Error Dynamics Research Articles

An ADCP Attitude Dynamic Errors Correction Method Based on Angular Velocity Tensor and Radius Vector Estimation

An acoustic Doppler current profiler (ADCP) installed on a platform produces rotational tangential velocity as a result of variations in the platform’s attitude, with both the tangential velocity and radial orientation varying between each pulse’s transmission and reception by the transducer. These factors introduce errors into the measurements of vessel velocity and flow velocity. In this study, we address the errors induced by dynamic factors related to variations in attitude and propose an ADCP attitude dynamic error correction method based on angular velocity tensor and radius vector estimation. This method utilizes a low-sampling-rate inclinometer and compass data and estimates the angular velocity tensor based on a physical model of vessel motion combined with nonlinear least-squares estimation. The angular velocity tensor is then used to estimate the transducers’ radius vectors. Finally, the radius vectors are employed to correct the instantaneous tangential velocity within the measured velocities of the vessel and flow. To verify the effectiveness of the proposed method, field tests were conducted in a water pool. The results demonstrate that the proposed method surpasses the attitude static correction approach. In comparison with the ASC method, the average relative error in vessel velocity during free-swaying movement decreased by 20.94%, while the relative standard deviation of the error was reduced by 17.38%.

Research on Pose Error Modeling and Compensation of Posture Adjustment Mechanism Based on WOA-RBF Neural Network

This paper is aimed to address the issue of decreased accuracy in the ship block docking caused by the structural errors of posture adjustment mechanism. First, inverse kinematic analysis is performed to investigate the sources of static errors in the mechanism. Subsequently, based on the closed-loop vector method, a pose error model for the moving platform is established, which includes eight categories of error terms. The impact of various structural errors on the pose accuracy of the moving platform is then compared and analyzed under both single-limb and multi-limb configurations. Therefore, a compensation method based on the whale optimization algorithm optimized radial basis function neural network is proposed. By transforming pose errors into actuator length errors, it establishes a predictive model between the theoretical pose of the dynamic platform and actuator length errors. After optimizing the network parameters, it yields the actuator length compensation to correct the actual pose of the dynamic platform. Simulation and experimental results validate the effectiveness of this method in enhancing the motion accuracy of the parallel mechanism. The mean pose accuracy of the moving platform is improved by 85.07%, demonstrating a significant compensation effect.

Adaptive Sliding Mode Control for AUV based on Backstepping and Neural Networks

Abstract Automatic Underwater Vehicle (AUV) inevitably suffers from various interference issues in the marine environment. Due to the limitations of underwater measurement methods and tools, as well as the complexity of AUV's control parameters in the underwater environment, dynamic measurement errors are easily cascaded and amplified, leading to the failure of the control system. In response to this phenomenon, this paper focuses on overcoming the influence of internal and external unknown factors in the tracking and control process of AUV trajectories. The internal factors are mainly the uncertainties generated by the model mismatch problem, and the external factors are mainly from the dynamic ocean currents. The AUV disturbances mainly affect the kinematics and dynamics levels directly or indirectly. In order to achieve the control of internal and external dynamic disturbances, we have designed a control system that employs backstepping (BS) and a sliding mode controller (SMC) with RBF neural networks to achieve the cascaded control of kinematics and dynamics. Comparison of multiple sets of simulations shows that our proposed algorithm has excellent anti-disturbance performance for dynamic conditions with low measurement accuracy.

Attack Reconstruction and Attack-Resilient Consensus Control for Fuzzy Markovian Jump Multi-Agent Systems

Driven by the rapid development of modern industrial applications, multi-agent systems (MASs), integrating computational and physical resources, have become increasingly important in recent years. However, the performance of MASs can be easily compromised by malicious false data injection attacks (FDIAs) due to the inherent vulnerability of the cyber layer. This work focuses on an event-triggered framework for secure reconstruction and consensus control in MASs subject to both sensor and actuator attacks. First, we introduce a class of Takagi–Sugeno fuzzy multi-agent systems that relax the traditional Lipschitz condition and incorporate realistic system dynamics by considering parameter variations governed by Markovian jump principles. Second, an adaptive fuzzy estimator is developed for the simultaneous reconstruction of states and attacks in MASs. The derived estimates are utilized to design an attack-resilient consensus control strategy that compensates for the effects of FDIAs on the closed-loop consensus error dynamics. Meanwhile, the sufficient conditions for the convergence of both estimation and consensus errors are presented and rigorously proved. Finally, evaluation results on an experimental platform through multiple truck-trailer systems are provided to demonstrate the effectiveness and performance of the proposed approach.

Adaptive Path-Tracking Control Algorithm for Autonomous Mobility Based on Recursive Least Squares with External Condition and Covariance Self-Tuning

This paper introduces an adaptive path-tracking control algorithm for autonomous mobility based on recursive least squares (RLS) with external conditions and covariance self-tuning. The advancement and commercialization of autonomous driving necessitate universal path-tracking control technologies. In this study, we propose a path-tracking control algorithm that does not rely on vehicle parameters and leverages RLS with self-tuning mechanisms for external conditions and covariance. We designed an integrated error for effective path tracking that combines the lateral preview distance and yaw angle errors. The controller design employs a first-order derivative error dynamics model with the coefficients of the error dynamics estimated through the RLS using a forgetting factor. To ensure stability, we applied the Lyapunov direct method with injection terms and finite convergence conditions. Each regression process incorporates external conditions, and the self-tuning of the injection terms utilizes residuals. The performance of the proposed control algorithm was evaluated using MATLAB®/Simulink® and CarMaker under various path-tracking scenarios. The evaluation demonstrated that the algorithm effectively controlled the front steering angle for autonomous path tracking without vehicle-specific parameters. This controller is expected to provide a versatile and robust path-tracking solution in diverse autonomous driving applications.

Adaptive Weighted Particle Swarm Optimization for Controlling Multiple Switched Reluctance Motors with Enhanced Deviatoric Coupling Control

Switched reluctance motors (SRMs) are widely used in industrial applications due to their advantages. Multi-motor synchronous control systems are crucial in modern industry, as their control strategies significantly impact synchronization performance. Traditional deviation coupling control structures face limitations during the startup phase, leading to excessive tracking errors and exacerbated by uneven load distribution, resulting in desynchronized motor acceleration and increased speed synchronization errors. This study proposes a modified deviation coupling control method based on an adaptive weighted particle swarm optimization (PSO) algorithm to enhance multi-motor synchronization performance. Traditional deviation coupling control applies equal reference torque inputs to each motor’s current loop, failing to address uneven load distribution and causing inconsistent accelerations. To resolve this, a gain equation based on speed deviation is introduced, incorporating self-tracking error and gain coefficients for dynamic synchronization error compensation. The gain coefficients are optimized using the adaptive weighted PSO algorithm to improve system adaptability. A simulation model of a synchronization control system for three SRMs was developed in the Matlab/Simulink R2023b environment. This model compares the synchronization performance of traditional deviation coupling, Fuzzy-PID improved structure, and adaptive PSO improved structure during motor startup, sudden speed increases, and load disturbances. The validated deviation coupling control structure achieved the initial set speed in approximately 0.236 s, demonstrating faster convergence and a 6.35% reduction in settling time. In both the motor startup and sudden speed increase phases, the two optimized methods outperformed the traditional structure in dynamic performance and synchronization accuracy, with the adaptive PSO structure improving synchronization accuracy by 54% and 37.17% over the Fuzzy-PID structure, respectively. Therefore, the PSO-optimized control system demonstrates faster convergence, improved stability, and enhanced synchronization performance.

Error Sensitivity Analysis of a 1T2R Kinematically Redundant Parallel Mechanism With Closed-Loop Chain

Abstract In this paper, a generalized method for error modeling of the spatial 1T2R three degrees-of-freedom kinematically redundant parallel mechanism with a closed-loop chain is proposed, which is based on the matrix differential method. First, the detailed process of generalized error modeling and error analysis are described. Based on the proposed method, the error model of the spatial 3PRR(RR)S-P (P—prismatic joint, R—revolute joint, S—spherical joint, and the underline indicates that the joint is the actuator) kinematically redundant parallel mechanism is established as an example, and the correctness of the error model is verified by combining forward with inverse kinematics. Then, the patterns affecting the output error of the moving platform are discussed for the case where the mechanism contains only static error or dynamic error, respectively. In addition, the error sensitivity indices are defined to evaluate the error sensitivity of the moving platform to different redundant parameters L4 under a certain pose. Finally, in order to identify the key error terms, the sensitivity of the output error of the mechanism to a single error term is analyzed. The results show that the error sensitivity of the spatial kinematically redundant parallel mechanism can be effectively reduced by adjusting the kinematically redundant parameters, so that the mechanism can maintain a low error sensitivity in a certain pose.

Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using Chatterjee’s correlation coefficient

This study revisits the cross-correlation between cosmic ray intensity (CRI) and solar activity (SA) by comparing traditional Pearson correlation with Chatterjee’s correlation coefficient. Traditional analyses using Pearson correlation are useful for identifying linear relationships and time lags. However, they may not fully capture more complex interactions in the data. Chatterjee’s correlation coefficient, while sensitive to different types of relationships, including nonlinear ones, provides a complementary perspective on the temporal relationships between CRI and SA. This approach broadens our understanding of potential dependencies, offering additional insights that may not be captured through Pearson correlation alone.The findings reveal that Chatterjee’s correlation complements Pearson’s insights by providing an alternative view of the relationship between cosmic ray intensity (CRI) and solar activity (SA). The results show that Chatterjee’s correlation coefficients are, on average, approximately 45–50% smaller than Pearson’s, which could reflect different sensitivities to the underlying data structure rather than solely indicating a nonlinear component. Additionally, the time lags identified using Chatterjee’s correlation are generally shorter and more consistent across different solar cycles compared to those obtained with Pearson’s correlation, suggesting that CCC may capture temporal patterns in a distinct manner.Further analysis using Dynamic Time Warping (DTW) and Mean Absolute Percentage Error (MAPE) metrics demonstrated that, in more than half of the scenarios considered, alignment based on Chatterjee’s time lags resulted in lower errors and better alignment of the series compared to Pearson’s lags. This indicates that Chatterjee’s method is particularly effective for capturing the immediate and nuanced responses of CRI to SA changes, especially in recent solar cycles.This comprehensive approach provides broader insights into the dynamic interactions between cosmic ray intensity (CRI) and solar activity (SA), highlighting the importance of considering multiple correlation measures, including both linear and nonlinear approaches, in space weather research. The results suggest that Chatterjee’s correlation offers a complementary perspective on these interactions, providing additional details about how SA influences CRI over time, which may not be fully captured by Pearson’s correlation alone.

Co-Designing Dynamic Mixed Reality Drill Positioning Widgets: A Collaborative Approach with Dentists in a Realistic Setup.

Mixed Reality (MR) is proven in the literature to support precise spatial dental drill positioning by superimposing 3D widgets. Despite this, the related knowledge about widget's visual design and interactive user feedback is still limited. Therefore, this study is contributed to by co-designed MR drill tool positioning widgets with two expert dentists and three MR experts. The results of co-design are two static widgets (SWs): a simple entry point, a target axis, and two dynamic widgets (DWs), variants of dynamic error visualization with and without a target axis (DWTA and DWEP). We evaluated the co-designed widgets in a virtual reality simulation supported by a realistic setup with a tracked phantom patient, a virtual magnifying loupe, and a dentist's foot pedal. The user study involved 35 dentists with various backgrounds and years of experience. The findings demonstrated significant results; DWs outperform SWs in positional and rotational precision, especially with younger generations and subjects with gaming experiences. The user preference remains for DWs (19) instead of SWs (16). However, findings indicated that the precision positively correlates with the time trade-off. The post-experience questionnaire (NASA-TLX) showed that DWs increase mental and physical demand, effort, and frustration more than SWs. Comparisons between DWEP and DWTA show that the DW's complexity level influences time, physical and mental demands. The DWs are extensible to diverse medical and industrial scenarios that demand precision.

Distributed Neuroadaptive Formation Control for Aerial Base Station-Assisted Hovercraft Systems with Mixed Disturbances

Effectively addressing the formation control of ABS-assisted hovercraft systems with heterogeneities, unavailable leaders’ convex combination states, nonlinearities, and mixed disturbances poses significant challenges. This paper proposes a distributed neuroadaptive formation tracking strategy of ABS-assisted hovercraft systems for the first time, where aerial base stations (ABSs) are composed of unmanned aerial vehicles (UAVs) for data distribution and computation offloading. Firstly, UAVs are designed to track the virtual-leader while shaping a fixed formation, and the observer is devised for each follower hovercraft to estimate the convex combination states of UAVs. Then, output regulation equations are employed to transform heterogeneous systems into a compact form via the Kronecker product, while neural networks (NNs) are introduced to compensate for model nonlinearities. Furthermore, based on random differential equations (RDEs) combined with Lyapunov theory, the noise-to-state practical stability in probability (NSPS-P) property of the error dynamics under mixed disturbances can be obtained. Finally, simulation examples demonstrate that the outputs of follower hovercrafts rapidly achieve a time-varying formation and rotate around convex combination states of leader UAVs simultaneously.

A Closed-Form Solution to Observer Design Problem for Ostensible Metzler Takagi-Sugeno Systems

This paper addresses the state estimation problems related to the generalized fuzzy observer design for ostensible Metzler Takagi-Sugeno (T-S) systems. Attention is focused on design constraints for the concept of diagonal stabilization and positivity of observer gain matrices. On the basis of some new interpretations, the parameterizations of ostensible Metzler T-S fuzzy systems is presented, which opens the way to the solution of the design problem using only the principle of linear matrix inequalities. The same approach is intended to ensure the stability of the dynamics of the estimation error. The presented method extends and generalizes the results that have been presented in the literature so far.

Trajectory error compensation method for grinding robots based on kinematic calibration and joint variable prediction

Trajectory accuracy, a crucial metric in assessing the dynamic performance of grinding robots, is influenced by the uncertain movement of the tool center point, directly impacting the surface quality of processed workpieces. This article introduces an innovative method for compensating trajectory errors. Initially, a strategy for error compensation is derived using differential kinematics theory. Subsequently, a robot kinematic calibration method utilizing ring particle swarm optimization (RPSO) is proposed to address static errors in the grinding robot. Simultaneously, a method for predicting robot joint variables based on a dual-channel feedforward neural network (DCFNN) is designed to mitigate dynamic errors. Finally, a simulation platform is developed to validate the proposed method. Simulation analysis using extensive data demonstrates an 89.3% improvement in absolute position accuracy and a 74.2% reduction in error fluctuation range, outperforming sparrow search algorithm (SSA), improved mayfly algorithm (IMA), multi-representation integrated predictive neural network (MRIPNN), etc. Algorithmic comparison reveals that kinematic calibration significantly reduces the average trajectory error, while joint variable prediction notably minimizes error fluctuation. Validation through trajectory straightness testing and a 3D printing propeller grinding experiment achieves a trajectory straightness of 0.2425 mm. Implementing this method enables achieving 86.1% surface machining allowance within tolerance, making it an optimal solution for grinding robots.

High-precision dynamic axial clearance measurement method based on an all-fiber heterodyne microwave-AMCW with an all-phase tracking algorithm

Rotor-stator axial clearance is critical to the safety and efficiency of major rotating machinery. However, factors such as high-speed rotation, narrow space, high temperature, and vibration present significant challenges for high-precision dynamic measurement of axial clearance. This paper proposes an axial clearance measurement method based on an all-fiber heterodyne microwave amplitude-modulated continuous wave (microwave-AMCW) system combined with an all-phase tracking algorithm, characterized by high precision, wide bandwidth, and a large measurement range. To mitigate environmental influences, a heterodyne all-fiber microwave-AMCW optical path structure is developed, and a compact dual-core fiber sensor probe is designed. The all-phase tracking algorithm is introduced to enhance dynamic precision and expand bandwidth. Additionally, what we believe to be a novel bandwidth test method based on time division multiplexing is proposed to evaluate the system's wide-bandwidth performance. The proposed system's performance is validated through simulations and experiments. The results demonstrate that the system exhibits excellent resistance to environmental interference, with a measurement range up to 24.5 mm and a static precision better than 4.5µm. Dynamic experiments further confirm the algorithm's effectiveness, achieving a precision better than 5.3µm at 100kHz bandwidth. Compared to other clearance measurement algorithms including the Hilbert transform and FFT, the proposed method reduces dynamic error by over 74%.

Sliding mode control for finite-time projective synchronisation in distinct Caputo fractional-order delayed neural networks with inconsistent orders

This manuscript delves into the realm of projective synchronisation in delayed neural networks governed by Caputo fractional-order dynamics, addressing the intricate challenges of attaining finite-time synchronisation in networks with distinct structures, functions, and orders. To start, the integration of a compensation controller within the control architecture is examined, aiming to formulate the projection error dynamics. By leveraging projection error system analysis alongside output observation and sliding mode control, a meticulously crafted derivative-based sliding mode surface along with a sliding mode controller are devised, ensuring both convergence and seamless sliding motion. Afterwards, the accessibility of the surface is assessed through relevant lemmas, Caputo derivative characteristics and the Lyapunov direct approach. The subsequent stability of sliding path is corroborated, and indispensable prerequisites for achieving finite-time projective synchronisation are outlined. Furthermore, the establishment of an upper bound for synchronisation time of distinct Caputo fractional-order delayed neural networks (CFDNNs) with inconsistent orders is carried out. Ultimately, simulations on distinct CFDNNs with consistent and inconsistent orders are conducted to exemplify our approach, employing the continuous frequency distribution model.

Improving the accuracy of dynamic inclination measurement by machine learning

With the diminishing availability of oil and gas resources, the Rotary Steerable System has become increasingly important. However, the vibrations and shocks during the drilling process pose challenges to the Measurement While Drilling. In recent years, the application of machine learning in the field of petroleum exploration has gradually expanded, especially in the estimation of geological parameters and lithology discrimination. However, there is still limited research on drilling tool attitude measurement. To address the above-mentioned issues, this study proposes a method that combines drilling tool attitude sensor data with artificial neural networks to improve the accuracy of dynamic inclination measurement. This method utilizes machine learning techniques, combining real-time z-axis acceleration signals and magnetic induction signals, and employs a deep learning model to invert the x and y-axis acceleration signals, thereby achieving high-precision measurement of dynamic inclination angles. Experimental results show that Long Short-Term Memory model, under simulated measurement conditions with different rotational speeds, yields dynamic inclination curve errors ranging from 0.4° to 0.7°, significantly reducing the errors compared to the original measurements. This method not only improves the accuracy of inclination angle measurement but also demonstrates strong adaptability to different rotational speeds, providing more accurate data support for drilling operations.

Direct Multi‐Thread Adaptive Control With Attracting Manifold Design

ABSTRACTThis article presents a novel multi‐thread attracting manifold (MTAM) adaptive control scheme. The novel contribution of this new controller lies in how the attracting manifold design method is spread across multiple estimates of the truth while simultaneously weighting between said individual estimates to arrive at an adaptive composite estimate which outperforms single thread adaptive controllers. A notable benefit of this new formulation is that it allows for both the weighting of multiple threads and monotonic decrease of parameter error to aid the performance of transient error dynamics, without arbitrarily increasing adaptation gains. The benefits of the proposed controller over existing adaptive control schemes are analyzed through two aerospace flight control applications from the literature.

Correction of dynamic magnetic field errors at the rapid cycling synchrotron of China Spallation Neutron Source

At a Rapid Cycling Synchrotron (RCS), dynamic magnetic field errors, such as magnetic field tracking errors and dynamic fringe field effects, can cause time-dependent tune shift during beam acceleration. If the tune shift is significant enough to pass through resonance lines, it can lead to emittance growth and beam losses. Correcting time-dependent tune shift during acceleration is crucial for a RCS. Modulating the exciting current and magnetic field of quadrupole magnets at a RCS, which are powered by resonant circuits, is challenging during the ramping process. Correcting time-dependent tune shift at a RCS poses a significant technical challenge. We have proposed a method for correcting time-dependent tune shift at the rapid cycling synchrotron of China Spallation Neutron Source (CSNS), based on waveform compensation at the quadrupole magnets. This approach involves modulating the magnetic field variation process by injecting time harmonic exciting current into the quadrupole magnets. This method has been validated during the CSNS beam commissioning and has been applied at the RCS of CSNS to correct various dynamic magnetic field errors.

A high-precision visual detection method for rail profile based on Scheimpflug condition

Rail profile is an important indicator of rail service status, which should be always kept in good condition. How to efficiently collect rail profiles with high precision is a critical issue for their condition-based maintenance. This paper focuses on the method for accurate visual detection of rail full profile (RFP), including optical modeling, visual calibration, and error compensation. The proposed optical unit, featuring double line structured-light sensors, introduces an innovative method under the Scheimpflug condition to avoid the limitation of depth of field in RFP measurement. Subsequently, double visual sensors are calibrated together using the common reference target to extract the internal and external parameters respectively. The dynamic errors resulting from the impact of vehicle vibrations are ultimately investigated to rectify the distorted profiles to the normal. Both laboratory and field tests are performed to verify the effectiveness of the proposed system in terms of precision and efficiency.

Velocity-free event-triggered control for a class of uncertain axis-motion systems with prescribed performance

This paper investigates the fixed-time prescribed performance control problem for a class of axis-motion servo systems subject to the external disturbances and parameter uncertainties. To eliminate the requirement for velocity measurements in the control process, an auxiliary observer is first designed to reconstruct the velocity signal of the controlled plant. Subsequently, an error transformation procedure incorporating a prescribed performance index is integrated into the control system architecture. To overcome the limitations of periodic control design, a robust event-triggered controller is developed, ensuring that the dynamic error of the closed-loop system exhibits fixed-time convergence. Through rigorous theoretical analysis and proofs, it is demonstrated that the proposed event-triggered strategy guarantees Zeno-behavior-free operation. Finally, simulation results are presented to validate the effectiveness of the proposed control algorithm.

Stubborn State and Disturbance Observer Co‐Design for Nonlinear Descriptor Systems With δQC$$ \delta \mathrm{QC} $$ via a Dynamic Event‐Triggered Mechanism

ABSTRACTThis article studies the state and disturbance simultaneous estimation problem for a class of nonlinear descriptor systems with using a dynamic event‐triggered mechanism. refers to incremental quadratic constraints, which can provide a unified description of many types of common nonlinear functions. To reduce the negative impact of measurement outliers on the identification estimation, a stubborn state and disturbance observer co‐design scheme is proposed for the first time by embedding dynamic saturation output estimation errors. Meanwhile, a dynamic event‐triggered mechanism is introduced to avoid the need for continuously available output information, which can reduce the pressure on communication resources. By constructing a Lyapunov function, existence conditions of the stubborn state and disturbance observer are obtained in the form of a convex optimization problem so that the error estimation maintains an acceptable estimation performance. Finally, simulation examples illustrate the universality and stubbornness of the proposed observer.