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Keywords = steering angle control

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24 pages, 12915 KB  
Article
Load Torque Feedforward and Dynamic Limiting Control Strategy for Electric Forklift Steering Systems Considering Voltage-Limit Constraints
by Fangbin Wang, Qufei Wu, Jiawei Ji and Xue Gong
World Electr. Veh. J. 2026, 17(6), 323; https://doi.org/10.3390/wevj17060323 (registering DOI) - 22 Jun 2026
Viewed by 129
Abstract
For low-speed heavy-load steering of electric forklifts, conventional three-loop proportional–integral (PI) control employs a fixed saturation limit on the position-loop output. Consequently, the maximum allowable speed cannot be adjusted according to load variations. Under light-load conditions, the steering motor speed is excessively constrained, [...] Read more.
For low-speed heavy-load steering of electric forklifts, conventional three-loop proportional–integral (PI) control employs a fixed saturation limit on the position-loop output. Consequently, the maximum allowable speed cannot be adjusted according to load variations. Under light-load conditions, the steering motor speed is excessively constrained, which wastes the available voltage margin. Under heavy-load conditions, the allowable speed may exceed the voltage limit, thereby causing voltage saturation. Moreover, load-torque feedforward compensation is commonly adopted to improve load-carrying capability. However, at medium and high speeds, excessive feedforward action may cause voltage saturation and current-vector offset. This can lead to loss of control of the steering motor. To address these issues, a voltage-limit-constrained dynamic saturation and load-torque feedforward control strategy is proposed for electric forklift steering systems. First, fuzzy PI control is adopted in the position loop. Then, considering the nearly identical direct-axis and quadrature-axis inductances of a surface-mounted permanent magnet synchronous motor (PMSM), the direct-axis current is set to zero. An analytical expression of the maximum safe speed is derived with the quadrature-axis current as the only independent variable. Based on this expression, a dynamic saturation limit is designed for the position-loop output. Finally, a reduced-order disturbance observer (DOB) is utilized to estimate the equivalent load torque in real time. The current feedforward gain is dynamically regulated according to the voltage margin. This compensates for torque limitation caused by speed-loop saturation while preventing voltage saturation. A Simulink simulation platform is developed using a forklift as the case study. The results demonstrate that, compared with the conventional three-loop PI controller, the proposed strategy reduces the no-load 180° step-response time by 30%. Under heavy-load and large-angle steering conditions, the voltage margin is maintained at approximately 10%. Full article
(This article belongs to the Section Vehicle Control and Management)
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16 pages, 3205 KB  
Article
Nonlinear Modeling and Differential-Voltage Control of an Electrostatic MEMS Micromirror for Miniaturized Laser Communication Terminals
by Xuan Wang, Chen Wang, Meilin Xie, Zengxin Liu and Junfeng Han
Micromachines 2026, 17(6), 753; https://doi.org/10.3390/mi17060753 (registering DOI) - 22 Jun 2026
Viewed by 108
Abstract
Electrostatic MEMS micromirrors provide a compact and low-power beam-steering solution for miniaturized laser communication terminals. However, when they are used for quasi-static beam pointing rather than resonant scanning, the nonlinear voltage–angle relationship, bidirectional actuation asymmetry, and terminal-level installation errors can significantly degrade pointing [...] Read more.
Electrostatic MEMS micromirrors provide a compact and low-power beam-steering solution for miniaturized laser communication terminals. However, when they are used for quasi-static beam pointing rather than resonant scanning, the nonlinear voltage–angle relationship, bidirectional actuation asymmetry, and terminal-level installation errors can significantly degrade pointing accuracy. In this paper, a nonlinear modeling and differential-voltage control method is investigated for a two-axis electrostatic MEMS micromirror used in a miniaturized laser communication terminal. The device under test is a bonded aluminum MEMS micromirror with a 5.0 mm aperture. Static and dynamic characterization results show that the micromirror achieves maximum mechanical deflection angles of 5.215° and 5.161° along the X and Y axes, respectively, with resonant frequencies of 317 Hz and 319 Hz. To improve the accuracy of quasi-static pointing, the differential-voltage actuation principle is analyzed, and a nonlinear voltage–angle model is established based on measured deflection data. Compared with a first-order linear model, the cubic nonlinear model reduces the root-mean-square fitting error from 0.142° to 0.0127° for the X axis and from 0.132° to 0.0109° for the Y axis. Furthermore, a terminal-level calibration architecture based on a quadrant detector is introduced to map the MEMS angular deflection to the received spot position. The proposed modeling and calibration approach provides an actuator-level basis for accurate beam pointing and closed-loop acquisition in miniaturized laser communication terminals. Full article
(This article belongs to the Special Issue MEMS/NEMS Devices and Applications, 4th Edition)
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20 pages, 10034 KB  
Article
A Two-Wheel-Centric Reconfigurable Mobility Platform Enabled by Compact Steering–Drive–Suspension Modules: Balance, Driving, and Cooperative Transport
by Junghyun Choi
Machines 2026, 14(6), 704; https://doi.org/10.3390/machines14060704 (registering DOI) - 19 Jun 2026
Viewed by 187
Abstract
Modern logistics and manufacturing environments simultaneously demand mobility platforms that are compact enough to navigate narrow aisles and powerful enough to transport oversized or heavy components. We previously developed a compact Steering–Drive–Suspension (SDS) module that integrates steering, in-wheel drive, and suspension within a [...] Read more.
Modern logistics and manufacturing environments simultaneously demand mobility platforms that are compact enough to navigate narrow aisles and powerful enough to transport oversized or heavy components. We previously developed a compact Steering–Drive–Suspension (SDS) module that integrates steering, in-wheel drive, and suspension within a single wheel envelope, achieving ±90 wide-angle steering with a single actuator. The present paper extends that hardware-centric work by treating the two-wheel (2WD) configuration assembled from two SDS modules as the unit module of the platform, building a four-wheel (4WD) operation by coupling two such 2WD units, and developing a unified balance and impedance-based control scheme. We derive a cart–pole inverted-pendulum model for the 2WD configuration and a planar 2-DOF bicycle model for the coupled and cooperative configurations, with full controllability proof and quantitative LQR robustness margins. Three Python 3.12 based scenarios validate the framework: (i) a 2WD inverted-pendulum tracking task, (ii) a forward and lateral relocation maneuver compared across SDS Crab, Ackermann, and four-wheel-steering modes, and (iii) cooperative transport of a 100kg steel plate by two impedance-coupled 2WD units. Across all scenarios the proposed controllers achieve sub-centimetre tracking gap, pitch deviation within ±2, and well-damped cooperative behavior without payload sloshing. The results substantiate the central design claim that the SDS module’s compactness enables a single hardware platform to act simultaneously as an autonomous small-payload mover, a building block of a 4WD platform, and a cooperative agent for oversized loads. Full article
(This article belongs to the Special Issue Advances in Automotive Mechatronics)
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31 pages, 6782 KB  
Article
Design and Control Strategy Verification of Electro-Hydrostatic Actuator for Ship Steering
by Xiaopeng Tan, Zijing Ding, Jian Liao and Mai Hao
Appl. Sci. 2026, 16(12), 6098; https://doi.org/10.3390/app16126098 - 16 Jun 2026
Viewed by 124
Abstract
To address the bottlenecks of conventional valve-controlled marine steering systems—characterized by high throttling losses, low efficiency, and high leakage risk—as well as the insufficient power density and impact resistance of electro-mechanical actuators (EMAs) for high-load steering of large vessels, this paper proposes and [...] Read more.
To address the bottlenecks of conventional valve-controlled marine steering systems—characterized by high throttling losses, low efficiency, and high leakage risk—as well as the insufficient power density and impact resistance of electro-mechanical actuators (EMAs) for high-load steering of large vessels, this paper proposes and validates a high-performance integrated solution for an electro-hydrostatic actuator (EHA) for ship steering. First, a fifth-order electro–hydraulic–mechanical coupled dynamic model comprising a permanent magnet synchronous motor, hydraulic pump, hydraulic cylinder, and load is established. The validity and applicability boundaries of three simplifying assumptions—neglecting leakage, pipeline pressure losses, and steady-state fluid compressibility effects—are quantitatively analysed, with a total introduced error ≤3%. These assumptions are justified under medium-pressure, short-pipeline, and well-sealed conditions typical of marine EHA systems. Second, a composite control architecture combining outer-loop sliding mode control with inner-loop motor PID dual-loop control is proposed. Parameter tuning is performed using pole placement for the sliding surface and the Ziegler–Nichols critical ratio method for the inner loops, effectively suppressing hydraulic system parameter perturbations and random wave-induced load disturbances. Quantitative comparisons show that the proposed method reduces overshoot by 11.63% and improves sinusoidal tracking accuracy by 90.13% compared to conventional single-loop PID control. An integrated drive-control structure is designed, and a three-phase full-bridge inverter main circuit with wide-voltage input capability—including EMI filtering, soft-start, and LC filtering—is developed to accommodate the ±20% voltage fluctuations typical of ship power grids, thereby enhancing system integration and grid adaptability. Phased bench tests demonstrate that the settling time from no-load start-up to 200 r/min is only 0.01 s. When a sudden 20 N·m load is applied, the speed drop is less than 3%, and the recovery time is less than 0.025 s. The steady-state steering angle error does not exceed 0.12°, the maximum average steering rate reaches 3.33°/s, and the steering response time is within 0.3 s. All core performance indicators exceed the general technical standards for marine steering systems, with a 65.7% improvement in steady-state accuracy and a 62.5% improvement in response speed over conventional PID control. The research findings provide an effective general technical solution and experimental data support for the performance optimization and engineering application of marine EHA systems. Full article
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18 pages, 6801 KB  
Article
Numerical Simulation of Horizontal Well Steering Fracturing Based on the Cohesive Zone Model
by Jian Shi, Peng Song, Jinsheng Zhao, Jun Yang, Jin Wang, Wantao Liu, Qiang Liu, Chen Yang and Mingyong Xu
Processes 2026, 14(12), 1951; https://doi.org/10.3390/pr14121951 - 15 Jun 2026
Viewed by 149
Abstract
Horizontal-well steering fracturing is an important completion strategy for unconventional reservoirs, where fracture growth is jointly controlled by wellbore azimuth, natural fractures, and inter-cluster stress interference. In this study, a two-dimensional fluid-solid-coupled hydraulic-fracturing model with embedded cohesive elements was developed to simulate fracture [...] Read more.
Horizontal-well steering fracturing is an important completion strategy for unconventional reservoirs, where fracture growth is jointly controlled by wellbore azimuth, natural fractures, and inter-cluster stress interference. In this study, a two-dimensional fluid-solid-coupled hydraulic-fracturing model with embedded cohesive elements was developed to simulate fracture initiation and growth at steering angles of 0°, 30°, 45°, 60°, and 90°. The Blanton, Warpinski-Teufel, and Blanton-Gao hydraulic-fracture/natural-fracture interaction criteria were used as mechanical benchmarks to interpret simulated capture, deflection, and penetration regimes. The simulations indicate that natural fractures preferentially guide fracture propagation: hydraulic fractures tend to be captured by, or propagate along, natural fractures at approach angles ≤30°, whereas penetration is more likely at approach angles ≥60°. In the single-stage single-cluster model, the 90° case produces the largest simulated fracture length and the highest failed-cohesive-element count. In the single-stage multi-cluster model with 3 m cluster spacing, the 30–45° interval shows more favorable fracture extension and interface activation than the 90° case because inter-cluster stress-shadow effects suppress fracture-network development at large steering angles. The resulting steering-angle window should be interpreted as a comparative result for the fixed mesh, deterministic natural-fracture realization, and baseline cluster-spacing configuration adopted here. These results provide a mechanistic basis for steering-fracturing design in hard-rock reservoirs while clarifying the applicability limits of the two-dimensional plane-strain approximation. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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38 pages, 7947 KB  
Article
Interpretable Prediction of Hydraulic Fracture Asymmetry in Shale Reservoirs Under Small-Sample Conditions
by Hanke Zuo and Yanhong Peng
Processes 2026, 14(12), 1900; https://doi.org/10.3390/pr14121900 - 11 Jun 2026
Viewed by 233
Abstract
To address the issues of strong inter-well interference during multi-well fracturing in shale reservoirs, low efficiency of conventional numerical simulation, and the tendency of machine learning models to overfit and lack interpretability under small-sample conditions, this paper constructs an explainable ensemble learning framework [...] Read more.
To address the issues of strong inter-well interference during multi-well fracturing in shale reservoirs, low efficiency of conventional numerical simulation, and the tendency of machine learning models to overfit and lack interpretability under small-sample conditions, this paper constructs an explainable ensemble learning framework for predicting hydraulic fracture asymmetry. A geology–engineering integrated numerical simulation is adopted to quantify the fracture asymmetry index η as an interference metric, and an initial dataset is constructed comprising natural fracture orientation, well spacing, and injection rate. Subsequently, Jensen–Shannon (JS) divergence-constrained Gaussian data augmentation and second-order interaction features are introduced, and the GBRT model parameters are optimized using particle swarm optimization (PSO). Furthermore, random forest and ridge regression are incorporated, and ensemble weights are determined via cross-validation to build a weighted ensemble prediction model. The results show that the proposed model achieves good predictive performance in repeated validation, with an average coefficient of determination R2 of 0.8484 and a 95% confidence interval of 0.8179–0.8790, while also demonstrating favorable overall accuracy in multiple baseline model comparisons and regularization-controlled experiments. Through leave-one-simulation-scenario validation, prediction interval analysis, and interpretability robustness testing, the model’s generalization boundary, prediction uncertainty, and explanation reliability under small-sample conditions are further evaluated. SHAP analysis and grouped permutation importance results indicate that the natural fracture angle is the dominant factor controlling asymmetric fracture response, while the interaction between well spacing and the natural fracture angle also significantly affects the predictions, suggesting that asymmetric fracture propagation is primarily governed by the combined effects of natural fracture steering and inter-well stress interference. The proposed framework can serve as a fast surrogate model for evaluating inter-well interference and screening fracturing designs within a given simulation parameter space, providing an interpretable data-driven approach for fracturing design optimization in shale reservoirs under small-sample conditions. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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39 pages, 3294 KB  
Article
Development in Surrogate-Based Polynomial Chaos with Adaptive Sobol Sensitivity Analysis for Uncertainty Quantification and Offshore 15 MW Wind Turbine Performance Prediction: Comparative, Icing, and Wind Farm Optimization Studies
by Mohamed Haris Baghli, Tewfik Baghdadli and Zakarya Ziani
Wind 2026, 6(2), 30; https://doi.org/10.3390/wind6020030 (registering DOI) - 10 Jun 2026
Viewed by 179
Abstract
Accurate performance prediction for large offshore wind turbines requires a principled treatment of uncertainty in both the wind resource and the rotor design parameters. In the present work, we develop a surrogate-based, multi-level uncertainty quantification (UQ) framework coupling a physics-based Blade Element Momentum [...] Read more.
Accurate performance prediction for large offshore wind turbines requires a principled treatment of uncertainty in both the wind resource and the rotor design parameters. In the present work, we develop a surrogate-based, multi-level uncertainty quantification (UQ) framework coupling a physics-based Blade Element Momentum (BEM) solver with a spectral Polynomial Chaos Expansion (PCE) surrogate that replaces the expensive Monte Carlo loop and apply it to the IEA 15 MW offshore reference wind turbine. The framework is completed by Sobol variance-based global sensitivity analysis. The contribution is methodological rather than algorithmic: although each individual ingredient (PCE, Sobol, BEM, and Jensen) is well established, their joint deployment in a single, internally consistent, end-to-end probabilistic workflow that simultaneously delivers (i) aerodynamic–structural UQ with analytical Sobol ranking, (ii) a like-for-like cross-comparison of three reference turbines, (iii) a quantitative leading-edge icing degradation study, and (iv) a farm-level wake-steering optimization on the same IEA 15 MW reference rotor yields a unified probabilistic envelope from which manufacturing tolerances, cold-climate investment thresholds, and farm-layout/control trade-offs can be read off consistently. Five input parameters are treated as random variables: hub-height wind speed (Weibull, k = 2.2, c = 9.8 m/s), air density, blade chord length, twist angle, and rotor speed. A degree-4 sparse PCE is built by non-intrusive spectral projection using N = 5000 Sobol quasi-random realizations, which allows the Sobol indices to be recovered analytically from the expansion coefficients at essentially no extra cost. Three parallel engineering studies complement the core UQ analysis: (A) a head-to-head comparison of the NREL 5 MW, DTU 10 MW, and IEA 15 MW reference turbines; (B) a quantitative assessment of leading-edge ice accretion at four severity levels; and (C) a Jensen-based wake optimization for a 25-turbine offshore array with static wake steering. The main results are as follows: the turbine reaches Cp,max = 0.480 at λopt = 8.51, and an annual energy production (AEP) of 71,261 MWh/year (PCE: 70,840 ± 2,140 MWh/year, 95% CI). Wind speed emerges as the dominant driver of Cp variance (S1 = 0.412), followed by blade twist (0.198) and chord (0.143). Severe icing (30 kg/m) reduces Cp by 18.2% and increases the blade-root Damage Equivalent Load (DEL) by 18.5%. For the array, the optimal spacing (sx = 8D, sy = 6D) gives a farm efficiency of 89.6% and 1296 GWh/year, and a 15° wake-steering offset adds a further +3.2% to farm AEP. Compared with plain Monte Carlo, the sparse PCE delivers the same statistics with about 36% fewer model evaluations and a relative error below 0.8%. Full article
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27 pages, 21641 KB  
Article
Vehicle Active Stabilizer Bar Composite Control and Optimization Based on Reinforcement Learning
by Zhenglin Tang, Xuesong Zhang and Qiang Zhao
Electronics 2026, 15(12), 2529; https://doi.org/10.3390/electronics15122529 - 8 Jun 2026
Viewed by 160
Abstract
During actual vehicle operation, working conditions are highly complex, involving both body roll induced by steering centrifugal force and attitude fluctuations caused by random road irregularities or sudden lateral wind disturbances. By optimizing the control of the active stabilizer bar (ASB), its torque [...] Read more.
During actual vehicle operation, working conditions are highly complex, involving both body roll induced by steering centrifugal force and attitude fluctuations caused by random road irregularities or sudden lateral wind disturbances. By optimizing the control of the active stabilizer bar (ASB), its torque compensation capability can be more effectively utilized, thereby improving vehicle ride quality and handling stability under extreme conditions. This paper first establishes a vehicle roll model with a passive stabilizer bar. Then, an active disturbance rejection control (ADRC) controller, a linear active disturbance rejection control (LADRC) controller, and a fuzzy proportional–integral and proportional–derivative (PI-PD) controller are designed and verified through simulation. The results show that all three active control methods improve roll stability compared with the passive system, and the ADRC controller achieves better control performance than the fuzzy PI-PD and LADRC controllers. Furthermore, a control strategy for the active stabilizer bar model is developed based on the deep deterministic policy gradient (DDPG) algorithm. The simulation results show that, using deep reinforcement learning for feedforward optimization, the fuzzy PI-PD, LADRC, and ADRC control methods reduce the body roll angle by 3.8%, 27.1%, and 25.0%, respectively. The front-axle anti-roll moments are reduced by 13.4%, 14.0%, and 16.5%, respectively, while the rear-axle anti-roll moments are reduced by 14.8%, 13.4%, and 14.5%, respectively. Full article
(This article belongs to the Section Systems & Control Engineering)
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25 pages, 2982 KB  
Article
Optimal Disturbance-Observer-Based Fuzzy PID Back-Stepping Control of a Self-Driving Car with a Steer-by-Wire System
by Haider Khazal, Ahmed Othman Alanazi, Younis K. Khdir, Nasser Firouzi and Przemysław Podulka
Vehicles 2026, 8(6), 124; https://doi.org/10.3390/vehicles8060124 - 3 Jun 2026
Viewed by 394
Abstract
This paper presents a robust dual-loop control strategy for the lateral motion and heading-angle regulation of an autonomous vehicle equipped with a Steer-By-Wire (SBW) system under unknown time-varying disturbances. The proposed framework comprises a fuzzy PID controller in the inner loop to generate [...] Read more.
This paper presents a robust dual-loop control strategy for the lateral motion and heading-angle regulation of an autonomous vehicle equipped with a Steer-By-Wire (SBW) system under unknown time-varying disturbances. The proposed framework comprises a fuzzy PID controller in the inner loop to generate the motor torque and track the front-wheel steering angle, and an optimal backstepping controller in the outer loop—integrated with a finite-time disturbance observer—to ensure lateral trajectory tracking and wind-disturbance rejection. The PID gains are tuned online by a Mamdani-type fuzzy inference system, while the backstepping parameters are optimized offline via a genetic algorithm. Beyond the bicycle-model-based design, the controller is evaluated through supplementary simulations using a 6-degree-of-freedom (6-DOF) vehicle model, as well as through a detailed robustness analysis that includes measurement noise and increasing lateral disturbance forces. The results demonstrate that the closed-loop system achieves precise path tracking, finite-time convergence of both tracking and estimation errors, and effective compensation of road vibrations and wind disturbances. Furthermore, the controller maintains stable performance under significant measurement noise and tolerates lateral disturbance forces up to at least 10,000 N without violating safety constraints. The effectiveness of the proposed method is consistently confirmed across both the reduced-order bicycle model and the higher-fidelity 6-DOF validation environment. Full article
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23 pages, 15935 KB  
Article
Integrated Dynamic Modeling and Ground Test Validation for Spacecraft Micro-Vibration Suppression Considering Disturbance, Isolation, and Pointing Control
by Hua Wang, Han Yan, Lei Tian, Xu Zang and Yingqing Zu
Sensors 2026, 26(11), 3534; https://doi.org/10.3390/s26113534 - 3 Jun 2026
Viewed by 252
Abstract
On-orbit micro-vibration has emerged as a critical constraint impairing the imaging performance and ultra-high pointing accuracy of space optical payloads. Most existing investigations separately concentrate on disturbance modeling, vibration isolation design, or line-of-sight (LOS) stabilization, leaving the full-link integrated dynamic modeling and analysis [...] Read more.
On-orbit micro-vibration has emerged as a critical constraint impairing the imaging performance and ultra-high pointing accuracy of space optical payloads. Most existing investigations separately concentrate on disturbance modeling, vibration isolation design, or line-of-sight (LOS) stabilization, leaving the full-link integrated dynamic modeling and analysis severely insufficient. To address this gap, this paper proposes an integrated dynamic modeling methodology for spacecraft equipped with optical payloads, which synergizes disturbance identification, finite element modeling, model order reduction, hybrid active–passive vibration isolation mechanism control, and fast steering mirror (FSM) regulation. The experimental and simulation results demonstrate that the root mean square (RMS) acceleration induced by flywheels and pumps at the mounting interface of the vibration isolation mechanism approximates 4.50 mg. Specifically, the passive vibration isolation scheme attains an attenuation of −16 dB, while the hybrid active–passive strategy achieves a remarkable −30 dB attenuation. Moreover, flywheels generate lower acceleration amplitude but more severe LOS jitter, owing to their time-varying disturbance characteristics and dispersed frequency energy distribution. Additionally, a full-spacecraft micro-vibration ground test incorporating horizontal gravity unloading via suspension is implemented to validate the model. The model-calculated acceleration and pointing angle exhibit excellent consistency with the experimental data, with the relative acceleration error below 7% and the angular error less than 9%. The proposed integrated dynamic model enables accurate prediction of micro-vibration transmission and suppression performance, laying a dependable theoretical foundation for design optimization of high-precision spacecraft systems. Full article
(This article belongs to the Special Issue Advances in Sensing Technologies for Inertial Stabilization)
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27 pages, 7871 KB  
Article
The Control of Handling Stability for Active Inward Tilt Vehicles Based on the Phase-Plane Lateral Stability Region
by Chen Zhang and Jialing Yao
Machines 2026, 14(5), 552; https://doi.org/10.3390/machines14050552 - 14 May 2026
Viewed by 210
Abstract
For autonomous vehicles, high-speed cornering can easily lead to degraded handling stability and increased risks of sideslip or even rollover. Therefore, vehicle phase-plane stability-region analysis has become an important topic in active safety-control research. However, most existing studies still construct phase-plane stability regions [...] Read more.
For autonomous vehicles, high-speed cornering can easily lead to degraded handling stability and increased risks of sideslip or even rollover. Therefore, vehicle phase-plane stability-region analysis has become an important topic in active safety-control research. However, most existing studies still construct phase-plane stability regions mainly based on simplified vehicle models, without sufficiently considering the influence of vertical load transfer during cornering on tire lateral forces and stability boundaries. To address this issue, this paper proposes a hierarchical control strategy based on phase-plane analysis for active inward tilt vehicles. This method adopts a three-degree-of-freedom vehicle dynamics model and a tire model. By carefully comparing the phase-plane stability regions of active inward tilt and passive roll vehicles and by further analyzing the state-trajectory convergence characteristics of active inward tilt vehicles under different longitudinal speeds, front wheel steering angles, and road adhesion coefficients, the effects of active inward tilt on stability-region expansion and vehicle-state convergence are revealed. Subsequently, a hierarchical control strategy is proposed as an integrated solution to improve vehicle handling stability. The upper-level controller dynamically adjusts the reference values and objective weights according to whether the vehicle state is located in the stable, critical, or dangerous region. The lower-level NMPC controller optimizes the front wheel steering angle and active suspension forces to achieve coordinated trajectory tracking and stability control. Double lane-change simulation results show that active inward tilt can improve the left–right vertical load distribution and expand the lateral stability region. Compared with passive roll and conventional active inward tilt control, the proposed strategy reduces the phase-plane state convergence area by 68% and 75%, respectively, thereby improving vehicle handling stability and active safety under extreme conditions. Full article
(This article belongs to the Section Vehicle Engineering)
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18 pages, 6201 KB  
Article
Lateral Stability and Synchronization Control for Dual-Motor Steer-by-Wire Vehicles
by Pengze Ma, Zonghao Li, Jinghui Zhao, Niaona Zhang and Zhe Zhang
Symmetry 2026, 18(5), 828; https://doi.org/10.3390/sym18050828 - 12 May 2026
Viewed by 367
Abstract
The steer-by-wire (SBW) system represents an optimal solution for achieving intelligent vehicle steering. However, the current reliability of SBW motors and electronic control units remains limited. Disturbances, including variations in the external road environment and time-varying parameters, can significantly impact vehicle stability. To [...] Read more.
The steer-by-wire (SBW) system represents an optimal solution for achieving intelligent vehicle steering. However, the current reliability of SBW motors and electronic control units remains limited. Disturbances, including variations in the external road environment and time-varying parameters, can significantly impact vehicle stability. To address these challenges, a hierarchical control strategy is proposed in this paper. In the upper layer, model predictive control (MPC) is employed to optimize the sideslip angle and yaw rate by tracking their reference values, thereby enhancing the stability of the SBW system. In the lower layer, a composite reaching law sliding mode control based on an extended state observer (ESO-CRLSMC) is developed to address dual-motor parameter mismatch and speed synchronization issues, thereby ensuring the reliability of the dual-motor system. Finally, hardware-in-the-loop experiments demonstrate that under time-varying disturbances and parameter mismatches, the proposed controller not only ensures vehicle handling stability but also improves steering response speed, robustness, and synchronization performance. Full article
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19 pages, 6276 KB  
Article
Misalignment Decoupling and Tilt-to-Length Suppression in a Micro-Actuated Beam Steering Mechanism via Nonlinear Cyclic Modulation
by Yang Li, Changkang Fu, Hongming Zhang, Hongyang Guo, Zhiqiang Zhao, Mengyang Zhao, Ruihong Gao, Qiang Wang, Chen Wang, Caiwen Ma, Dong He and Yongmei Huang
Micromachines 2026, 17(5), 587; https://doi.org/10.3390/mi17050587 - 10 May 2026
Viewed by 313
Abstract
Tilt-to-length (TTL) coupling is a critical noise source in high-precision interferometric measurements, particularly in systems involving angular actuation and beam steering. This paper proposes a nonlinear cyclic modulation method to identify lateral misalignment and suppress the associated TTL coupling. By applying controlled sinusoidal [...] Read more.
Tilt-to-length (TTL) coupling is a critical noise source in high-precision interferometric measurements, particularly in systems involving angular actuation and beam steering. This paper proposes a nonlinear cyclic modulation method to identify lateral misalignment and suppress the associated TTL coupling. By applying controlled sinusoidal angular excitation and evaluating the complex modulus ratio between the optical path difference (OPD) and the beam angle at the modulation frequency, the TTL noise induced by the point-ahead angle mechanism (PAAM) is separated and quantified in the frequency domain. Experimental results demonstrate that lateral offset correction reduces TTL noise by 94%, corresponding to a suppression factor of 15.5 and enabling pointing control better than 21 µm/rad. Meanwhile, the parasitic displacement noise of the PAAM is reduced from 10 pm/Hz1/2 to below 4 pm/Hz1/2. These results validate the effectiveness of the proposed modulation-based identification framework and demonstrate its applicability to precision interferometric systems. Full article
(This article belongs to the Section A1: Optical MEMS and Photonic Microsystems)
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25 pages, 2302 KB  
Article
Path Tracking for Autonomous Vehicles Integrating HOCBF-Based Reinforcement Learning and Model Predictive Control
by Zhengyu Song, Wenxin Wen, Junze Li, Junjie Wang, Minghui Ye, Mengna Li, Bowen Li, Zhuo Wang, Changqun Sun, Aidong Luan, Meng Zhang, Changpeng Liu, Yantao Si and Bo Leng
Electronics 2026, 15(10), 2031; https://doi.org/10.3390/electronics15102031 - 10 May 2026
Viewed by 275
Abstract
High-precision path tracking is crucial for the safe operation of autonomous vehicles. However, the performance of Model Predictive Control (MPC) depends heavily on the accuracy of the vehicle dynamics model, whereas Deep Reinforcement Learning (DRL) generally lacks formal safety guarantees during training and [...] Read more.
High-precision path tracking is crucial for the safe operation of autonomous vehicles. However, the performance of Model Predictive Control (MPC) depends heavily on the accuracy of the vehicle dynamics model, whereas Deep Reinforcement Learning (DRL) generally lacks formal safety guarantees during training and exploration. To address this issue, this paper proposes a hybrid path-tracking framework, termed CRL-MPC, which integrates High-Order Control Barrier Function (HOCBF)-based reinforcement learning feedforward control with model predictive feedback control. Specifically, a Deep Deterministic Policy Gradient (DDPG) agent generates nominal feedforward steering commands, which are then corrected online by a High-Order Control Barrier Function (HOCBF)-based safety filter through a Quadratic Programming (QP) problem. During training on a high-fidelity CarSim–Simulink–Python co-simulation platform, the HOCBF-based safety filter constrains exploration within physically feasible regions, thereby preventing simulator failure caused by dynamically unsafe actions and improving training stability and sample efficiency. Meanwhile, the MPC controller provides feedback correction to compensate for residual errors. Comparative simulations were conducted against two baseline architectures: a standalone conventional MPC controller and a reinforcement-learning-based MPC (RL-MPC) hybrid architecture without the HOCBF-based safety filter. The results show that CRL-MPC achieves superior overall performance in path-tracking accuracy, control smoothness, and lateral dynamic stability. Compared with conventional MPC, CRL-MPC reduces the maximum lateral displacement error and its root mean square error (RMSE) by 54.1% and 62.7%, respectively, and reduces the maximum heading-angle error and its RMSE by 18.1% and 27.1%, respectively. Full article
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26 pages, 2936 KB  
Article
Design, Optimization, and Field Evaluation of an Automatic Steering System for Agricultural Tractors Using Metaheuristic PID Tuning
by Ali Karamolachab, Saman Abdanan Mehdizadeh and Yiannis Ampatzidis
Agriculture 2026, 16(9), 1004; https://doi.org/10.3390/agriculture16091004 - 3 May 2026
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Abstract
This paper presents the design and field evaluation of a low-cost automatic steering system for agricultural tractors. The system employs a PID controller whose gains are tuned using a metaheuristic optimization method. Core hardware includes an ESP32 microcontroller, an MPU9250 inertial measurement unit, [...] Read more.
This paper presents the design and field evaluation of a low-cost automatic steering system for agricultural tractors. The system employs a PID controller whose gains are tuned using a metaheuristic optimization method. Core hardware includes an ESP32 microcontroller, an MPU9250 inertial measurement unit, a GPS module, and a servo motor for closed-loop yaw angle control, with a complementary filter fusing gyroscope and magnetometer data for robust heading estimation. Nine optimization algorithms were systematically compared: Grid Search, Random Search, Bayesian Optimization, Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Moth-Flame Optimization (MFO), Sine Cosine Algorithm (SCA), Whale Optimization Algorithm (WOA), and Salp Swarm Algorithm (SSA). A cost function combining overshoot and settling time was used. Step response analysis showed that WOA achieved the best performance, with an integral absolute error of 6.31°·s, a settling time of 2.15 s, and a minimal overshoot of 0.08°. In field tests on asphalt and farmland, the WOA-tuned system reduced lateral deviation by 69% (from 12.4 cm to 3.8 cm) and 67% (from 18.7 cm to 6.2 cm), respectively, compared to manual steering. Repeated-measures ANOVA and paired t-tests confirmed statistically significant improvements (p < 0.001) with large effect sizes (Cohen’s d > 2.7). The core components cost under $150 USD. The study offers a reproducible pipeline for comparative metaheuristic evaluation in agricultural vehicle guidance. Full article
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