Linear Feedback Model Research Articles

Ankle torque variance is a better indicator of balance control performance than plantar perceptual sensitivity threshold.

We explored whether ankle torque variability or plantar perceptual threshold explains human balance control more effectively. We hypothesized that ankle torque variance is a better indicator of center of pressure (COP) velocity variance than plantar perceptual sensitivity. Two conditions were tested: loaded (23-kg vest added) and unloaded, as loading should diminish plantar sensitivity and increase COP velocity variability. We created a linear feedback model to assess the noise change in the sensorimotor loop induced by loading. Plantar sensitivity was quantified using a psychophysical approach while participants stood barefoot. A linear motor applied a force impulse on the participant's heel. A "yes-no" method of limits was selected to identify plantar sole sensory thresholds in both conditions. We observed reduced plantar sensitivity in loaded compared with unloaded conditions. In the loaded condition, participants exhibited greater COP velocity variance, with significant positive Pearson's correlations confirming a substantial association between ankle torque and COP velocity variances for both loaded [variance accounted for (VAF): r2 = 44.56%, P = 0.018] and unloaded conditions (VAF: r2 = 58.83%, P = 0.004). No significant correlation existed between COP velocity variance and plantar sensitivity threshold for both loaded (VAF: r2 = 0.002%, P = 0.99) and unloaded conditions (VAF: r2 = 21.81%, P = 0.35). The model confirmed an ∼88% rise in sensorimotor loop noise in the loaded condition. Ankle torque variance assesses the precision of nonperceptual and perceptual detection mechanisms in evaluating whole body motions and the accuracy in converting sensory cues into ankle torque.NEW & NOTEWORTHY Plantar cutaneous information contributes to balance control by modulating motor commands, but plantar perceptual sensitivity is a suboptimal indicator of balance performance. Multiple sensory cues encode whole body dynamics, guiding sensorimotor mechanisms to minimize body sway variability. Ankle torque variance is proposed as a superior measure for explaining balance control performance and evaluating the sensorimotor loop's functioning in balance control.

Consensus Control of Heterogeneous Uncertain Multiple Autonomous Underwater Vehicle Recovery Systems in Scenarios of Implicit Reduced Visibility

This paper investigates consensus control in heterogeneous and uncertain multiple autonomous underwater vehicle (AUV) systems under implicit reduced visibility conditions. We address challenges such as environmental uncertainties and system nonlinearity by utilizing a unified connectivity approach to model low-visibility interactions and heterogeneous multi-AUV dynamics. Our main contributions include developing a feedback linearization model for heterogeneous multi-AUV systems that accounts for uncertainties, introducing an adaptive consensus controller based on relative positioning that effectively manages implicit visual interaction limitations and validating our strategies through stability analysis and numerical simulations. Our simulations demonstrate approximately a 60% improvement in accuracy compared to previous algorithms, highlighting the practical value of our approach in AUV recovery operations. These advancements provide a robust solution for consensus control in complex underwater environments.

Combined translational and rotational perturbations of standing balance reveal contributions of reduced reciprocal inhibition to balance impairments in children with cerebral palsy.

Balance impairments are common in cerebral palsy. When balance is perturbed by backward support surface translations, children with cerebral palsy have increased co-activation of the plantar flexors and tibialis anterior muscle as compared to typically developing children. However, it is unclear whether increased muscle co-activation is a compensation strategy to improve balance control or is a consequence of reduced reciprocal inhibition. During translational perturbations, increased joint stiffness due to co-activation might aid balance control by resisting movement of the body with respect to the feet. In contrast, during rotational perturbations, increased joint stiffness will hinder balance control as it couples body to platform rotation. Therefore, we expect increased muscle co-activation in response to rotational perturbations if co-activation is caused by reduced reciprocal inhibition but not if it is merely a compensation strategy. We perturbed standing balance by combined backward translational and toe-up rotational perturbations in 20 children with cerebral palsy and 20 typically developing children. Perturbations induced forward followed by backward movement of the center of mass. We evaluated reactive muscle activity and the relation between center of mass movement and reactive muscle activity using a linear feedback model based on center of mass kinematics. In typically developing children, perturbations induced plantar flexor balance correcting muscle activity followed by tibialis anterior balance correcting muscle activity, which was driven by center of mass movement. In children with cerebral palsy, the switch from plantar flexor to tibialis anterior activity was less pronounced than in typically developing children due to increased muscle co-activation of the plantar flexors and tibialis anterior throughout the response. Our results thus suggest that a reduction in reciprocal inhibition causes muscle co-activation in reactive standing balance in children with cerebral palsy.

Torque modulation mechanism of the knee joint during balance recovery

Exploring the torque modulation mechanisms of human joints is critical for analyzing the human balance control system and developing natural human-machine interactions for balance support. However, the knee joint is often overlooked in biomechanical models because of its limited range of motion during balance recovery. This poses a challenge in establishing mathematical models for the knee joint's torque modulation mechanisms using computer simulations based on the inverted pendulum model. This study aims to provide a simplified linear feedback model inspired by sensorimotor transformation theory to reveal the torque modulation mechanism of the knee joint. The model was validated using data from experiments involving support-surface translation perturbations. The goodness-of-fit metrics of the model, including R2 values and root mean square errors (RMSE), demonstrated strong explanatory power (R2 ranged from 0.77 to 0.90) and low error (RMSE ranging from 0.035 to 0.072) across different perturbation magnitudes and directions. Through pooling samples across various perturbation conditions and conducting multiple fits, this model revealed that knee torque is modulated using a direction-specific strategy with adaptable feedback gains. These results suggest that the proposed simplified linear model can be used to develop assistive systems and retrieve insights on balance recovery mechanisms.

Energy digital twins in smart manufacturing systems: A case study

Among core Industry 4.0 technologies, the Digital Twin represents a promising smart technology and tool that researchers are investigating to help improve energy efficiency at the shopfloor level by analyzing and optimizing energy consumption. Energy Digital Twins are a relatively new area of research, only gaining popularity in industry applications and academia recently. where a comprehensive literature review uncovered only one ‘true’ Energy Digital Twin application across published research to date. To address this research gap, an Energy Digital Twin for smart manufacturing systems was developed and evaluated in this study. In particular, the study focused on bidirectional parameter communication between the physical and the virtual part with the aim of optimizing the energy used in the manufacturing process. To address this research gap, the research objective is to create and evaluate an application of an energy optimizing Digital Twin for a Heating Tunnel. Following the definition of a Digital Twin, the research methodology and experimental setup have three major components: i) the Heating Tunnel as the physical object, ii) the digital counterpart constructed using Python to house the digital control logic and linear energy optimization feedback model, and iii) the connecting fabric, in form of a bidirectional OPC UA communication protocol. The optimization model ingests input parameters of setpoint temperature, power level, and targeted overshoot time, and after running the simulation, returns a calculated value of the required turn off temperature to the real-time heating process of the physical system. Results show that the Energy Digital Twin is effective at maintaining the maximum temperature range of the Heating Tunnel during the heating process, in addition to reducing the energy consumption and cost for all trial runs compared to the original process. Overall, the study successfully created and evaluated a functioning energy optimizing Digital Twin with bidirectional, automated feedback. The results of this research emphasize the potential impact of Energy Digital Twin applications in any manufacturing process and show the promise of future work in this realm of Energy Digital Twins.

Formation Trajectory Tracking of Discrete-Time Distributed Multi-AUVs with Nonconvex Control Inputs and Weak Communication

This paper considers the formation trajectory tracking problem of discrete-time distributed multi-AUVs (multiple autonomous underwater vehicles) with control input in a nonconvex set and weak communication. Firstly, a linear model of a single AUV is obtained by the feedback linearization of a single AUV model using the Lie derivative theory. Then, a linear equation of multi-AUV formation is obtained, and the formation coordinated control system of multi-AUVs based on the feedback linearization model is given. Secondly, the formation trajectory tracking problem of multi-AUVs is transformed into the coordination control problem of leader–followers formation. The coordination controller of the leader–followers formation under a weak communication environment is designed, and the controller satisfies the nonconvex constraints. Next, the coordination control problem of leader–followers formation is transformed into the stability of the error of leader and followers at zero by coordinate transformation. By establishing an appropriate Lyapunov–Krasovskii function, the corresponding linear matrix inequalities are obtained, and the condition of zero stability is obtained by solving the linear matrix inequalities of the leader–followers formation. Under this condition, stable trajectory tracking can be achieved in the multi-AUV formation. Finally, the stability of the designed coordination controller is verified by simulation experiments.

Stochastic capacity analysis for a distributed connected automated vehicle virtual car-following control strategy

Capacity analysis of the pure connected automated vehicle (CAV) traffic remains a challenging problem due to the high-dimensional factors involved in the control design. Especially, the communication loss and communication topology greatly impact the headway variation of CAVs and hence capacity with stochastic properties. This study provides a stochastic framework to mathematically derive multiple factors’ impact including free-flow speed, control gains, communication loss, and traffic arrival pattern on the pure CAV traffic capacity based on a virtual car-following control strategy targeting a single-lane highway and merging section. To begin with, we first mathematically derive the stochastic capacity for a single-lane highway based on a multi-predecessor-based linear feedback and feedforward car-following model for generic stochastic communication loss models. For a further illustration, a detailed analysis is conducted based on a well-known Signal-to-Interference-plus-Noise Ratio (SINR) communication loss model. We then extend the derivation to a merging section by a virtual car-following concept considering traffic arrival pattern’s stochasticity. Numerical sensitivity analyses have been conducted to systematically evaluate the impact of multiple factors mentioned. As the result indicated, the stochastic communication loss and traffic arrival pattern do have a significant impact on the pure CAV traffic capacity of the above scenarios.

Three-way gravity models with multiplicative unobserved effects

Summary This paper investigates three-way gravity models with multiplicative unobserved effects, which are popular in bilateral trade analysis and many other contexts. Such models are usually estimated by the fixed effects Poisson pseudo maximum likelihood method. As an alternative, we extend the estimation strategy proposed by Jochmans (2017) to our new settings by constructing moment conditions that are independent of the unobserved effects. Our method entails estimation of the conditional mean of a variety of functional forms. The generalized method of moments (GMM) estimator based on these moment conditions is N-consistent and asymptotically normally distributed. We also discuss the estimation of dynamic models by extending the linear feedback models to our three-way settings. Through various simulation designs, we show that our GMM estimator outperforms the competing Poisson pseudo maximum likelihood estimator. As an empirical application, we estimate the effects of the currency unions on exports.

Attitude stabilization of spacecraft simulator based on modified constrained feedback linearization model predictive control

AbstractThis paper aims to discuss the approach of constrained modified feedback linearization model predictive control for the spacecraft simulator. By utilizing the high accuracy and constrained properties of model predictive control (MPC), an optimum MPC is designed for the spacecraft feedback linearized system. The composite controller has the ability to control both the attitude and angular velocity of the reaction wheels (i.e. steering the angular momentum to zero at the end of the maneuver). The simulation and experimental results demonstrate that the proposed hybrid controller has an insignificant calculative cost and facilitates the spacecraft to perform regulation maneuver with sufficient precision in the presence of external torques and actuator saturations.

Improved Adaptive Fault-Tolerant Control of a Variable Structure Fighter with Multiple Faults Based on an Extended Observer

In this paper, an improved adaptive fault-tolerant control (FTC) scheme is presented based on an extended state observer (ESO) for a highly maneuverable variable structure fighter (VSF) with simultaneous faults of the rudder surface and sensor. The feedback linearization model of the attitude system with faults and external disturbances is introduced. In order to realize the real-time observation of the rudder and sensor faults, a neural network estimator is used to approximate sensor faults, and the ESO is designed to estimate the rudder surface fault and attitude variables. On this basis, the estimated value is used to replace the measured value for state variables to design the adaptive fault-tolerant controller for the inner and outer loop, combined with the second-order command filter to offset the phenomenon of backstepping differential amplification system noise. Finally, the proposed FTC scheme realizes the variable structure self-repairing of multiple positions, multiple types of faults in VSF using fault estimation. The Lyapunov theory and Barbalat’s lemma prove the stability of the designed observer and controller. The effectiveness of the FTC scheme is verified by a simulation experiment.

Synchronous control for multiple electrohydraulic actuators with feedback linearization

Based on some research of electrichydraulic servo system (EHSS), the synchronous control problem of multiple electrohydraulic actuators (MEHAs) is investigated to guarantee the MEHAs’ system stability and leader-following synchronization with third-order nonlinear dynamics and unknown external load. Firstly, the EHA model is linearized by Lie derivatives technique to obtain the third-order linear isomorphic model of MEHAs with unknown external load. Then the disturbance observer is adopted to estimate unknown external load caused by the driven force of mechanical plant. Meanwhile, the state-feedback matrix is firstly designed by pole placement technique to guarantee the feedback linearization model Hurwitz. Furthermore, the synchronous controller is designed by Lyapunov technique and LMI to guarantee that n EHAs follower states synchronize the leader state with arbitrarily small zeros neighborhood under directed spanning tree. The effectiveness of the synchronous controller is verified by both comparative simulation and experimental bench.

Robust model predictive control for hypersonic vehicle with state‐dependent input constraints and parameter uncertainty

AbstractIn this article, a robust model predictive control strategy based on sum‐of‐squares (SOS‐RMPC) is proposed for hypersonic vehicle with state‐dependent input constraints and uncertain parameters. Based on feedback linearization model of hypersonic vehicle, the polytopic linear parameter varying error model with bounded disturbance is established for reference trajectory tracking. The real limits of the actual control inputs are transformed into the constraints of the virtual inputs equivalently with the state‐dependent nonlinear functions. Further, the multivariate linear fitting is used to approximate the state‐dependent input constraints into polynomials. A weighted composite virtual control is formulated as the combination of unconstrained control and auxiliary control. SOS technique is introduced to cast the polynomial constraints into the convex matrix SOS conditions via linear matrix inequality. The virtual control law can be obtained by solving a SOS‐RMPC convex optimization with infinite horizon. The invariant set is designed for the undisturbed error states and the norm‐bounding theory is applied to ensure that the predictive error states with disturbance can remain in the same invariant set. The real control law is obtained by inverse control. The simulation verifies the performance of the designed controller.

Robust fault-tolerant control design for hypersonic vehicle with input saturation and actuator faults

This study investigates the flight longitudinal tracking control problem of hypersonic vehicle in presence of the input saturation, external disturbances, model parametric uncertainties, and actuator faults. First, the velocity and altitude subsystem are established with disturbances based on the feedback linearization model. Second, two robust anti-saturation fault-tolerant controllers are designed for the velocity subsystem and altitude subsystem by the utilization of the tangent function, Nussbaum function, and adaptive nonlinear filter. Finally, Lyapunov stability theory is used to prove that the states of the closed-loop system are bounded. And, the effectiveness and robustness of the control strategy are proved by numerical simulations.

Finite-time Dynamic Surface Fault-tolerant Control for Hypersonic Vehicle with Mismatched Disturbances

This paper studies the tracking control problem of hypersonic vehicle in the process of external disturbance, parameters uncertainties and actuator faults. Firstly, a non-triangular velocity and altitude nonlinear subsystem with mismatched disturbances and actuator faults are established based on the feedback linearization model. Secondly, adaptive dynamic surface fault-tolerant controllers are designed for velocity and altitude subsystems by combining nonlinear filter, adaptive control and back-stepping method. Finally, the Lyapunov stability theory and numercial simulation are carried out to verify the availability of the proposed control strategy.

Eddy current de-tumbling large geostationary debris based on feedback linearization model predictive control

In this paper, we investigate the application of Feedback Linearization Model Predictive Control (FLMPC) for the eddy current de-tumbling of space tumbling targets. Based on the Clohessy-Wiltshire (C-W) equation and the Euler rotational equations of motion, the dynamic model of the eddy current de-tumbling process is established, and the error dynamic model is further derived. After that, the safety constraint of the eddy current de-tumbling process is deduced and linearized. On this basis, real-time optimal trajectory is obtained with the optimal equilibrium solver, and FLMPC is proposed to control the system. In order to ensure the simplicity and rapidity of the controller, the feedback linearization input constraint is directly used as the global prediction constraint and the MPC constraint problem is converted into the form of Quadratic Programming (QP) which can be effectively solved. Simulation results show that the proposed algorithm can realize quick and safe de-tumbling of the target with the various constraints ensured and a very small range of steady-state errors.

Model Predictive Controller for Quadcopter Trajectory Tracking Based on Feedback Linearization

In this study, a feedback linearization model predictive control algorithm is designed for quadcopter trajectory tracking. By applying feedback linearization to the quadcopter nonlinear model, the quadcopter nonlinear model is transformed into a linear system as the foundation for further controller design. By feedback linearization, the linear control schemes can be used to control the quadcopter. A model predictive controller is then designed for the linearized quadcopter model without considering the external disturbance. A disturbance observer is designed to estimate the external disturbance, keeping the estimation error BIBO stable to compensate for the external disturbance. Numerical simulations are performed to evaluate the proposed control algorithm. The simulations are performed in two test scenarios to examine the tracking performance. The quadcopter is commended for reaching a waypoint (scenario. I) and tracking a helical trajectory (scenario. II) in the simulations, and the root means square errors are calculated to demonstrate the tracking effectiveness. The simulation results show that the designed control algorithm can effectively ensure the quadcopter tracks a given trajectory under constant or continuous disturbances.

Toward a Reinforcement Learning Environment Toolbox for Intelligent Electric Motor Control.

Electric motors are used in many applications, and their efficiency is strongly dependent on their control. Among others, linear feedback approaches or model predictive control methods are well known in the scientific literature and industrial practice. A novel approach is to use reinforcement learning (RL) to have an agent learn electric drive control from scratch merely by interacting with a suitable control environment. RL achieved remarkable results with superhuman performance in many games (e.g., Atari classics or Go) and also becomes more popular in control tasks, such as cart-pole or swinging pendulum benchmarks. In this work, the open-source Python package gym-electric-motor (GEM) is developed for ease of training of RL-agents for electric motor control. Furthermore, this package can be used to compare the trained agents with other state-of-the-art control approaches. It is based on the OpenAI Gym framework that provides a widely used interface for the evaluation of RL-agents. The package covers different dc and three-phase motor variants, as well as different power electronic converters and mechanical load models. Due to the modular setup of the proposed toolbox, additional motor, load, and power electronic devices can be easily extended in the future. Furthermore, different secondary effects, such as converter interlocking time or noise, are considered. An intelligent controller example based on the deep deterministic policy gradient algorithm that controls a series dc motor is presented and compared to a cascaded proportional-integral controller as a baseline for future research. Here, safety requirements are particularly highlighted as an important constraint for data-driven control algorithms applied to electric energy systems. Fellow researchers are encouraged to use the GEM framework in their RL investigations or contribute to the functional scope (e.g., further motor types) of the package.

Anti-disturbance control of oxygen feeding for vehicular fuel cell driven by feedback linearization model predictive control-based cascade scheme

The accurate control of automotive fuel cell oxygen excess ratio (OER) is necessary to improve system efficiency and service life. To this end, an anti-disturbance control driven by a feedback linearization model predictive control (MPC)-based cascade scheme is proposed. It considers strong nonlinear coupling and disturbance injection of fuel cell oxygen supply. A six-order nonlinear fuel cell oxygen feeding model is presented. It is further formulated using an extended state observer to rapidly reconstruct the OER, to overcome the slow response and interference errors of sensor measurements. In the proposed cascade control, the outer loop is the anti-disturbance control which is used to realize the optimized OER tracking and the inner loop via the feedback linearization to linearize the oxygen feeding behaviors conducts MPC to regulate the air compressor output mass flow. The feedback linearization demonstrates a robust tracking performance of nonlinear outputs, and the integral absolute error of anti-disturbance control is 0.3021 lower than that of PI control under a custom test condition. Finally, the numerical validation on a hybrid driving cycle indicates that the proposed cascade control can regulate the fuel cell OER with an average absolute error of 0.02313 in the high air compressor operation efficiency zone.

Employ the Principle Components in the Detection of Feedback

In linear dynamic feedback models, the relationship between two input series input and output shows that the approach is a propose to discover a feedback in linear dynamic system through examining autocorrelation function and partial autocorrelation function for principle components by using few tests of time series identification and exact using Ljung-Box test depending on Simulation approach to show the efficiency of the suggested approach and application on linear and nonlinear models within and without feedback, The obtained result is good and encourage.

Nonlinear adaptive NeuroFuzzy feedback linearization based MPPT control schemes for photovoltaic system in microgrid.

Renewable energy resources connected to a single utility grid system require highly nonlinear control algorithms to maintain efficient operation concerning power output and stability under varying operating conditions. This research work presents a comparative analysis of different adaptive Feedback Linearization (FBL) embedded Full Recurrent Adaptive NeuroFuzzy (FRANF) control schemes for maximum power point tracking (MPPT) of PV subsystem tied to a smart microgrid hybrid power system (SMG-HPS). The proposed schemes are differentiated based on structure and mathematical functions used in FRANF embedded in the FBL model. The comparative analysis is carried out based on efficiency and performance indexes obtained using the power error between the reference and the tracked power for three cases; a) step change in solar irradiation and temperature, b) partial shading condition (PSC), and c) daily field data. The proposed schemes offer enhanced convergence compared to existing techniques in terms of complexity and stability. The overall performance of all the proposed schemes is evaluated by a spider chart of multivariate comparable parameters. Adaptive PID is used for the comparison of results produced by proposed control schemes. The performance of Mexican hat wavelet-based FRANF embedded FBL is superior to the other proposed schemes as well as to aPID based MPPT scheme. However, all proposed schemes produce better results as compared to conventional MPPT control in all cases. Matlab/Simulink is used to carry out the simulations.