strengthened by examining potential dose-response relationships that correlate a clinical intervention with a patient outcome. Despite being a classic criterion for establishing causality, dose-response testing can be difficult to interpret in clinical medicine due to multiple diverse pitfalls. This review introduces a cautionary framework for investigators considering dose-response relationships in observational research to support evidence-based medicine. Each pitfall is illustrated with a specific example relevant when analyzing a dose-response relationship. Several pitfalls stem from faulty interpretation including confounding by indication and fallible range selection. Additional pitfalls relate to improper analysis including fitting a nonlinear model and misclassification error. Further pitfalls arise in special situations including subjective self-report and artifacts from survival bias. These caveats are common sources of misunderstanding in analyses that examine the link between varying exposures and the intensity of clinical outcomes. Awareness of specific pitfalls, we suggest, might help advance the conduct, application, and translation of dose-response relationships in observational research to inform evidence-based medical care.

Nonlinear Error Correction for Magnetic Encoders

Magnetic encoders are used as angle sensors to control motors for precise positioning in many industrial manufacturing processes. However, nonideal factors such as installation misalignment lead to angle measurement errors. This study analyzed a nonlinear model of the measurement error due to eccentricity of a magnetic encoder and developed a method of compensating for this error. An experimental calibration system consisting of a two-phase stepping motor was used to provide a standard reference angle for calculating the measurement error of the encoder. The fast Fourier transform algorithm was used to demonstrate that the measurement error can be modeled as a multifrequency composite cosine wave with low-frequency components. Compensation of the measurement error was performed using the calculated experimental parameters of each frequency component in the nonlinear error model. The proposed method was experimentally verified, and the accuracy of the 14-bit AS5047D magnetic encoder was improved from 8~9 bits to 11~12 bits.

A novel adaptive nonlinear Kalman filter scheme for DVL-aided SINS alignment in underwater vehicles

The rapid and accurate initial alignment of a strapdown inertial navigation system (SINS) aided by a Doppler velocity logger (DVL) still poses a significant challenge in unmanned underwater vehicle navigation. In this study, a novel adaptive nonlinear filtering alignment scheme is developed for a SINS with a large misalignment angle. In previous studies, the frame-inconsistency problem of the nonlinear SINS error model was neglected. Thus, a modified nonlinear error model of a SINS is derived here rigorously as the process model of the nonlinear Kalman filter. In addition, the noise amplification of applying Sage-Husa adaptive Kalman filter (SHAKF) in alignment is analyzed, and a novel arctangent fading memorial factor is introduced to dynamically adjust the weight of current measurements. Simulations and field experiments indicate that the proposed algorithm is efficient in underwater DVL/SINS in-motion alignment. The alignment accuracy and convergence rate of the modified model are significantly improved compared to those of the traditional model. The arctangent fading memorial SHAKF can reliably estimate the measurement noise and improve the performance of alignment.

A Polar Integrated Alignment Assisted by DVL Under Large Azimuth Misalignment

The gravity tends to coincide with the earth’s rotation vector in the polar region, degrading the coarse alignment azimuth of the strapdown inertial navigation system (SINS) to a large misalignment. Under a large azimuth misalignment, the linear error model inevitably renders unacceptable theoretical errors in the integrated alignment. In addition, polar region challenge such sensors as a star sensor of celestial navigation, which fails to provide high-precision attitude reference for integrated alignment. Therefore, in allusion to the misalignment mentioned above based on SINS for the polar region, an integrated alignment algorithm is proposed, assisted by the Doppler Velocity Log (DVL). Notably, the work first investigates the extent to which azimuth accuracy deteriorates in the polar region. On the premise of large azimuth misalignment, the nonlinear error model under the transverse frame is derived from the ellipsoid earth model. Additionally, the state and measurement models are constructed, combined with the velocity of DVL as an observation. An adaptive measurement variance matrix is designed for the unscented Kalman filter (UKF) to estimate the attitude error. Eventually, the semi-physical experiments demonstrate that the proposed algorithm significantly improves the initial alignment accuracy of the polar region.

Separation and compensation of nonlinear errors in sub-nanometer grating interferometers.

In this paper, to separate and compensate the nonlinear error in the grating interferometer, we analyze the source and generation mechanism of this error, deduce the nonlinear error model of the measured signal and the calculated phase signal, and study the characteristics of the established nonlinear error model. The reason why the frequency multiples of ideal phase signals and higher-order nonlinear errors caused by ghost reflections and angular errors of the laser's z-axis are not integers is explained. Then, a nonlinear error separation and compensation method based on cross-correlation coefficient is proposed. Experiments show that the frequency multiplier relationship between the high-order nonlinear error and the ideal interference signal is close to but not equal to 3-fold. The peak-to-peak value of the compensated nonlinear error is reduced from 17.40 nm to 7.05 nm.

A Deep Residual Recurrent Neural Network Model-Augmented Attention With Physical Characteristics: Application to Turntable Servo System

Turntable servo systems are affected by working status changing in actual work, thus, bringing some uncertain factors. Having models that have accurate predictive capabilities can be valuable for control and decision-making purposes. This article proposes a deep residual recurrent neural network (DRRNN) model-augmented attention with physical characteristics, which is used to build an accurate speed prediction model for a turntable servo system. Integrating the known physical features into the design of the residual network model can increase the interpretability of the overall model. Meanwhile, the recurrent neural network-augmented attention model is used to represent the unknown nonlinear characteristics. The addition of the attention mechanism can effectively improve the accuracy of the nonlinear model. Finally, this article proposes an iterative identification method based on the linear and nonlinear model error with alternative compensation. Through alternating error compensation, the linear model’s accuracy can be continuously improved, then the overall and the nonlinear part of the model can be established accurately by retraining the whole model. Experimental results show that the DRRNN model designed in this article can predict the rotational speed in single-step or multistep well. Compared with the traditional mechanism modeling method, the modeling accuracy can be greatly improved.

Adaptive fuzzy nonlinear integral sliding mode control for unmanned underwater vehicles based on ESO

An adaptive fuzzy nonlinear integral sliding mode control strategy based on an extended state observer (ESO) is proposed for trajectory tracking of unmanned underwater vehicles (UUVs) in the presence of unknown external disturbances and model parameter uncertainties. A nonlinear dynamics error model of the UUV is established; the estimation of the lumped disturbances are estimated using ESO, and the control variables are compensated for in real time. A nonlinear integral sliding mode controller with saturation characteristics is designed to improve the transient and steady-state performance of the system, and the switching gain of the sliding mode control is adaptively adjusted using the fuzzy logic system, such that the weight of the output changes with the sliding mode surface; thus, the chattering of the control variables is weakened. The asymptotic stability of the control system is verified using Lyapunov stability theory. The simulation and experimental results demonstrated that the designed control strategy effectively suppresses the system lumped disturbances with high tracking accuracy and robustness.

Trajectory Tracking Control Method Based on Adaptive Higher Order Sliding Mode

To resolve the problem of high-precision trajectory tracking control under interference conditions in a missile’s mid-guidance phase, according to the constructed nominal trajectory, an improved adaptive high-order sliding mode trajectory tracking controller (AHSTC) is proposed. In this method, the open-loop nominal trajectories are established according to the nonlinear programming and Gaussian pseudospectra method. A high-precision trajectory tracking controller is developed by designing a nonlinear sliding mode surface and an adaptive high-order sliding mode approaching law combined with the trajectory tracking nonlinear error model. To verify the effectiveness and superiority of the proposed method, analysis and simulation are carried out through the example of a missile mid-guidance phase tracking control. Compared to the linear quadratic regulator (LQR) and active disturbance rejection controller (ADRC) method, the simulation results show that the proposed AHSTC method shows faster convergence and improved tracking effect. Therefore, the proposed AHSTC method has a good results and engineering application value.

Trajectory tracking control for mecanum wheel mobile robot by time-varying parameter PID controller

This paper presents the design method a proportional integral derivative (PID) controller with time-varying parameters for trajectory tracking of a mecanum-wheeled robot with a minor error. First, a nonlinear kinematic error model of the robot is established and linearized around the working point. Then a PID controller with time-varying parameters is designed based on this linear model. The coefficients of KP, KI, and KD control parameters are determined by trial and error technique to ensure that the robot moves along the desired trajectory with minimal error. A platform mecanum-wheeled mobile robot has been designed and manufactured to demonstrate the proposed controller. Simulation and experimental results are presented to verify the effective and accuracy of the proposed controller. It shows that can apply this research to control of a four mecanum-wheeled mobile robot in logistics services in practice.

Extended bounded real lemma based sum of squares for static output feedback H∞ heading control

AbstractAim at the fore and aft asymmetry of unmanned surface vehicle (USV) and the loss of linear velocity, a static output feedback (SOF) control method is proposed by the sum of squares (SOS) based on two types of extended bounded real lemmas (EBRL) for heading regulation to guarantee the robustness and improve the rapidity. First, an asymmetric nonlinear heading error model with hydrodynamic parameters is established by the consideration of lack of linear velocity. Second, SOF controller with performance is presented for the asymmetric nonlinear USV model, and it's SOS conditions to solve controller parameters is deduced from EBRL by homogeneous Lyapunov function (HERBL) to maintain the system robustness. Further, the solution of SOF controller relies on the state feedback gain matrix, EBRL is deduced by quadratic Lyapunov function (QEBRL) to obtain the SOS conditions without the addition of an extended matrix to cut computing cost for the solution of the state feedback gain matrix. Finally, the heading control simulations for USV indicate that, QEBRL method takes less time for SOS conditions to solve the state feedback gain matrix, and SOF system of HERBL has a superior performance on the transient response and the robustness.

Nonlinear Error Compensation Method for 3D Sensing System Based on Grating Image Projection

Correcting the sensing error caused by the gamma nonlinear response of the three-dimensional (3D) sensing system (SS) is a key factor in improving the accuracy of sensing. To deal with the nonlinear error of the SS, we propose a sub-area Hilbert transform (SA-HT) method. First, we employ Hilbert transform (HT) on the grating image captured by the camera sensor. Then the coefficient of the nonlinear error model can be fitted in the reference area. Second, the phase disturbance (PD) area is detected. We calculate the phase maps in spatial domain and in HT domain. Then the PD area can be detected according to the absolute phase difference in the two domains. Finally, the Newton iteration method is adopted to obtain the truth-phase in the PD area. In addition, the phase values in spatial domain and in HT domain are averaged outside of the PD area. The results of experiments show that the proposed method can avoid the influence of non-smooth reflectively (NSR) when performing nonlinear error compensation on 3D sensing.

An improved initial alignment method based on adaptive robust CKF algorithm

When the misalignment angle is a large angle in the strapdown inertial navigation system (SINS), it is necessary to establish a nonlinear error model to estimate the error. Hence, an improved initial alignment method based on adaptive robust CKF algorithm is proposed in this paper. Firstly, based on the analysis results, SINS/GPS nonlinear error model is established. Secondly, in the view of observation gross errors and inaccurate noise statistical characteristics, adaptive robust CKF algorithm is designed. Finally, according to simulation analysis and experiment, adaptive robust CKF algorithm can augment the stability, improve filter estimation accuracy and convergence rate, which significantly improves the initial alignment ability of strapdown inertial navigation system at large azimuth misalignment angle.

The Quaternion-Based Attitude Error for the Nonlinear Error Model of the INS

In this paper, the quaternion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> -frame based nonlinear error model is proposed for the INS. According to the definition of the attitude error, the quaternion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> -frame based nonlinear error model has been derived by additive and multiplicative relationship. Then, a discussion and analysis is made to compare the proposed model in additive and multiplicative relationship with the quaternion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -frame based nonlinear error model. In addition, an analysis and comparsion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> -frame and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -frame based nonlinear error model is made to have a theoretical justification to describe why <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> -frame is superior to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -frame based nonlinear error model. Finally, field tests are carried out to access the performance of the quaternion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> -frame and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -frame based nonlinear error model in the additive and multiplicative relationship for the INS.

Application of Adaptive Robust CKF in SINS/GPS Initial Alignment with Large Azimuth Misalignment Angle

When the strapdown inertial navigation system does not perform coarse alignment, the misalignment angle is generally a large angle, and a nonlinear error model and a nonlinear filtering method are required. For large azimuth misalignment, the initial alignment technology with a large azimuth misalignment angle is researched in this paper. The initial alignment technology with a large azimuth misalignment angle is researched in this paper. First, the SINS/GPS nonlinear error model is established. Secondly, in the view of observation gross errors and inaccurate noise statistical characteristics, an adaptive robust CKF algorithm is proposed. Finally, according to the simulation analysis and experiment, the adaptive robust CKF algorithm can augment the stability and improve the filter estimation precision and convergence rate.

Vibration Error Correction for the FOGs-Based Measurement in a Drilling System Using an Extended Kalman Filter

Fiber-optic gyroscopes (FOGs)-based Measurement While Drilling system (MWD) is a newly developed instrument to survey the borehole trajectory continuously and in real time. However, because of the strong vibration while drilling, the measurement accuracy of FOG-based MWD deteriorates. It is urgent to improve the measurement accuracy while drilling. Therefore, this paper proposes an innovative scheme for the vibration error of the FOG-based MWD. Firstly, the nonlinear error models for the FOGs and ACCs are established. Secondly, a 36-order Extended Kalman Filter (EKF) combined with a calibration method based on 24-position is designed to identify the coefficients in the error model. Moreover, in order to obtain a higher accurate error model, an iterative calibration method has been suggested to suppress calibration residuals. Finally, vibration experiments simulating the drilling vibration in the laboratory is implemented. Compared to the original data, compensated the linear error items, the error of 3D borehole trajectory can only be reduced by a ratio from 10% to 34%. While compensating for the nonlinear error items of the FOG-based MWD, the error of 3D borehole trajectory can be reduced by a ratio from 44.13% to 97.22%. In conclusion, compensation of the nonlinear error of FOG-based MWD could improve the trajectory survey accuracy under vibration.