PSO Optimized ADRC Motor Speed Controller for Two Mass System with Backlash

In this study, a type of direct-drive gearshift system integrated into a motor-transmission coupled drive system is introduced. It used two electromagnetic linear actuators (ELAs) to perform gearshift events. The adoption of ELAs simplifies the architecture of the gearshift system and has the potential to further optimize gearshift performance. However, a number of nonlinearities in the gearshift system should be investigated in order to enhance the performance of the direct-drive gearshift system. An active disturbance rejection control (ADRC) method was selected as the principal shifting control method due to the simple methodology and strong reliability. The nonlinear characteristics of the electromagnetic force produced by the ELA were subsequently reduced using the inverse system method (ISM) technique. The ADRC approach also incorporated an acceleration feedforward module to enhance the precision of displacement control. The extended state observer (ESO) module used a nonlinear function in place of the original function to improve the ability to reject disturbances. Comparative simulations and experiments were carried out between the ADRC method and improved ADRC (IADRC) method. The outcomes demonstrate the effectiveness of the designed control method. The shift force fluctuates less, and the shift jerk decreases noticeably during the synchronization procedure. In conclusion, combined with the optimized IADRC method, the direct-drive gearshift system equipped with ELAs shows remarkable gearshift performance, and it has the potential to be widely used in motor−transmission coupled drive systems for EVs.

This paper presents a simplified active disturbance rejection control (ADRC) method for implementing the DC capacitor voltage in Z-source constant. Active disturbance rejection control method is the development of PID control. It is suit ab le for the inverter with variable input. A simplified ADRC method is used in this paper to reject the disturbance from variable input in Z-source inverter. In its ESO module part, Kalman filter is used to estimate the state and the disturbance, which can approach the true value at the extreme, and reduce the computation time. The simulation result shows the control method can achieve the control requirement satisfactory.

Considering the internal and external disturbances of the direct‐driven wind energy conversion systems, i.e. multi‐variable coupling, non‐linear characteristic and modelling error, and the environmental disturbances, an adaptive sliding mode observer with active disturbance rejection control (ADRC) method for a direct‐driven permanent magnet synchronous generator (PMSG) based wind power conversion system is proposed to track the maximum power point precisely. First, adaptive sliding mode observer based on phase‐locked loop can effectively observe the rotor position information of PMSG, and weak the inherent chattering of traditional sliding mode. Second, ADRC can enhance the anti‐disturbance ability when the system is under linear state feedback. Finally, the simulation results show that this method can estimate the rotor position exactly, and the system has the strong robustness and the optimum power tracking performance.

Electromechanical actuators (EMA) are becoming more and more widely used. As the core technology of EMA, servo control technology determines their performance. In this paper, an active disturbance rejection control (ADRC) method with an improved extended state observer (ESO) is proposed to design a cascade controller of EMA based on permanent magnet synchronous motor (PMSM). The mathematical model of PMSM in a two-phase rotating coordinate system is established, then it is decoupled by an id=0 current control method to realize the vector control of the motor. In a three closed-loop vector control system, a PID controller including current loop, speed loop and position loop is designed. To solve the problems caused by measurement noise, the filter link and system are modeled as a whole, and an improved ESO is constructed. On this basis, an ADRC controller of the speed loop and position loop of PMSM is designed and simulated based on Simulink. Based on the physical test platform, a load step test and load disturbance test of ADRC are completed. The results show that, in comparison to the PID method, the ADRC method shortens the response time by 25% on average, and reduces the overshoot by 60% on average. So, it can be concluded that ADRC has good static and dynamic performance, which has a good guiding role for engineering practice.

For high‐order systems, strong nonlinearities, parameter uncertainties and external disturbances pose significant control challenges. Several improved active disturbance rejection controller (ADRC) methods are proposed, including input modified ADRC (MADRC), time‐delay ADRC (DADRC) and Smith‐like ADRC (SLADRC). These improved ADRC methods are systematically compared with conventional proportional integral (PI) control and regular ADRC, focusing on key performance metrics such as tracking accuracy and disturbance rejection capability. The effectiveness of the proposed improved ADRC methods is validated via numerical simulations of a typical superheated steam temperature (SST) system. The integral absolute error (IAE) of ADRC, MADRC, DADRC and SLADRC shows a reduction of around 30, 50, 33 and 35, respectively, relative to that of PI. The outcomes of numerical simulations demonstrate that improved ADRC methods achieve satisfactory control performance, whereas MADRC stands out with the best overall performance. Thus, field application data show that compared with PI, MADRC exhibits significant reductions in key deviation metrics, with the maximum positive deviation decreasing by 33, the maximum negative deviation decreasing by 8, the average positive deviation decreasing by 25, the average negative deviation decreasing by 11 and the variance deviation decreasing by 18.

An active disturbance rejection control (ADRC) method is proposed for configuration maintenance of an electromagnetically controlled spacecraft cluster. In this paper, the stability of the ADRC controller is analyzed. First, the ADRC controller is introduced. Furthermore, a Lyapunov function is constructed, and according to the positive definiteness of Lyapunov function matrix, a sufficient condition for ADRC controller is derived. Finally, numerical simulations are performed to verify the effectiveness of the controller, and the controller is confirmed to be Lyapunov asymptotically stable.

Because of the strong non-linearity, uncertainty and typical underactuated properties, as well as the restraints of rudder, the design of ship tracking controller is yet a challenge work. In this paper, the problem was investigated by utilizing the active disturbance rejection control (ADRC) method. Firstly, the ADRC was introduced briefly and the characteristics of ship tracking motion were analyzed. And the systempsilas nonlinear mathematical model with restraints and uncertainties was established. Then the system was described as a series structure, and the tracking ADRC controller was designed based on a kind of three order polynomial trajectory planning algorithm. At last, the simulations were performed. The results show that the controller designed can achieve high precision on ship tracking control and has strong robustness to ship parameter perturbations and environment disturbances.

The intelligent motion control technology of Autonomous Underwater Vehicle (AUV) is the basis of long-distance voyage for AUV. The motion control capability in vertical plane is an important technical for AUV to complete multifarious missions. So, it is important and realistic significance to research on motion control in vertical plane of AUV. Motion control problem of AUV in vertical plane, especially depth control problems is researched based on active disturbance rejection control (ADRC) method in this paper. The kinetic and dynamic model in vertical plane of AUV is established and simplified. The active disturbance rejection controller design method is introduced. Detailed algorithms of each part for active disturbance rejection controller are discussed according to separability principle of ADRC. Based on ADRC, the depth controller is designed and applied in AUV. At last, simulation results indicate that the method is feasibility and effectiveness for AUV depth control.

In this paper, the problem of attitude tracking control for a class of vertical take-off landing (VTOL) aircraft in the presence of uncertain disturbances is addressed. The active disturbance rejection control (ADRC) method is utilized to address uncertain disturbances, while the radial basis function (RBF) neural network is considered for handling unknown nonlinear dynamics. By incorporating a modified tracking differentiator, a nonlinear state error feedback controller, and an extended state observer, the disturbance observation problem in the aircraft system is solved. These disturbances, seen as a combined disturbance in the aircraft system, are counteracted through the extended state observer. Furthermore, the unknown nonlinear dynamics within the aircraft system are approximated using the RBF neural network. Subsequently, the paper suggests adaptive ADRC strategies based on neural network and formulates adaptive control laws to estimate unknown parameters. The Lyapunov stability theory proves the effectiveness of the proposed control strategies. The simulation results show that the attitude tracking control problem of VTOL aircraft can be achieved under the proposed control strategies and adaptive control laws.

This study investigates the impact of time-varying jet reaction forces on ship-cleaning manipulators, focusing on joint torque fluctuations, high-frequency chatter, and the deterioration of end-effector positioning accuracy. An enhanced active disturbance rejection control (ADRC) method is proposed, which integrates jet reaction force modeling, joint torque feedforward compensation, and improvements to both the extended state observer (ESO) and the nonlinear state error feedback (NLSEF). Simulation results show that the enhanced ADRC reduces the joint stabilization time from 10 to 2 seconds, suppresses over 70% of the initial torque spikes, and decreases the ESO observation errors by more than 60%. Compared with the classical sliding mode control (SMC), the proposed method effectively eliminates high-frequency chattering phenomena and reduces control signal aggressiveness during the startup phase. This method improves trajectory tracking accuracy under strong disturbances while smoothing the control output and significantly reducing high-frequency joint chatter. These results confirm that the enhanced ADRC method improves stability and responsiveness, providing a robust framework for the reliable operation of ship-cleaning manipulators in high-disturbance environments.

To address the issue that the pressure balance between the anode and cathode of the fuel cell stack is susceptible to disturbances, a novel fuzzy active disturbance rejection control (ADRC) method is developed for fuel cell hydrogen supply systems (HSSs). According to the operating characteristics of the hydrogen fuel cell, a control-oriented third-order HSS model is established. Then, an extended state observer (ESO) is designed by integrating ADRC theory with fuzzy control theory. Furthermore, the controller is constructed by using the anode-cathode pressure difference as the input and the regulating valve opening as the output. Finally, the simulation results show that the proposed fuzzy ADRC method demonstrates excellent response speed, accuracy, and anti-interference ability in pressure tracking control. Through online estimation and dynamic compensation mechanisms, it effectively mitigates the impact of the system disturbances.

This chapter deals with the active disturbance rejection control (ADRC) method to the lateral control of small air-to-ground missiles for helicopters. The main difficulties that arise in lateral control design of small missiles are related to the highly uncertain, nonlinear aerodynamic forces and force movements, thus it is difficult to obtain an accurate dynamic model. Besides, the huge variations of dynamic pressure make controller parameters, and are difficult to adapt to the whole flight envelope. To handle them, the design of the controller is based on ADRC, a nonlinear control design approach which is based on the extended state observer (ESO), and can estimate and compensate the uncertainty of the system, including structural errors, random, and other system errors. Six-degree freedom equations are established for the lateral channel, the equations are linearization with small disturbance theory, then the aerodynamic derivatives are obtained through wind tunnel test, the dynamic model is made and the aerodynamic features are analyzed. One-order ESO equations of lateral channel are deduced, the controller of the lateral channel which is based on the ESO is designed and parameters are adjusted, and finally, semi-physical simulations are made. Through the comparison with classical proportion integral differential (PID) controller, the controller based on ADRC has strong robustness and it could track control command rapidly and accurately.

<div class="section abstract"> <div class="htmlview paragraph">The growth of the electric vehicle market has driven the advancement of technologies related to energy storage and lithium-ion cells, which stand out for their fast charge and discharge capabilities, high energy density, and long service life. This paper proposes a thermal control strategy for lithium-ion battery packs using the Active Disturbance Rejection Control (ADRC) method. The model is developed in Simcenter Amesim software, using cylindrical 21700 cells in a pack equipped with a water-cooling system, and was adapted for export in FMU format and integrated into MATLAB/Simulink, where the control algorithms were designed and simulated. From step input tests, a first-order transfer function was identified with a fitting of 97.67%, supporting the adoption of a first-order ADRC. The tests involved scenarios with changes in temperature reference and current disturbances typical of vehicle operation. Results indicate that ADRC performs satisfactorily in temperature tracking, even under actuator saturation, and particularly excels in disturbance rejection, outperforming the proportional-integral-derivative (PID) controller in speed and precision. Furthermore, ADRC proved robust to system degradation—an essential feature in the thermal management of batteries subject to aging. The proposed approach shows promise for real-world applications, offering thermal stability and extended system lifespan. For future work, experimental validation through Hardware-in-the-Loop (HiL) is suggested.</div> </div>

The net power of the automotive fuel cell system varies with air mass flow and pressure. To enhance net power across different operating conditions, this study introduces an adaptive control strategy that integrates operational parameter optimization. Initially, the two-dimensional particle swarm optimization (TDPSO) method is proposed to select appropriate reference signals for the oxygen excess ratio (OER) and pressure to maximize net power. Furthermore, to coordinate the air compressor and flow valve, a feedback-linearization decoupling controller is designed to achieve independent control of air flow and cathode pressure. Additionally, to address time-varying and nonlinear interference, an active disturbance rejection control (ADRC) method has been developed to enhance dynamic response and stability. Through a series of simulation and hardware-in-the-loop (HIL) tests, the proposed control strategy is demonstrated to optimize net power under various operating conditions, showing superior transient and steady-state performance compared to traditional methods. Quantitative comparisons further illustrate the advantages of optimization algorithms and adaptive control techniques in improving power and control system performance.

Nowadays, the electro-hydraulic actuator plays an important role in some modern tactical missiles. High power, great robustness and high tracking precision are the most significant demands for the missile actuator. Therefore an advanced method of active disturbance rejection control (ADRC) is presented aiming at the dynamics of the system are highly nonlinear and have large extent of model uncertainties, such as tremendous changes in load. Firstly, a novel ADRC controller is designed for estimating and compensating disturbance based on the mathematical model of missile electro-hydraulic actuator. Then, the influence of rudder load on the system performance is analyzed in this paper. Simulation results show that the ADRC control approach can decrease the tracking error and enhance the robustness of missile electro-hydraulic actuator system when the rudder load changed tremendously. But the phenomenon of Anti-Control has disadvantageous effect on the transition period of actuator loop and evenly causes the system divergence.