Error Dynamics Research Articles

Pulsed vector atomic magnetometer using an alternating fast-rotating field

We introduce a vector atomic magnetometer that employs a fast-rotating magnetic field applied to a pulsed 87Rb scalar atomic magnetometer. This approach enables simultaneous measurements of the total magnetic field and its two polar angles relative to the rotation plane. Operating in gradiometer mode, the magnetometer achieves a total field gradient sensitivity of 35 fT/Hz (0.7 parts per billion) and angular resolutions of 6 nrad/Hz at a 50 μT Earth field strength. The noise spectra remain flat down to 1 Hz and 0.1 Hz, respectively. Here we show that this method overcomes several metrological challenges commonly faced by vector magnetometers and gradiometers. We propose a unique peak-altering modulation technique to mitigate systematic effects, including a newly identified dynamic heading error. Additionally, we establish the fundamental sensitivity limits of the sensor, demonstrating that its vector sensitivity approaches scalar sensitivity while preserving the inherent accuracy and calibration benefits of scalar sensors. This high-dynamic-range, ultrahigh-resolution magnetometer offers exceptional versatility for diverse applications.

Limitations to Dynamical Error Suppression and Gate-Error Virtualization from Temporally Correlated Nonclassical Noise

Realistic multiqubit noise processes often result in error mechanisms that are not captured by the probabilistic Markovian error models commonly employed in circuit-level analyses of quantum fault tolerance. By working within an open-quantum system Hamiltonian formulation, we revisit the validity of the notion of a constant gate error in the presence of noise that is both and , and the impact of which is mitigated through perfect instantaneous dynamical decoupling subject to finite timing constraints. We study a minimal exactly solvable single-qubit model under Gaussian quantum dephasing noise, showing that the fidelity of a dynamically protected idling gate can depend strongly on its location in the circuit and the history of applied control, even when the system-side error propagation is fully removed through perfect reset operations. For digital periodic control, we prove that, under mild conditions on the low-frequency behavior of the nonclassical noise spectrum, at a value that is strictly smaller than the one attainable in the absence of control history; the presence of high-frequency noise peaks is also found as especially harmful, due to the possible onset of . We explicitly relate these features to the evolution of the bath statistics during the computation, which has not been fully accounted for in existing treatments. We find that only if decoupling can keep the qubit highly pure over a time scale larger than the correlation time of the noise, the bath approximately converges to its original statistics and a stable-in-time control performance is recovered. Our work highlights the significance of the full bath evolution between circuit locations and suggests that additional trade-offs and design constraints may arise in layered quantum fault-tolerant architectures from the need to appropriately reequilibrate the quantum bath statistics, particularly when Markovian noise is present alongside temporally correlated noise. Published by the American Physical Society 2025

Control Error Convergence Using Lyapunov Direct Method Approach for Mixed Fractional Order Model Reference Adaptive Control

Abstract: This paper extends Lyapunov stability theory to mixed fractional order direct model reference adaptive control (FO-DMRAC), where the adaptive control parameter is of fractional order, and the control error model is of integer order. The proposed approach can also be applied to other types of model reference adaptive controllers (MRACs), provided the form of the control error dynamics and the fractional order adaptive control law are similar. This paper demonstrates that the control error will converge to zero, even if the derivative of the classical Lyapunov function is positive during a transient period, as long as tends to zero as time approaches infinity. Finally, this paper provides application examples that illustrate both the convergence of the control error to zero and the behavior of .

Nonlinearity Harmonic Error Compensation Method Based on Intelligent Identification for Rate Integrating Resonator Gyroscope

This paper presents an improved intelligent optimizing algorithm based on parameter identification and drift compensation for the rate-integrating resonator gyroscope (RIRG). Besides damping and frequency imperfections, the RIRG measurement accuracy still suffers from limitations due to nonlinear error. Therefore, the dynamic nonlinear error model for RIRG has been established to reveal the relationship between the pattern angle and harmonic drifts. Based on this, a dynamic analysis of the gyroscope operating state is carried out using nonlinear motion equations. The optimal harmonic error parameters are then identified by a particle swarm optimization (PSO) algorithm for the drift error compensation. To further improve the measurement accuracy, chaotic technology is integrated with PSO, leading to more precise identification. Subsequently, the harmonic parameters of the bias drifts are efficiently compensated. Experimental results demonstrate that the bias drift is reduced by over 90% after harmonic error compensation, demonstrating the validity of the proposed method in enhancing the measurement accuracy of RIRGs.

Functional interval estimation for continuous-time linear systems with time-invariant uncertainties

This paper investigates functional interval estimation for continuous-time linear systems subject to both time-varying and time-invariant uncertainties. Two novel methods are proposed based on peak-to-peak functional observer design and interval analysis. First, we present a splitting-based method that splits the estimation error dynamics into two subsystems to handle the time-invariant disturbances and provide accurate estimation results. Then, to further enhance the estimation accuracy, we present an augmentation-based method that considers the time invariance in both functional observer design and reliable interval estimation. The relationship between a state-of-art method and the proposed methods are analysed theoretically. Finally, simulation results are provided to demonstrate the performances of the proposed methods.

Investigation on the dynamic characteristics of gears considering spatial crack propagation

Abstract Considering the failure of gear space cracks caused by uneven load distribution, local material defects and installation errors, the effect of gear crack space propagation path on dynamic characteristics was investigated based on the extended finite element model and gear dynamics model. The effect of the initial crack location and angle on the extent of crack expansion and the dynamic characteristics of the gear was discussed, and experimental verification was conducted. The results demonstrated that with the expansion of the spatial crack, the time-varying meshing stiffness TVMS gradually decreases, which leads to the periodic impact response of the dynamic meshing force and dynamic transmission error, and sidebands appear around the meshing frequency and harmonic components. Furthermore, the location and angle of the initial crack lead to different crack propagation paths in space, which in turn lead to different variations of gear dynamic characteristics.

Nonlinear real-time correction in homodyne interferometers by multi-area spatial sampling and dimensionality-reduced ellipse fitting

Homodyne interferometers are susceptible to signal instability, including the amplitude, relative phase, and DC bias of interference signals, which lead to dynamic nonlinear errors that require real-time correction to ensure full-range displacement measurement accuracy. To address these issues, this paper proposes a real-time, non-iterative FPGA-based nonlinear correction method, designed to balance accuracy and computational efficiency. The method employs peak detection to simplify the elliptical fitting matrix and utilizes feature-based segmented sampling to perform reduced-order correction. Experimental results show that when elliptical signals are unstable, this method reduces residual error from 1.14 nm to 0.12 nm, effectively compensating for nonlinear errors. In a 25 µm displacement test, this method maintains nonlinear error deviation within the sub-nanometer range compared to traditional correction methods, while reducing the computational load by two orders of magnitude, achieving a balance between correction accuracy and efficiency.

Phase control method for generating orbital angular momentum beams using coherent beam combining based on deep learning

In recent years, orbital angular momentum (OAM) beams have shown great potential for applications in laser communication, laser processing, optical imaging, and detection. For free-space optical communication, high-power, high-quality vortex beams with a high signal-to-noise ratio are critical for long-distance communication. Coherent beam combining (CBC) of vortex beams enables the enhancement of power while maintaining high beam quality. Considering the orbital angular momentum spectrum as a new dimension of optical wave resources, achieving rapid phase locking of specific phases is crucial for increasing communication capacity. Traditional phase control methods based on wavefront intensity distribution face limitations in optimization, particularly for centrosymmetric laser phased arrays. To address this, we propose a deep learning-based method using spiral phase modulation. By designing a loss function that eliminates phase periodicity, we establish a nonlinear mapping between the sub-beam phases and the far-field image. To improve the phase prediction accuracy of the deep learning model, we introduce a power-in-the-bucket (PIB) metric for the vortex beam’s main lobe, which mitigates dynamic phase errors caused by thermal and environmental disturbances. This method holds promise for application in high-power vortex beam optical systems with coherent combining of fiber laser phased arrays.

A Review of Diagnostic Methods for Yaw Errors in Horizontal Axis Wind Turbines

Yaw errors occur in wind turbines either during the installation stage or because of the aging of devices. It reduces the wind speed in the rotor axial direction and increases the structural loads in the lateral direction. Diagnosing yaw error rapidly and accurately is crucial for avoiding the introduced under-performance. In this review paper, we first introduce the fundamental concepts and principles of wind turbine yaw control strategies, and we discuss two types of yaw errors (i.e., the static yaw error and the dynamic yaw error) with their corresponding causes. Subsequently, we outline the existing yaw error diagnostic methods, which are based on the LiDAR (light detection and ranging) data, the SCADA (supervisory control and data acquisition) data, or a combination of the two, and we discuss the advantages and disadvantages of various methods. At last, we emphasize that the diagnostic performance can be improved via the combination of the LiDAR data and the SCADA data, and it benefits from an in-depth understanding of the salient features and influential factors associated with the yaw error. Meanwhile, the potential of intelligent clusters and digital twins for detecting yaw errors is discussed.

Banking Market Structure and Heterogeneous Response of Bank Lending to Monetary Policy: Evidence from Uganda

This paper investigates the heterogeneous response of bank lending following a monetary policy change. The study was conducted in the context of developing countries and is based on dynamic panel error correction methods using quarterly Ugandan bank level data for the period 2009 - 2019. Results support the presence of heterogeneity in bank lending response to monetary policy changes by bank size and ownership type. Specifically, monetary policy pass through is weaker in large foreign banks and stronger in smaller Pan African banks. Moreover, bank lending response to monetary policy is asymmetric with insignificant effects when the policy rate is falling. Risk, government borrowing, capital, and liquidity at the bank level, competition at the industry level, and inflation at the macro level are some of the factors that explain the response of bank lending to monetary policy.

Enhancing weather predictions: Initial condition sensitivity and error dynamics in data assimilation

Enhancing weather predictions: Initial condition sensitivity and error dynamics in data assimilation

Event-triggered hybrid stubborn ESO for networked systems with uncertain disturbances and stochastic deception attacks.

In this paper, the state estimation problem is investigated for a general class of nonlinear networked systems subject to both external disturbances and stochastic deception attacks. In the presence of deception attacks, a novel hybrid stubborn extended state observer (ESO) is established to estimate the states and total disturbances, simultaneously. In addition, the event-triggered mechanism (ETM) is introduced utilizing the estimation errors to relieve the burden of the transmission networks. Then, an inter-trigger output predictor is adopted based on the estimation state of the hybrid stubborn ESO to predict the information between two consecutive triggering moments. To overcome the disadvantage of the outliers induced by the deception attack, the saturation nonlinearity is adopted as the gain function of the hybrid stubborn ESO. Sufficient conditions are established to ensure that the estimation error dynamics is locally mean-square bounded in a domain of attraction, and then an iterative linear matrix inequality (ILMI) approach is employed to design the desired hybrid stubborn ESO. Moreover, the Zeno behavior can be avoided when the designed ETM is utilized. Some numerical simulations are conducted to demonstrate the validity of the proposed methodology.

Features extraction of complex dynamic electricity signals for testing dynamic errors in electricity meters

Features extraction of complex dynamic electricity signals for testing dynamic errors in electricity meters

3-axis force compensated piezo stage combination for high-speed SPM

Abstract Scanning stages are immanent for scanning probe microscope type tools and highly impact most of their properties, such as scanning speed and positioning accuracy. In this contribution, a serial assembly of an in open-loop operated 3-axes monocrystalline piezo stage with an in closed-loop operated 6-axes polycrystalline piezo stage is presented. The monocrystalline piezo stage is applied to enhance the limited bandwidth of the polycrystalline piezo stage and includes an internal compensation mechanism for reaction forces. The compensation mechanism is designed to operate the scanner as a no retroactive stage by reducing the dynamic scanning motion errors in high-speed application to a minimum. It works for sinusoidal oscillations and shows a frequency dependence. The monocrystalline piezo stage has a position noise of <0.1 nm (1σ) in z-direction, positioning bandwidth >1 kHz and travel range 1 × 1 × 1 μm in x-, y-, z-direction, respectively. The 6-axes piezo stage complements this assembly with a position noise of <0.35 nm (1σ) in x-, y- and z-direction, a closed-loop bandwidth >200 Hz, a rotation range of ±0.5 mrad, and a travel range 45 × 45 × 45 μm in x-, y-, z-direction, respectively.

Sampled Robust Control for Constrained Unicycle Mobile Robots

The aim of this paper is to design a sampled robust controller for the trajectory tracking problem in constrained unicycle mobile robots. The proposed swithched controller is composed by an aperiodic control law and a periodic control law. The aperiodic control consists on an state–feedback–based event–triggered control wich is designed by means of the attractive ellipsoid method and the barrier Lyapunov function. The periodic sampled control part is designed taking into account a maximum sampling time. A safe set where the state constraints are not violated, and a switching set that determines the region where each part of the controller is active are provided. The proposed strategy guarantees the input–to–state stability of the tracking error dynamics with respect to external disturbances. The feasibility of the proposed approach is demonstrated through simulation results.

A Controller Design for Evaders Considering Single Integrator Dynamics

This paper presents a novel controller for the evader in the pursuit–evasion game, when each player is modeled as a single integrator. The resulting control design does not require any information on the pursuer control, only requires information on the pursuer state. The resulting control ensures the escape of the evader from the pursuer under an adequate selection and design of the evader controller parameters. Additionally, the synthesis of this controller is constructive and can be tuned straightforwardly since it is obtained from the solution of an LMI. The stability analysis of the tracking error dynamics is carried out considering a Lyapunov–like function and the effectiveness of the proposed result is illustrated through some simulations.

Coupled vibration characteristics of a drive system during automatic transmission power shifting

To elucidate the vibration principle and effectively mitigate noise during power shifting in an automatic transmission, this study investigates a power split automatic transmission. The transmission principle and power flow path are analyzed using the centralized mass method and Lagrange equation. A vibration model that encompasses both clutches and gears is established for the coupling system. The dynamic model and vibration principle of clutches during power shifting are determined. Subsequently, the dynamic vibration characteristics are solved considering engine speed as a time-domain excitation source, while analyzing the dynamic transmission error. By optimizing gear modification parameters and structural stiffness, measures to reduce both dynamic transmission error and vibrational response during power shifting are obtained. Through vehicle-based vibration analysis and testing, a comparison is made between optimized gear parameters’ vibrational response characteristics and noise test data; revealing significant improvement in vibration performance by 3%–6%. A new approach is suggested for studying the vibration characteristics and dynamic response of automatic transmissions during power shifting, which provides both theoretical importance and practical benefit in effectively minimizing vehicle vibrations and noise.

Nonlinear Adaptive Optimal Control Design and Implementation for Trajectory Tracking of Four-Wheeled Mecanum Mobile Robots

This study proposes a nonlinear adaptive optimal control method, the adaptive H2 control method, applied to the trajectory tracking problem of the wheeled mobile robot (WMR) with four-wheel mecanum wheels. From the perspective of solving mathematical problems, finding an analytical adaptive control solution that satisfies the adaptive H2 performance criterion for the trajectory tracking problem of the WMR with four-wheel mecanum wheels is an extremely challenging task due to the high complexity of the dynamic system. To analytically derive the control law and adaptive control law for this trajectory tracking problem, a proportional-derivative (PD) type transformation is employed to formalize the trajectory tracking error dynamics between the WMR and the desired trajectory (DT). Based on an in-depth analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from the highly complex nonlinear dynamic system equations. This control law provides a solution to the trajectory tracking problem of the WMR while satisfying the adaptive H2 performance criterion. The proposed adaptive nonlinear control method offers a simple control structure and advantages such as improved energy efficiency. Finally, simulations and experimental implementations were conducted to verify the performance of the proposed adaptive H2 control method and the H2 control method in tracking the DT. The results demonstrate that, compared to the H2 control method, the adaptive H2 control method exhibits superior trajectory tracking performance, particularly in the presence of significant model uncertainties.

An airborne gravity gradient compensation method based on residual backpropagation

Abstract Airborne gravity gradient dynamic measurement error compensation is a crucial aspect of data processing in gravity gradient dynamic measurements. This study introduces a deep learning approach based on a residual backpropagation (Res-BP) neural network for post-error compensation in airborne gravity gradient dynamic measurement. The network employs residual connections to facilitate identity mapping, thereby enabling gradient propagation across layers. This strategy preserves the original information while acquiring additional information through nonlinear operations, effectively mitigating the gradient vanishing issue and enhancing the neural network's fitting capability. The method proposed in this paper is applied to both simulation data from a gravity gradiometer and high-altitude dynamic measured data of an airborne gravity gradient. Compared to traditional neural network multilayer perceptron (MLP), the Res-BP method significantly improves compensation accuracy through its application in high flight experiment of the southern section of
Zhangguangcai Ridge on the western side of Mudanjiang City, Heilongjiang Province.

Precise Orbit Determination of Mars-crossing Asteroids

This study investigates the orbit determination of the Mars-crossing asteroids (MCAs) with a focus on the possibility of detecting their Yarkovsky signals. We analyze the influences of force model uncertainties on MCA orbits, including the uncertainty of the main asteroid belt, and the uncertainty of the major planets’ ephemeris. The main asteroid belt is modeled using 343 asteroids and a ring structure. The Yarkovsky effect’s quadratic nature allows it to dominate over extended observation periods. To address dynamical errors and potential interactions with the main asteroid belt, we employ not only a traditional seven-dimensional differential corrector but also a nine-dimensional differential corrector that considers radial, vertical, and transversal forces. Comparison shows that the latter approach enhances the fit to observational data. However, the reliability of the Yarkovsky parameter is not enhanced because the estimation of the radial component is physically unacceptable. Despite incorporating precise Gaia data, our analysis does not conclusively detect a Yarkovsky effect on MCAs due to uncertainties in the force model. Nevertheless, our research advances our understanding of MCA dynamics, identifying five potential candidates whose Yarkovsky effect may be observable.