To enhance the tracking performance and anti-disturbance capability of the Permanent Magnet Synchronous Motor (PMSM) against various disturbances such as parameter mismatch and load torque fluctuation, this paper proposes a sliding mode control method based on an improved disturbance observer. First, an integral terminal sliding mode surface is designed to improve the steady-state control accuracy and ensure the tracking error converges in finite time. On the basis of the exponential reaching law, a variable function gain term based on system state variables and a power term of the sliding mode surface are introduced to increase the convergence speed while suppressing the chattering phenomenon. An improved disturbance observer is developed, in which a new reaching law and a terminal sliding mode surface are incorporated to improve the disturbance observation accuracy and guarantee the finite-time convergence of the observation error. Real-time compensation of disturbances is achieved through a feedforward compensation mechanism. The stability of the proposed control method is proven using the Lyapunov function. The results demonstrate that the proposed control method outperforms other control methods mentioned in this paper in terms of response speed and control accuracy under different operating conditions. It demonstrates stronger robustness under disturbances, boosting speed tracking performance.

Abstract Direct-drive electro-hydrostatic actuator (DEHA) has become an important development direction in the field of hydraulic drive due to its advantages of high power density, compact structure and energy saving. The traditional linear control strategy is difficult to effectively deal with the inherent nonlinear characteristics and disturbances in the position control of DEHA system. This paper proposes an improved active disturbance rejection controller (IADRC) based on the IFAL function. Firstly, the state space model of DEHA is established, and the nonlinear part of the system and the external disturbance are regarded as the total disturbance for estimation and compensation. Secondly, by modifying the normal distribution function with zero mean and adjustable standard deviation, an odd function g ( x,σ ) was constructed. Based on this odd function, the IFAL function was designed. The IFAL is applied to the nonlinear state error feedback and the extended state observer (ESO) to replace the traditional fal function, and finally the IADRC is formed. At the same time, the convergence condition of improved ESO is analyzed by combining the Lyapunov stability theory. The results demonstrate that, compared to the other controllers, IADRC accelerates the response speed under the step condition while simultaneously reducing the steady-state error by more than 25%. Furthermore, when the excitation signal frequency increases and the system is subjected to external disturbances, IADRC exhibits superior tracking precision and anti-interference capability.

Aiming at the influence of parameter uncertainty and external disturbance on the force control performance in the force control process of direct-drive electro-hydrostatic actuator, this paper analyzes the influence of system parameters on the control performance, and proposes a Model Predictive-Improved Active Disturbance Rejection Control method based on load torque compensation. Firstly, the system state space equation and refined joint simulation model considering nonlinear factors such as friction and leakage are established, and the influence of key structural parameters on the dynamic performance of direct-drive electro-hydrostatic actuator is analyzed. It is concluded that the flux linkage of permanent magnet synchronous motor, the working clearance of bidirectional gear pump, the leakage in the system and the change of oil bulk modulus have great influence on the stability and tracking performance of the system. By means of proportional term and hyperbolic tangent function fitting, the improved fal function is designed to solve the problem that the fal function is not derivable at the segmentation point and easy to cause high-frequency chattering of the system, so as to design an improved active disturbance rejection controller. The compensation flow required by the system is analyzed, and the load torque of the system is compensated by the state prediction and rolling optimization of the model predictive control, and then the Model Predictive-Improved Active Disturbance Rejection Control is designed. The results show that the control method in this paper can not only ensure high control accuracy, but also improve the response speed.

Aiming at the requirements of high integration, high precision, and strong robustness of the braking system put forward by the development of distributed braking technology, a pump-controlled direct-drive brake-by-wire unit is proposed. The hydraulic pump is directly driven by the motor to realize the pressure building and regulating of the brake wheel cylinder. Compactness and efficiency of the system is enhanced by direct drive technology. A sliding mode control method based on radial basis function (RBF) neural network is designed. The total disturbances caused by uncertainties such as parameter changes, friction, and external disturbances are included in the dynamic equation. A sliding mode controller based on the second-order reaching law is designed to improve the response speed of the system. The recursive loop of the RBF neural network controller is designed to enhance the dynamic learning ability of the controller network, and then estimate and compensate for the total disturbances. The results show that the pump-controlled direct-drive brake-by-wire unit can quickly build and regulate the pressure. It also provides a new technical solution for distributed braking. The proposed control method can effectively improve the response speed, control accuracy and robustness of the system.

To improve ride comfort and address the limited fail-safe capability and energy utilization of electromagnetic actuators in commercial vehicle cab suspensions, a hybrid electromagnetic linear actuator (HELA) is proposed. HELA coaxially integrates a hydraulic damper and an electromagnetic linear actuator, enabling active force generation, energy regeneration, and passive fail-safe damping within the original installation space. A three-degree-of-freedom quarter-cab suspension model is established to determine the passive damping coefficient and actuator force, stroke, and velocity requirements using linear quadratic regulator (LQR) control. From the initial structure, Morris sensitivity analysis and hierarchical optimization target seven key parameters to avoid magnetic saturation, reduce radial size, and balance thrust output with detent-force suppression. The optimized actuator reduces detent force by 50.13%, increases average thrust by 8.09% to 487.75 N, and lowers the thrust ripple ratio to 7.42%. On a Class C road at 54 km/h, the hybrid mode achieves peak/average regenerative powers of 93.02/5.02 W and reduces net actuator energy consumption by 83.4%. Prototype tests confirm short-circuit damping capability and an approximately linear current-thrust relationship, with the measured thrust showing reasonable consistency with finite-element predictions.

To address gain faults and coil group faults in electromagnetic energy regenerative shock absorbers (EMERSAs), this paper proposes a fault diagnosis and classified fault-tolerant control strategy based on an improved sliding mode learning observer (ISMLO) and gap metric. First, a mathematical model of the EMERSA fault system is established by considering external disturbances, nonlinear friction, and measurement noise. Subsequently, an ISMLO is designed to accurately estimate system states and faults under external disturbances. Then, a gap-metric-based fault detection and classification method is developed, in which faults are classified into three severity levels: minor, medium, and major faults. Based on the fault classification results, three corresponding fault-tolerant controllers are designed, including a primary fault-tolerant controller, a secondary fault-tolerant controller, and a mode-switching fault-tolerant controller. Each controller is designed to compensate for faults within the same severity level, thereby reducing controller design redundancy. Moreover, the stability of the error dynamic system is established by employing linear matrix inequalities (LMIs) and the Lyapunov stability theorem. Finally, the effectiveness of the proposed method is validated through hardware-in-the-loop (HIL) testing.

A displacement estimation technique based on BP neural networks is suggested to enhance the super-twisting sliding mode observer in order to address the installation challenges,cost rise,and stability reduction of electromagnetic linear actuators induced by the usage of displacement sensors.Combined with an adaptive integral robust control algorithm,the displacement sensorless control of the electromagnetic linear actuator is realized.A non-singular fast terminal sliding mode surface is designed with the continuous hyperbolic tangent function as the switching function in order to reduce the buffeting phenomenon and enhance the displacement estimation performance of the super-twisting sliding mode observer;in terms of the observer's parameter adjustment,the BP neural network is designed to dynamically adjust the super-twisting sliding mode observer's gain using the input of the mover speed.The motion control performance test platform of the electromagnetic linear actuator is established,and the displacement estimation and feedback control results are analyzed.The results show that the maximum displacement estimation error of the improved sliding mode observer is reduced by 16.22%under the step condition and 9.10%under the sine condition with the frequency of 2 Hz compared with the super-twisting sliding mode observer;the control performance of displacement sensorless control is equivalent to that of displacement sensor control.The steady state error of the two is 0.03 mm under the 8 mm step condition,and the maximum error is 0.43 mm under the sinusoidal condition with the frequency of 2 Hz.This proves the effectiveness and practicability of the displacement sensorless control of the electromagnetic linear actuator based on an improved super-twisting sliding mode observer.

Abstract The electro-hydraulic brake-by-wire system of engineering vehicles is a strongly nonlinear electromechanical-hydraulic system whose pressure control performance is susceptible to parameter uncertainties, unknown disturbances, and varying operating conditions. Existing nonlinear control and model-based disturbance estimation methods suffer from insufficient tracking accuracy and robustness, as well as limited disturbance estimation performance under complex operating conditions. To address these issues, this study proposes an adaptive robust pressure control method based on radial basis function neural networks. A radial basis function neural network observer is designed to estimate lumped disturbances in real time, while weight update laws enable the network parameters to be updated online without extensive offline training. The estimated disturbances are incorporated into the control system through feedforward compensation. Furthermore, the backstepping method, Lyapunov stability theory, and parameter adaptation are integrated to design an adaptive robust feedback controller that compensates for neural network estimation errors and system uncertainties. The main novelty lies in the coordinated integration of online neural-network-based disturbance estimation, feedforward disturbance compensation, and adaptive robust feedback within a unified closed-loop control framework. Stability analysis demonstrates that all closed-loop error signals are ultimately bounded. The comparison results demonstrate that the proposed method effectively improves pressure response speed, tracking control accuracy, and robustness under different operating conditions.

In response to the global energy transition toward carbon emission reduction, proton exchange membrane fuel cell (PEMFC) hybrid energy systems (FCHES) are increasingly adopted in marine power systems due to their clean energy potential. Efficient energy management strategies are critical, but current research often overlooks PEMFC performance degradation and multi-time scale states. This study addresses these gaps by proposing a predictive model-integrated PEMFC degradation-aware vectorized dynamic programming (PM-DVDP) strategy. The method employs a hybrid deep learning model to extract temporal features from historical data, integrated into the VDP algorithm for past-current-future multi-time scale coordination. A novel optimization metric combines PEMFC degradation modeling with equivalent consumption minimization strategy (ECMS). Simulations comparing PM-DVDP with conventional ECMS, VDP, and degradation-aware VDP demonstrate that PM-DVDP reduces hydrogen consumption by 4.14% compared to DVDP while maintaining a low PEMFC degradation rate of 0.003698%, achieving a balance between economy and durability. The work highlights the importance of predictive multi-scale coordination for enhancing system longevity in complex scenarios, with lessons underscoring the effectiveness of integrating temporal predictions to mitigate dynamic risks.

Aiming at the problem that various parameter uncertainties and disturbances degrade the tracking control performance in the direct-drive electro-hydrostatic actuator, an improved sliding mode control based on adaptive neural network is proposed in this paper. First, a new sliding mode reaching law is designed. On the basis of the exponential reaching law, a variable gain term based on system state variables, a piecewise function with power terms of the sliding surface and a new switching function are introduced, which improves the response speed, enhances the anti-disturbance capability and suppresses chattering. Secondly, a new adaptive radial basis function neural network observer based on the minimum learning parameter is designed. The outputs of the high-gain observer are taken as the inputs of the radial basis function neural network. An adaptive learning rate dynamically varying with the observation error is developed and incorporated into the weight updating law of the neural network, which improves the real-time nonlinear approximation accuracy for unknown disturbances. The stability was proved through the Lyapunov function. The results demonstrate that the proposed control method outperforms the other control methods in terms of both response speed and control accuracy.

To improve the ride comfort and attitude stability of the vehicle under complex driving conditions, this paper proposes a distributed model predictive control (DMPC) strategy with an adaptive weight-tuning mechanism based on the deep deterministic policy gradient (DDPG) algorithm for the active suspension system. The proposed method addresses the strong coupling among body vertical, pitch, and roll vibration-control objectives. It also reduces the reliance of conventional controllers on empirical parameter tuning and improves their adaptability to varying conditions. This study establishes a seven-degree-of-freedom full-vehicle active suspension model and decomposes it into a body subsystem and four wheel subsystems according to the coupling relationships. Then, a distributed predictive control framework is constructed. In this framework, local receding-horizon optimization and limited information exchange are used to achieve coordinated control. Furthermore, the DDPG algorithm learns the dynamic characteristics of the system online and adaptively adjusts the weighting parameters of the DMPC controller in real time. This enables dynamic allocation of control effort under varying operating conditions. The simulation results obtained from a high-fidelity CarSim co-simulation platform show that the proposed method effectively suppresses body vertical, pitch, and roll vibrations under different operating conditions. In addition, the proposed strategy reduces the average computation time compared with conventional MPC. Hardware-in-the-loop experiments further validate the effectiveness and real-time performance of the proposed controller.

To address the challenges of low positioning accuracy and poor disturbance rejection capabilities in permanent magnet synchronous motor (PMSM) position servo control systems, this paper proposes an active disturbance rejection control (ADRC) strategy based on cascade observers. The mathematical model of the PMSM is first established. Design a nonlinear function combining polynomial and trigonometric function to improve the nonlinear function, so that the function has continuity and smoothness at piece wise points, and the saturation function is introduced to improve the instability of the system in high error states. Designing cascaded state observers to estimate external perturbations, ESO1 makes an initial observation of the perturbation, and ESO2 observes the perturbation observed by ESO1 as a known part of the remaining perturbation, double estimation is achieved to reduce the observation error. The results prove the effect of the improved nonlinear function and the cascade state observer. At the same time, it is proved by comparison that the proposed control strategy has better control accuracy, response speed and robustness than PI control, ADRC control, MADRC control and NADRC control.

Proton exchange membrane fuel cell (PEMFC) is increasingly adopted as clean energy solutions for global carbon reduction. Efficient nonlinear control is critical for PEMFC air supply stability. Current research predominantly focuses on oxygen flow control while overlooking cathode pressure imbalance. This study proposes a reinforcement learning-optimized dual complex sliding mode controller (DCSMC) method to achieve coordinated oxygen flow and cathode pressure regulation. This approach constructs a PEMFC operational model parameter-based observation space and reward function integrating controller performance indicators for deep deterministic policy gradient (DDPG), enabling post-training DCSMC optimization, resolving complex sliding surface configuration challenges. Meanwhile, a Parameter Reduction Method (PRM) compresses sliding surface parameters from seven to five dimensions, alleviating computational constraints while enhancing action space efficacy. Simulations demonstrate the controller's superior oxygen/pressure regulation versus MPC, FC, and DSMC. This employed DDPG also outperforms AE/ME algorithms in computational speed and convergence efficiency through multi-parameter co-optimization. This work integrates neural network theory with sliding mode control, advancing coordinated control strategies for PEMFC air supply systems.

An improved active disturbance rejection control method based on Actor-Critic reinforcement learning (A-C ADRC) is proposed for disturbance compensation and parameter tuning of electro-hydrostatic actuators (EHA). This artificial intelligence-enhanced approach specifically addresses the adverse effects of system parameter uncertainties and time-varying disturbances encountered in EHA operation. Structurally, the cost function and value function are approximated by the radial basis function (RBF) neural network. The critic neural network uses the Lagrangian performance index to construct the value function, evaluate the control effect and feedback to the input end of the actor neural network. The actor neural network uses gradient descent to adaptively update the weights so that realizes the mapping from the system state to the control parameters. The stability and convergence of the closed-loop system are proved by the Lyapunov function. The results show that the proposed control method has made the error of the system converge to the neighborhood of zero without prior knowledge, and has parameter self-tuning ability. Under different target signals, the control parameters respond quickly and converge. Under load disturbance or white noise disturbance, the weights of actor and critic neural networks’ output are always bounded, and the control performance remains unchanged under similar disturbances of different sizes. The control method has good anti-disturbance performance.

To address the issues of slow braking response time and low clamping force control accuracy in Electro-mechanical braking systems (EMB), a constrained backstepping sliding mode control method based on a Barrier Lyapunov Function (BLF) is proposed. Firstly, considering the nonlinear characteristics of the EMB system, a state-space model in strict feedback form is established. Secondly, a time-varying tangent-type Barrier Lyapunov Function is constructed, where an exponentially decaying time-varying function is used as the constraint boundary, and an integral term is introduced to reduce the steady-state error caused by unmodeled dynamics. On this basis, the control law is designed by combining the backstepping method with nonsingular fast terminal sliding mode control to achieve fast and accurate tracking of braking clamping force. Finally, the stability of the system is proven based on the Lyapunov stability theorem, and experimental validation is conducted. The results indicate that under step conditions, the response time of the proposed control method is improved by 58%. In terms of control accuracy, the standard errors under triangular wave and sinusoidal wave conditions are reduced by 29.48% and 31.78%, respectively. This verifies the superiority of the proposed control method.

Electro-Mechanical Brake (EMB) is a highly promising development direction for brake-by-wire technology. The signal of the force sensor is the key to system control. However, force sensors are expensive and their stability decreases after frequent braking. One of the urgent problems to be solved is to obtain the force signal of EMB actuator without a force sensor. This article proposes a clamping-force estimation method for EMB actuator based on an enhanced adaptive extended state observer. Firstly, the extended state of the system was defined by simplifying the motor torque balance equation, and an adaptive extended state observer (AESO) was designed. In order to ensure the estimation accuracy when there is a significant change in clamping-force, a dual gain adaptive adjustment method for the observer based on estimation error is designed. When the estimation error is large, the adaptive gains are increased to enhance the estimation ability of disturbance, that is, to enhance the estimation ability of clamping-force, when the estimation error is small, the adaptive gains are reduced to improve the performance of noise suppression. The stability of the observer was proved through Lyapunov theorem. The AESO estimation method was compared with the Extended Luenberger Observer estimation method. The results show that AESO has higher estimation accuracy and stronger anti-disturbance ability through the gain adaptive adjustment method of observer based on estimation error, especially ensuring the estimation accuracy when the clamping-force continuously changes and undergoes large sudden changes, which helps to improve safety under conventional braking conditions and emergency braking conditions.

To solve the problem of position tracking control of the surface permanent magnet synchronous motor(PMSM)servo system,a compound control strategy based on non-singular fast terminal sliding mode control(NFTSMC)using an improved fast super-twisting algorithm(STA)and adaptive extend sliding mode disturbance observer(AESMDO)is proposed.Firstly,the mathematical model of surface PMSM with disturbance is established.Secondly,a fast super-twisting nonsingular fast terminal sliding mode controller is designed to prevent singularity and chattering.The improved fast STA is used as the switching control law of the approach phase,which has a faster approach speed than the traditional second-order sliding mode.In order to improve the system's ability to resist disturbance,finally,an AESMDO is designed to estimate the disturbance and compensate by the feedforward method.The stability and convergence of the system in finite time are proved by Lyapunov's theorem,and the experiment is carried out.The outcomes demonstrate how well the developed controller can monitor and regulate the system's specified value,effectively remove the buffeting phenomenon,and increase the system's resilience.

To improve both ride comfort and energy efficiency, this study proposes a semi-active suspension system equipped with an electromagnetic linear energy-regenerative magnetorheological damper (ELEMRD). The ELEMRD integrates a magnetorheological damper (MRD) with a linear generator. A neural network-based surrogate model was employed to optimize the key parameters of the linear generator for better compatibility with semi-active suspensions. A prototype was fabricated and tested. Experimental results show that with an excitation current of 1.5 A, the prototype generates a peak output force of 1415 N. Under harmonic excitation at 5 Hz, the no-load regenerative power reaches 11.1 W and 37.3 W at vibration amplitudes of 5 mm and 10 mm, respectively. An energy-regenerative magnetorheological semi-active suspension model was developed and controlled using a Linear Quadratic Regulator (LQR). Results indicate that, on a Class C road at 20 m/s, the proposed system reduces sprung mass acceleration and suspension working space by 14.2% and 7.5% compared to a passive suspension. The root mean square and peak regenerative power reach 49.8 W and 404.2 W, respectively. The proposed semi-active suspension also exhibits enhanced low-frequency vibration isolation, demonstrating its effectiveness in improving ride quality while achieving energy recovery.

Electromagnetic linear actuators are widely used in direct drive systems. To mitigate the effects of internal parameter disturbances and external uncertainties, this paper proposes an improved active disturbance rejection sliding mode control method. The position loop employs active disturbance rejection control with an enhanced sliding mode control rate and a dual hierarchy expanding state observer, while the current loop uses Proportional-Integral (PI) control. System stability is verified using Lyapunov theory. The dual hierarchy linear expansion state observer effectively estimates position and velocity, while a terminal complementary sliding mode controller replaces the traditional linear controller to enhance response speed and accuracy, reducing chattering associated with conventional sliding mode control. Simulation and experimental results show that compared with the traditional ADRC and ISM-ADRC, the improved method reduces the steady-state error by 45.5% and 29.4%, respectively. The maximum error at 1 hz and 2 hz sine conditions is 0.50 mm and 0.52 mm, respectively. In addition, the root mean square error (RMSE) was reduced by 15.13% and the maximum error was reduced by 7.4% compared to the traditional ADRC, showing greater robustness under different loads. These results verify the effectiveness and practicability of the proposed electromagnetic linear actuator control method.

To address the performance degradation of hydraulic shaking table under nonlinear disturbances, an improved segmental active disturbance rejection controller (IS-ADRC) based on a switching control law is designed. A self-coupling PID (SC-PID) control law is designed, and an adaptive speed factor model is proposed to enhance the system’s response speed without compromising disturbance observation ability, thus avoiding oscillations and instability caused by high-gain observer. To overcome the jitter issue in traditional nonlinear state error feedback (NLSEF) control laws, an improved control law (INLSEF) based on a smooth Fal-M function is designed to replace the traditional fal function. Moreover, considering the potential for integral saturation, a switching principle is designed to switch from the SC-PID control law to the INLSEF control law at small errors, ensuring smooth system convergence. The stability of the controller is proved using Lyapunov stability theory. Results demonstrate that the proposed IS-ADRC improves the response speed and anti-disturbance ability of the hydraulic shaking table. Furthermore, the Fal-M function effectively reduces the jitter phenomenon compared to traditional ADRC.