Feedback Delay Research Articles

Delayed optical feedback-regulated artificial soliton molecule in a femtosecond optical parametric oscillator

Soliton molecules (SMs) play a crucial role in nonlinear optical systems, enriching our understanding of nonlinear science through the study of their interaction dynamics. While passively mode-locked fiber lasers offer an efficient platform for generating diverse types of SMs, the complex internal dynamics of the laser often pose challenges in achieving predetermined temporal separations between SMs. Here, we implement a delayed optical feedback technique within a femtosecond optical parametric oscillator, enabling the generation of SMs with precise and controllable temporal separations. A theoretical model, which models the intracavity iterations of the signal with a simplified Ikeda map, is proposed to study the impact of parametric gain, intracavity feedback delay, and cavity length on the internal separations of the SMs. Our experimental results confirm that adjusting the cavity length allows for producing desired temporal separations within SMs. To reveal the evolution dynamics of the SMs, we further develop a rigorous numerical model using the carrier-resolved Forward Maxwell Equation, which is capable of modeling ultra-broadband complex dynamics based on a single equation without relying on the slowly-varying envelope approximation. The numerical model unveils the rich formation dynamics of the SMs at various separations, which confirms the critical role of the gain window provided by the pump. This work opens up new opportunities for the on-demand generation of SMs and provides valuable insights into the complex dynamics in femtosecond optical parametric oscillator systems with optical delayed feedback.

Active pendulum vibration absorber utilizing a rotating inertia actuator with time delay in the position feedback

This paper presents a comprehensive analysis of an active pendulum vibration absorber (APVA) that utilizes a rotating inertia actuator (RIA) and takes into account the time delay in the position feedback. Here, the primary system is represented as a base-excited system, which includes a linear spring, damper, and mass. The absorber consists of a pendulum with a rotating inertia actuator attached to one end, a spring-damping system attached to the pendulum mass, and a delayed controller. The active control force is generated by the RIA in the proposed model, thereby preventing stroke saturation, an issue that may result in feedback controller instability. This is because, unlike proof mass actuators, the RIA does not have end-stops that limit its motion. The equations of motion describing the dynamical behavior of the primary system and APVA were derived and simulated in MATLAB Simscape and Simulink. Multi- frequency and harmonic base excitations are utilized as inputs. The simulation results show that the proposed APVA can greatly reduce vibration induced by the excitation of both single and multiple frequencies.

Analysis of athletes’ technical action based on deep learning

In order to raise athletes’ technical proficiency and overall performance, this paper uses deep learning technology to precisely assess table tennis technical activities. The paper builds a hybrid neural network model for technical action analysis of table tennis players, based on Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) in deep learning. First, CNN extracts the spatial characteristics from the video frames. After that, an LSTM processes these data in a time series to accurately recognize and classify the movements of athletes. Lastly, through trials, the model is trained and evaluated using the Table Tennis Tracking Network (TTNET) dataset. The experimental findings demonstrate that: (1) In table tennis technical action analysis, the suggested deep learning model performs better than other comparative models. The efficacy of combining convolution with sequence learning is fully demonstrated by the CNN-LSTM hybrid model, which performs best in all indicators when compared to the CNN, LSTM, Multi-Objective Function (MOF), and Convolutional Neural Network—Long Short-Term Memory (CNN-LSTM) combined models. Its accuracy rate, precision rate, recall rate, and F1 score are 0.923, 0.918, 0.925, and 0.921, respectively. In contrast, the performances of LSTM and CNN are also excellent, but the performance of MOF model is relatively low; (2) In the classification of technical actions, the model has the highest classification accuracy of service, reaching 0.930, and the classification accuracy of other technical actions such as forehand stroke, backhand stroke and spike is also above 0.9, and the time sequence consistency index also maintains a high level, indicating that the model can effectively identify and analyze table tennis technical actions. In addition, the performance evaluation of real-time feedback shows that the model can achieve low processing time and feedback delay in video data processing with different lengths, which ensures the real-time and reliability in practical applications. These results show that the proposed model can not only provide accurate technical action recognition, but also provide timely and effective feedback in practical application, which has high practical value. The results of this paper prove the potential of deep learning technology in the analysis of athletes’ technical actions, and provide scientific basis and effective tools for the technical training and optimization of table tennis players.

Improved sliding mode disturbance observer-based model-free finite-time terminal sliding mode control for IPMSM speed ripple minimization

The model-free sliding mode control with sliding mode disturbance observer (SMDO) for interior permanent magnet synchronous motor (IPMSM) is affected by feedback delays caused by mismatch of motor parameters. The observer is lagged behind the change of external disturbances, the speed tracking accuracy and transient control performance for IPMSM drives are reduced. In order to solve the issues, an improved higher-order sliding mode disturbance observer-based model-free finite-time terminal sliding mode control (HOSMDO-MFFTTSMC) strategy is proposed in this paper. First, a finite-time terminal sliding mode surface (FTTSMS) is designed, and a rotation speed-loop-based MFFTTSMC strategy is designed by combining the ultra-local model. The system control state is converged in finite time and the accurate tracking of observation error is realized. In addition, the non-singular fast terminal sliding mode is introduced into the observer, the higher-order SMDO is designed. The unknown part of disturbances is observed and compensated in real time, the fast-tracking response capability and anti-disturbance capability for IPMSM are improved, and the stator current harmonics are effectively suppressed. Finally, the proposed HOSMDO-MFFTTSMC strategy is experimentally demonstrated with a 6.6kW motor. The correctness and effectiveness of the HOSMDO-MFFTTSMC strategy are verified by simulation and experimental results.

Adaptive Neural Delay Feedback Control of a Typical Robot on a Slope

ABSTRACTIn this article, an adaptive neural delay feedback control strategy is proposed for the motion control of a two‐wheel self‐balancing robot (TWSBR) on a slope with an input delay. Based on the Lagrange equation, the dynamic model of the robot is derived. Given a target trajectory vector, the corresponding error system is obtained. An input delay and uncertainties are considered. First, the system with an input delay is transformed into a delay‐free one. Second, a quadratic performance optimization criterion is defined, and a linear quadratic regulator (LQR) controller is designed to minimize the error between the system's state vector and the target vector. Thirdly, an integral sliding mode controller is added to the LQR controller to enhance the system's robustness. To reduce the “chattering” phenomenon, an adaptive neural delay feedback control scheme is developed based on the adaptive learning of the uncertainties' upper bound by a radial basis function neural network (RBFNN). It is demonstrated that a relaxation process exists at the beginning of the upslope motion. As the input delay increases, the swing range of the center of gravity of the pendulum expands. The angle can converge to the steady state more quickly, but the relaxation time is still 0.031 s which has nothing to do with the input delay. An example of the back‐and‐forth motion of a TWSBR on a slope can verify an excellent agreement between theoretical analysis and numerical results.

Stochastic resonance in time-delayed bistable coupled network systems driven by Gaussian white noise

In this paper, we study the stochastic resonance (SR) behavior of time-delayed bistable coupled network systems under the action of Gaussian white noise and periodic signal. The model consists of a finite number N of coupled oscillators interconnected with each other, where the oscillators interact to produce complex nonlinear behavior. The original system is reduced and approximated by using the mean field theory and the small delay approximation method, and the simplified model is obtained. Analytical expression for the signal-to-noise ratio (SNR) is derived in the adiabatic limit. Additionally, statistical complexity measure is also given to verify the validity of the SNR. The numerical results demonstrate that the coupled system exhibits SR. Then, the effect of system scale on time-delayed coupled systems is discussed. It is found that when the system scale increases to a certain extent, SNR curve evolves from single peak to double peak, indicating the occurrence of double SR in the system. And, the effects of time delay, system parameters and periodic signal parameters on SR and double SR behavior of the system are analyzed respectively. It is found that the effect of time delay on the system depends on the positive or negative of the time delay feedback strength. The influence of time delay on double SR in this system is weaker than its influence on single SR.

New asymptotic study on the non-autonomous NFDEs involving Haddock conjecture

The classical Haddock conjecture is extended to a kind of non-autonomous neutral functional differential equations (NFDEs) incorporating time-varying delays in this paper. By using the Dini derivative theory and inequality analyses, without requiring the strictly monotonically increasing property of the delay feedback function, it is demonstrated that every solution of the considered NFDEs is bounded and converges to a constant, which fully refines and generalizes the existing findings.

Global existence and decay of a viscoelastic wave equation with logarithmic source under acoustic, fractional, and nonlinear delay conditions

This study is concerned with a nonlinear viscoelastic wave equation with logarithmic source term. By considering the nonlinear distributed delay feedback influenced by acoustic and fractional boundary conditions at the boundary coupling, we establish the global existence and general decay results under appropriate assumptions, even in the case of a general kernel. This result extends and complements some previous results.

Three-dimensional finite element analysis of biological signal feedback in the mechanical properties of sound production

In response to the problems of low reliability and long time consumption in traditional research on sound production, this article used electromyography (EMG) signals as input signals to build a high-precision sound production mechanics model. A Proportional-Integral-Derivative (PID) controller was used to dynamically adjust the model and develop a real-time feedback system. This article established a detailed three-dimensional (3D) finite element model including the vocal cords and throat, defined the nonlinear elastic properties and linear elastic properties of different tissues, and used tetrahedral grid partitioning technology to improve the computational accuracy of the model. Through a EMG sensor, an individual EMG was collected and filtered to remove noise. The processed EMGs were used as input parameters for the finite element model to drive the muscle units in the model. By using a PID controller to receive real-time EMG input, the error was calculated and the model was adjusted, enabling accurate simulation of the mechanical properties of vocal cord vibration under different vocal states and achieving real-time feedback. Considering the complexity of vocal cord vibration driven by biological signals, this article simulated and analyzed the modal characteristics of vocal cord vibration, and analyzed the differences in vocal cord vibration characteristics under different vocal states. The sound pressure distribution and resonance frequency were simulated and analyzed to understand the propagation characteristics of sound. Finally, by comparing and analyzing the simulated data with the actual collected data, it was found that the maximum relative error rate of the model under different sound states was 6.14%, and the overall error rate of the model was relatively low, which verified the reliability of the model. The findings demonstrated that the feedback delays of the model in different sound states were all within 100 milliseconds, indicating that the system had high real-time performance and accuracy, which was promising in practical applications.

Bayesian inference of state feedback control parameters for fo perturbation responses in cerebellar ataxia.

Behavioral speech tasks have been widely used to understand the mechanisms of speech motor control in typical speakers as well as in various clinical populations. However, determining which neural functions differ between typical speakers and clinical populations based on behavioral data alone is difficult because multiple mechanisms may lead to the same behavioral differences. For example, individuals with cerebellar ataxia (CA) produce atypically large compensatory responses to pitch perturbations in their auditory feedback, compared to typical speakers, but this pattern could have many explanations. Here, computational modeling techniques were used to address this challenge. Bayesian inference was used to fit a state feedback control (SFC) model of voice fundamental frequency (fo) control to the behavioral pitch perturbation responses of speakers with CA and typical speakers. This fitting process resulted in estimates of posterior likelihood distributions for five model parameters (sensory feedback delays, absolute and relative levels of auditory and somatosensory feedback noise, and controller gain), which were compared between the two groups. Results suggest that the speakers with CA may proportionally weight auditory and somatosensory feedback differently from typical speakers. Specifically, the CA group showed a greater relative sensitivity to auditory feedback than the control group. There were also large group differences in the controller gain parameter, suggesting increased motor output responses to target errors in the CA group. These modeling results generate hypotheses about how CA may affect the speech motor system, which could help guide future empirical investigations in CA. This study also demonstrates the overall proof-of-principle of using this Bayesian inference approach to understand behavioral speech data in terms of interpretable parameters of speech motor control models.

Data-driven room acoustic modeling via differentiable feedback delay networks with learnable delay lines

Over the past few decades, extensive research has been devoted to the design of artificial reverberation algorithms aimed at emulating the room acoustics of physical environments. Despite significant advancements, automatic parameter tuning of delay-network models remains an open challenge. We introduce a novel method for finding the parameters of a feedback delay network (FDN) such that its output renders target attributes of a measured room impulse response. The proposed approach involves the implementation of a differentiable FDN with trainable delay lines, which, for the first time, allows us to simultaneously learn each and every delay-network parameter via backpropagation. The iterative optimization process seeks to minimize a perceptually motivated time-domain loss function incorporating differentiable terms accounting for energy decay and echo density. Through experimental validation, we show that the proposed method yields time-invariant frequency-independent FDNs capable of closely matching the desired acoustical characteristics and outperforms existing methods based on genetic algorithms and analytical FDN design.

Time-delay feedback control on vertical vibration of maglev train under unsteady aerodynamic force

The stability and safety of maglev trains are significantly affected by unsteady aerodynamic forces during high-speed operation. In this paper, we employ a time-delay feedback control strategy to suppress the nonlinear vertical vibrations of maglev train under periodic unsteady aerodynamic force. Firstly, the amplitude-frequency response equation of the maglev vehicle is derived using the multiple scales method, and the stability of the steady-state solutions is determined. Then, the influences of velocity feedback gain coefficient and velocity time delay on the nonlinear vibrations of the maglev vehicle are investigated. The optimal value range of the time delay is identified. The results demonstrate that the time delay feedback control can effectively suppress the nonlinear vibration of maglev vehicles and enhance their operational stability under the premise of reasonable selection of time delay parameters. The theoretical research presented in this paper can serve as a theoretical reference for the design, improvement, and optimization of control systems for high-speed maglev trains.

Existence and Stability Results for Thermodiffusion Laminated Beam System with Delay Feedback

Existence and Stability Results for Thermodiffusion Laminated Beam System with Delay Feedback

Vibration control of nonlinear viscoelastic systems with displacement delay feedback

In this study, the nonlinear vibration characteristics of a nonlinear Zener model under harmonic excitation, equipped with linear and nonlinear displacement delay feedback control, were investigated. The amplitude–frequency curve of the system’s main resonance was computed using the multi-scale method. Stability conditions for the system were then established based on the Lyapunov stability theory. The influence of several parameters on the system’s dynamic behavior was also analyzed, including time delay, displacement feedback gain coefficient, nonlinear term coefficient, damping coefficient, and external excitation. The findings revealed that the nonlinear displacement feedback gain coefficient was observed to exert a more substantial effect on the system’s amplitude than other factors. Further, the nonlinear displacement delay feedback gain coefficient and time-delay value diminish the amplitude of the vibration, leading all solutions to achieve a stable state. In instances with time-delay control, the impact of the main system parameters on system vibration was significantly diminished. The aim of this study is to provide a theoretical basis for the implementation of displacement delay controllers in nonlinear viscoelastic systems.

Performance Analysis of Antenna-relay Selection in CNOMA Systems under Practical Impairments

Selection strategies prove to be a valuable approach in mitigating complexity associated with antenna selection (AS) and relay selection (RS), optimizing signal transmission through a streamlined number of antennas/relays, and enhancing overall system performance. This paper offers a comprehensive analysis, deriving closed-form expressions for the outage probability (OP) and throughput in proposed scenarios that leverage the best relay selection (BRS) and transmit antenna selection (TAS) protocol for cooperative non-orthogonal multiple access (CNOMA), along with partial relay selection (PRS) and TAS protocol for CNOMA. The study extends to Rayleigh fading channels, considering practical impairments such as successful interference cancellation (SIC) error, channel estimation error (CEE), and feedback delay error. In comparing the proposed system to conventional CNOMA, our findings highlight the substantial impact of SIC, CEE, and feedback delay imperfections on the performance of both proposed scenarios. Notably, the application of BRS-based TAS protocol outperforms PRS-based TAS in terms of OP and throughput. The close alignment between analytical, asymptotic, and simulation results attests to the credibility of conducted analysis.

Multi-image encryption based on 3D space scrambling and new spatiotemporal chaotic system

This paper introduces a groundbreaking spatiotemporal chaotic system, named DCMLMDF, and a novel encryption method that synergizes scrambling and diffusion synchronization for multi-image encryption. The DCMLMDF system, which incorporates a dynamic coupling approach and a random delay feedback mechanism, significantly enhances the randomness and complexity of the encryption process. By applying this system within the newly designed multi-image encryption framework, the method achieves three-dimensional space scrambling and diffusion synchronization, overcoming traditional encryption challenges such as extended encryption time and periodic vulnerabilities. The results demonstrate that this innovative approach not only effectively confuses image data but also substantially improves overall system security, marking a significant advancement in the application of chaotic systems to image encryption.

Bridging the gaps – A mixed methods approach to evaluating novel feedback surveys of children on school buildings

Feedback is critical to improve the sustainability of all buildings. Current post occupancy feedback is not useful for architects and designers and barriers to obtaining post-occupancy data have been well documented. In addition, there are delays in feedback of research conclusions appearing in Continuing Professional Development. Therefore, architects need timely feedback on their own building designs and methods they can use to obtain feedback for themselves. Previously, a literature review and survey of architects were conducted to identify gaps in feedback for school buildings compared to an Integral Sustainable Design (ISD) framework. A suite of ISD comprehensive on-line surveys were developed for various school user groups to target the identified gaps. This paper presents data from testing a novel survey of children in a case study and comparison of some questions to instrument measurement. The results show that the spatial questions with reasons yielded valuable insights. Some qualitative questions will require amendment to yield useful information. Univariate analysis shows that some thermal comfort questions would be suitable as a substitute for instrument measurement whereas lighting questions would not. Conversely, the question on vocal comprehension provided clear responses, supported by instrument measurement. Likert-style questions regarding sense of place, connection to outside, feelings of safety, etc. Were generally successful. Overall, the new ISD children's survey provides useful information for architects to address feedback gaps identified and will continue to improve with lessons from this case study.

A 13.56-MHz 93.5%-Efficiency Optimal On/Off Timing Tracking Active Rectifier with Digital Feedback-Based Adaptive Delay Control.

This paper presents an adaptive active rectifier with digital feedback delay controllers (DFDC) which quickly tracks optimal on/off timing against input voltage and load variations. To efficiently generate the on/off transition, the proposed active rectifier adopts dynamically controlled coarse/fine delay lines rather than using conventional power-hungry static comparators, while removing the risk of unwanted multiple driving pulses to pass transistors. DFDC conducts the dual-loop digital feedback to independently adjust on/off timing with high-speed 13.56-MHz loop bandwidth, improving the voltage conversion ratio (VCR) and power conversion efficiency (PCE). DFDC can enable real-time power-saving mode control that automatically masks clock-toggling to non-essential blocks to minimize dynamic power loss while driving power transistors. To validate the efficacy of the proposed adaptive rectifier during digital feedback and settling procedures, experiments were carried out with 0.25 μm CMOS prototype at the carrier frequency of 13.56-MHz, input voltages between 1.7 and 2.6 V, and load ranges from 0.33 to 2.2 kΩ. The proposed active rectifier employing DFDC achieves a peak PCE of 93.5% and the peak VCR of 96.3% at the output power of 12.52 mW and 2.02 mW, respectively.

A class of nonlinear ship stability analysis: Stochastic dynamics with time-delayed control in crosswind and wave conditions

The impact of ocean waves and crosswinds on ships has long been a focal point of research for many scholars. This paper proposes a stochastic ship rolling model influenced by crosswinds, ocean waves, and time delays. The safe operating region for ship navigation is presented through the phase space of the system. A quantitative discussion of the system is conducted using the stochastic Melnikov function, and the stochastic P-D bifurcation of the system is discussed using topological data analysis techniques. The research indicates that incorporating time delay feedback can effectively enhance the system’s stability.

Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability

Abstract Spacecraft models that mimic the Planck satellite’s behaviour have produced information on cosmic microwave background radiation, assisting physicists in their understanding of the composition and expansion of the universe. For achieving the intended formation, a framework for a discrete fractional difference spacecraft model is constructed by the use of a discrete nabla operator of variable order containing the Mittag–Leffler kernel. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as exterior disruptions, parameterized variations, time-varying feedback delays, and actuator defects. The implementation of the Banach fixed-point approach provides sufficient requirements for the presence of the solution as well as a distinctive feature for such mechanisms Furthermore, the consistent stability is examined. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of spacecraft systems to provide justification for structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the spacecraft system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional orders in the offered system. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the spacecraft chaotic model is an intriguing and crucial subject for research.