Nonlinear Active Disturbance Rejection Control Research Articles

An Improved Nonlinear Active Disturbance Rejection Controller via Sine Function and Whale Optimization Algorithm for Permanent Magnet Synchronous Motors Speed Control

Permanent magnet synchronous motors (PMSMs) speed control has gained wide application in various fields. Specifically, there is a disadvantage that nonlinear functions in the conventional active disturbance rejection controller (ADRC) is non‐differentiable at the piecewise points. Thus, an improved nonlinear active disturbance rejection controller (NLADRC) for permanent magnet synchronous motor speed control via sine function and whale optimization algorithm (WOA), abbreviated as NLADRC‐sin‐IWOA, is proposed to overcome this drawback. Considering the unsatisfactory control effect caused by the poor active disturbance resisting ability of the traditional PMSM controllers, this paper proposes an improved NLADRC for PMSM, that reconstructs a novel differentiable and smooth nonlinear function, the novel nonlinear function grounded on primitive function by the function of inverse hyperbolic, sine, square functions, and with difference fitting approach; and designs an improved whale optimization algorithm via convergence factor nonlinear decreasing, Gaussian variation and adaptive cross strategies. The experimental results findings show that the improved NLADRC‐sin‐IWOA has the advantages of response fast, small steady‐state error and tiny overshoot. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Efficient nonlinear model predictive and active disturbance rejection control for trajectory tracking of unmanned vehicles

This article proposes an efficient trajectory tracking control strategy of unmanned vehicles. The method is based on nonlinear model predictive control (NMPC) and active disturbance reject control (ADRC). The designed control algorithm considers three challenges including nonlinear characteristics, multiple constraints, and external disturbance. First, NMPC method is presented for the nonlinear vehicle model with multiple constraints. To relax inequality constraints and reduce the heavy calculation burden, the penalty term with the variable factor is added to the cost function, an improved continuous/generalized minimum residual method is proposed to solve NMPC online optimization problem. Then, an ADRC scheme is designed to estimate the unknown disturbance via extended state observer, and compensate them by feedback control law in real time, the corresponding parameters are obtained by a novel particle swarm optimization algorithm to further improve the control precision. It ensures the stability to a certain extent. Finally, the results indicate the designed algorithm can raise the calculation efficiency and meet the real-time requirements, and obviously increase the tracking accuracy and robustness performance.

An improve nonlinear robust control approach for robotic manipulators with PSO-based global optimization strategy

During the trajectory tracking of robotic manipulators, many factors including dead zones, saturation, and uncertain dynamics, greatly increase the modeling and control difficulty. Aiming for this issue, a nonlinear active disturbance rejection control (NADRC)-based control strategy is proposed for robotic manipulators. In this controller, an extended state observer is introduced on basis of the dynamic model, to observe the extend state of model uncertainties and external disturbances. Then, in combination with the nonlinear feedback control structure, the robust trajectory tracking of robotic manipulators is achieved. Furthermore, to optimize the key parameters of the controller, an improved particle swarm optimization algorithm (IPSO) is designed using chaos theory, which improves the tracking accuracy of the proposed NDRC strategy effectively. Finally, using comparative studies, the effectiveness of the proposed control strategy is demonstrated by comparing with several commonly used controllers.

Active disturbance rejection control for piezoelectric cantilever beam with time delay

This Letter presents an active control method for the vibration of piezoelectric structures. First, a controller based on nonlinear extended state observer is designed to improve the disturbance rejection capability of the vibration structure. Additionally, an improved nonlinear active disturbance rejection control (IMNADRC) method is combined with Smith predictor for time delay compensation, resulting in Smith predictor-based IMNADRC. Finally, numerical simulations and experiments are carried out for active vibration suppression of piezoelectric beam under fixed harmonic excitation and variable harmonic excitation, respectively. The results show that the proposed method has good control effect on structural vibration suppression and is highly adaptable to various external excitations.

A Nonlinear Active Disturbance Rejection Feedback Control Method for Proton Exchange Membrane Fuel Cell Air Supply Subsystems

The control strategy of the gas supply subsystem is very important to ensure the performance and stability of the fuel cell system. However, due to the inherent nonlinear characteristics of the fuel cell gas supply subsystem, the traditional control strategy is mainly based on proportional integral (PI) control, which has the disadvantages of large limitation, large error, limited immunity, and inconsistent control performance, which seriously affects its effectiveness. In order to overcome these challenges, this paper proposes an optimal control method for air supply subsystems based on nonlinear active disturbance rejection control (ADRC). Firstly, a seven-order fuel cell system model is established, and then, the nonlinear ADRC and traditional PI control strategies are compared and analyzed. Finally, the two strategies are simulated and compared. The validation results indicate that the integral absolute error (IAE) measure of PI control is 0.502, the integral square error (ISE) measure is 0.1382, and the total variation (TV) measure is 399.1248. Compared with the PI control, the IAE and ISE indexes of ADRC were reduced by 61.31% and 58.03%, respectively. ADRC is superior to PI control strategy in all aspects and realizes the efficient adjustment of the system under different working conditions. ADRC is more suitable for the nonlinear characteristics of the gas supply system and is more suitable for the oxygen excess ratio (OER).

Self-immunity study of quadrotor UAV based on Modelica system modeling and disturbance feed-forward compensation

For addressing the challenges of decreased attitude and trajectory tracking accuracy and a delayed response in the flight control operations of quadcopter unmanned aerial vehicles (UAVs) under the uncertainties of model parameters and external disturbances, this study leverages the advantages of the non-causal declarative modeling language Modelica in system modeling and simulation. In addition, it incorporates the nonlinear Active Disturbance Rejection Control (ADRC) framework for disturbance observation, estimation, and compensation. A state observer is designed to mitigate the impact of external disturbances and model uncertainties through feed-forward compensation, and stability analysis is conducted. Numerical simulations for hover resistance demonstrate that, compared to the cascade proportional integral differential (PID) control strategy, PID-NLADRC reduces the maximum deviation induced by wind disturbances by ∼50% and shortens the disturbance influence time by around 40%. Simulations for different trajectories, such as planar or spatial, smooth or abrupt changes, indicate that under the PID-NLADRC control strategy, the real-time spatial distance deviation mean is reduced by 69.5%, and the peak time is shortened by 75.7%. Validation through multi-objective applications and physical experiments highlights the advantages of PID-NLADRC in terms of positioning accuracy, rapid tracking, and disturbance suppression, aligning well with the fast, precise, and robust flight control requirements of quadcopter UAVs.

Improved linear/nonlinear active disturbance rejection switching control for bearingless induction motor

ABSTRACT To achieve high-performance operation control for bearingless induction motor (BIM) systems, an improved linear/nonlinear active disturbance rejection switching control strategy is proposed (SADRC). The key innovation lies in the automatic switching between linear and nonlinear control modes based on system stability and disturbance magnitude. First of all, based on the principle of air-gap magnetic field directional control of the BIM, the first-order and second-order ADRC are designed for the rotating and suspending parts of the BIM, respectively. In addition, the nonlinear active disturbance rejection control (NLADRC) has the shortcoming of tracking performance degradation when the disturbance amplitude is large. Then, an active disturbance rejection controller that can automatically switch between linear and nonlinear based on the stability of the system and the magnitude of the disturbance is designed with the introduction of linear active disturbance rejection control (LADRC). The trigonometric function is introduced to improve the fal function to optimise the abrupt change at the linear interval and the high-frequency chattering phenomenon at the origin. The unknown parameters are rectified using the bandwidth method and the particle swarm algorithm, respectively, to ensure the robustness and adaptiveness of the control strategy. Finally, both simulation and experimental results show that the proposed SADRC strategy not only combines the advantages of linear and nonlinear self-anti-disturbance control but also improves the BIM rotor suspension performance and anti-disturbance capability.

Nonlinear Active Disturbance Rejection Controller Design for Drag-Free Satellite with Two Test Massess

Nonlinear Active Disturbance Rejection Controller Design for Drag-Free Satellite with Two Test Massess

A Dual-FSM GI LiDAR Imaging Control Method Based on Two-Dimensional Flexible Turntable Composite Axis Tracking

In this study, a tracking and pointing control system with a dual-FSM (fast steering mirror) two-dimensional flexible turntable composite axis is proposed. It is applied to the target-tracking accuracy control in a GI LiDAR (ghost imaging LiDAR) system. Ghost imaging is a multi-measurement imaging method; the dual-FSM GI LiDAR tracking and pointing imaging control system proposed in this study mainly solves the problems of the high-resolution remote sensing imaging of high-speed moving targets and various nonlinear disturbances when this technology is transformed into practical applications. Addressing the detrimental effects of nonlinear disturbances originating from internal flexible mechanisms and assorted external environmental factors on motion control’s velocity, stability, and tracking accuracy, a nonlinear active disturbance rejection control (NLADRC) method based on artificial neural networks is advanced. Additionally, to overcome the limitations imposed by receiving aperture constraints in GI LiDAR systems, a novel optical path design for the dual-FSM GI LiDAR tracking and imaging system is put forth. The implementation of the described methodologies culminated in the development of a dual-FSM GI LiDAR tracking and imaging system, which, upon thorough experimental validation, demonstrated significant improvements. Notably, it achieved an improvement in the coarse tracking accuracy from 193.29 μrad (3σ) to 87.21 μrad (3σ) and enhanced the tracking accuracy from 10.1 μrad (σ) to 1.5 μrad (σ) under specified operational parameters. Furthermore, the method notably diminished the overshoot during the target capture process from 28.85% to 12.8%, concurrently facilitating clear recognition of the target contour. This research contributes significantly to the advancement of GI LiDAR technology for practical application, showcasing the potential of the proposed control and design strategies in enhancing system performance in the face of complex disturbances.

Robust tracking control of flexible manipulators using hybrid backstepping/nonlinear reduced-order active disturbance rejection control

This study presents a novel hybrid control strategy for single-link flexible-joint robot manipulators, addressing inherent uncertainties and nonlinear dynamics. By integrating nonlinear reduced-order active disturbance rejection control (NRADRC) with backstepping control, the proposed method effectively estimates and mitigates nonlinear dynamics and external disturbances. Utilizing a nonlinear reduced-order extended state observer (NRESO) enhances resilience to internal and external uncertainties. The global stability of the proposed controller is rigorously established using the Lyapunov approach. Numerical comparisons with state-of-the-art nonlinear control methods demonstrate the superior efficiency and robustness of the proposed approach, especially under varying payloads and disturbances, advancing robotic control solutions.

Improved nonlinear active disturbance rejection control based on hierarchical expected improvement for high-speed elevator horizontal vibration suppression

In this paper, an improved NADR control method based on hierarchical expected improvement (HEI) optimization is studied to suppress the horizontal vibration of high-speed elevator car under complex coupled disturbances to improve high-speed elevator ride comfort. First, a nonlinear 8-DOF dynamic model for the horizontal vibration of the high-speed elevator car is constructed. Then, a 4-level parallel NADR main control system based on the fal-function is designed to observe the total disturbance in real time, which can be quickly compensated by fuzzy sliding mode control. Meanwhile, the adaptive law is used to adjust fuzzy rules and sliding mode switching term coefficients to ensure the stability and adaptability of the control system. To address the problem of multiple bandwidth parameters and high sensitivity of the observer in the NADR control system, the comprehensive RMS experimental data fusion model based on hierarchical Gaussian process is constructed. With the goal of achieving the optimal value of comprehensive RMS, a hierarchical expectation improvement search strategy that balances exploratory and developmental aspects is studied to improve the optimization accuracy of bandwidth parameters. Finally, the results show that the proposed method can reduce the horizontal vibration acceleration and tilt angle acceleration of the car system by more than 68%.

Feedback control of the COVID-19 outbreak based on active disturbance rejection control

The outbreak of COVID-19 causes a serious threat to human health and life around the world and puts enormous pressure on the healthcare system. The lockdown policy has effectively reduced the number of cases and suppressed the spread of the COVID-19 epidemic, but it also requires high social and economic costs. In this paper, we aim to use feedback control to help decision-makers establish lockdown policies, which can effectively constrain the spread of the COVID-19 pandemic with minimal financial loss. The time-dependent susceptible-infected-removed (SIR) model is used for the dynamics of the COVID-19 pandemic. The feedback control is based on a modified nonlinear active disturbance rejection controller (ADRC) that includes modified nonlinear extended state and nonlinear state error feedback with parameters tuned by particle swarm optimization, and the performances are compared with a well-known proportional-–integral–-derivative (PID) controller. The final simulation results show that the modified nonlinear ADRC has better performances and is more robust against uncertainties in the parameters of the epidemiological model.

Improved nonlinear active disturbance rejection control for a continuous-wave pulse generator with cascaded extended state observer

The generator rotor is crucial for the high-rate and reliable continuous-wave mud pulse transmission system. However, its dynamic responses are constrained by resistant load shocks and harsh operating environments. This study proposes an enhanced nonlinear active disturbance rejection control (EADRC) that integrates cascaded extended state observer (CESO) and enhanced nonlinear state error feedback (NLSEF) to address the abovementioned issues. The rotor motion model considering hydraulic torque is analyzed to characterize external load shocks, and an optimized nonlinear function, fal(·), is designed to improve slow convergence speed in high-error states. CESO is constructed to achieve timely and accurate disturbance estimations, while enhanced NLSEF is established to combine current and future system information for efficient feedback. Moreover, estimation capability and stability are theoretically proven based on the Lyapunov function. Simulations and experiments show that the proposed EADRC exhibits rapid response, high accuracy, and strong robustness in rotor speed control.

Design and extensibility analysis of a variable buoyancy system for small autonomous underwater vehicles

PurposeA switching depth controller based on a variable buoyancy system (VBS) is proposed to improve the performance of small autonomous underwater vehicles (AUVs). First, the requirements of VBS for small AUVs are analyzed. Second, a modular VBS with high extensibility and easy integration is proposed based on the concepts of generality and interchangeability. Subsequently, a depth-switching controller is proposed based on the modular VBS, which combines the best features of the linear active disturbance rejection controller and the nonlinear active disturbance rejection controller.Design/methodology/approachThe controller design and endurance of tiny AUVs are challenging because of their low environmental adaptation, limited energy resources and nonlinear dynamics. Traditional and single linear controllers cannot solve these problems efficiently. Although the VBS can improve the endurance of AUVs, the current VBS is not extensible for small AUVs in terms of the differences in individuals and operating environments.FindingsThe switching controller’s performance was examined using simulation with water flow and external disturbances, and the controller’s performance was compared in pool experiments. The results show that switching controllers have greater effectiveness, disturbance rejection capability and robustness even in the face of various disturbances.Practical implicationsA high degree of standardization and integration of VBS significantly enhances the performance of small AUVs. This will help expand the market for small AUV applications.Originality/valueThis solution improves the extensibility of the VBS, making it easier to integrate into different models of small AUVs. The device enhances the endurance and maneuverability of the small AUVs by adjusting buoyancy and center of gravity for low-power hovering and pitch angle control.

Research on permanent magnet synchronous motor algorithm based on linear nonlinear switching self-disturbance rejection control

This paper presents a linear-nonlinear switching control strategy, called Switching Active Disturbance Rejection Control (SADRC), to enhance the disturbance rejection capability of the speed controller in a servo system. SADRC combines the advantages of Linear Active Disturbance Rejection Control (LADRC) and Nonlinear Active Disturbance Rejection Control (NLADRC), and introduces a parameter to switch between nonlinear and linear control, thereby improving the robustness of the servo system. Firstly, the mathematical model of the motor is analyzed as the starting point of the paper. Then, the basic principles of Active Disturbance Rejection Control (ADRC) are analyzed, and improvements are made to address its limitations, resulting in the design of SADRC. The parameters introduced in SADRC are analyzed to determine their appropriate ranges. Finally, the performance of SADRC is validated by comparing the rotational effects of Permanent Magnet Synchronous Motor (PMSM).

Multiscenarios Parameter Optimization Method for Active Disturbance Rejection Control of PMSM Based on Deep Reinforcement Learning

In this article, a multi-scenarios parameter optimization method for active disturbance rejection controller (ADRC) of permanent magnet synchronous motor (PMSM) based on deep reinforcement learning (DRL) is proposed as MSPO-DRL. The parameter setting of nonlinear ADRC has always been one of the difficulties affecting the optimal performance of ADRC, and there will be different optimal parameters under different control requirements. In this article, artificial intelligence algorithm is introduced into the parameter optimization process of ADRC, and the DRL parameter optimization model which can automatically optimize and adjust the ADRC parameters in different application scenarios is constructed so that the ADRC can achieve the best control effect conveniently, and the limitation of current methods has been solved. ADRC is applied to the speed loop of flux weakening control of PMSM for more electric aircraft, and the mathematical model of ADRC in this environment is built above all. The Markov decision process is integrated into ADRC. The interface module and reward function between ADRC and MSPO-DRL are designed. The concept of ADRC control scenario is defined and integrated into the concept of Markov decision process to improve the generalization of DRL. Then the MSPO-DRL model is established, and the deep deterministic gradient strategy is used as the gradient descent strategy to converge the parameters optimization. After the model learning is completed, different environmental conditions are randomly selected for simulation and experiments to verify the optimization effect and generalization performance of the algorithm. Optimizations which are carried out by the heuristic algorithms are used for comparisons, and the superiority and feasibility of the proposed algorithm is verified.

Linear/Nonlinear Active Disturbance Rejection Switching Control for Near−Space Morphing Vehicles Based on Type−2 Fuzzy Logic System

This paper is concerned with the problems of robust switching control for near-space morphing vehicles (NMVs) with a large range of parameter uncertainty and external disturbance. For this purpose, a novel linear/nonlinear active disturbance rejection switching control method for the longitudinal dynamical model of NMVs based on the type−2 fuzzy logic system is proposed. Both linear active disturbance rejection control (LADRC) and nonlinear active disturbance rejection control (NLADRC) were designed for the velocity and altitude subsystems of NMVs. Then, the stability analysis of the cascade closed−loop and switching control systems were carried out. Furthermore, a switching control strategy based on the interval type−2 fuzzy logic system was developed, and the change rules of aerodynamic parameters with Mach number and angle of attack were examined. Finally, the experimental results validated the superior switching performance of the proposed control strategy.

Modified Nonlinear Active Disturbance Rejection Control for PMSM Speed Regulation With Frequency Domain Analysis

Strong robustness and smooth speed are two crucial goals of the high-performance permanent magnet synchronous motor (PMSM) drive systems. Conventional active disturbance rejection control (ADRC) strategy generally increases the bandwidth of the extended state observer (ESO) to improve the unsatisfactory disturbance rejection ability, which will inevitably amplify the measurement noise. To address this tough issue, a nonlinear extended state observer (NESO) using finite-time technique is constructed in this paper to enhance the anti-disturbance property. On this basis, the NESO with small bandwidth is sufficient to guarantee strong robustness without sacrificing noise suppression performance. Utilizing the frequency sweep method, the advantages of the proposed NESO based modified ADRC (MADRC) system can be analyzed in terms of frequency domain characteristics, which is more practical than traditional theoretical analysis from a mathematical point of view. Meanwhile, a quasi-resonant (QR) controller is combined with MADRC system to attenuate the main harmonic component of torque ripple for smooth speed. Experimental results are carried out to verify the effectiveness of the proposed control scheme and frequency sweep analysis method.

Nonlinear active disturbance rejection control for deformable mirror

The disturbance in the adaptive optical system includes not only the low-frequency broadband disturbance but also the high-frequency narrow-band disturbance caused by the vibration of system components and atmospheric turbulence. A nonlinear active disturbance rejection control (NLADRC) method is proposed to solve the control problem of a deformable mirror under high-frequency narrow-band disturbance. This method does not completely depend on the mathematical model, and the algorithm structure is simple. The differential tracker flattens the abrupt part of the signal, and the extended state observer is used to estimate the disturbance in real time. Finally, the nonlinear control rate is used to compensate the disturbance. The simulation results show that compared with the classical PID control and the classical linear active disturbance rejection control, the NLADRC method can effectively improve the bandwidth of the control system and show good suppression performance against high-frequency narrow-band disturbance, and the system is more robust. Both in time domain and frequency domain, it can accurately track the system state, reduce the system delay and system error, and has better dynamic performance.

An Enhanced Nonlinear ADRC Speed Control Method for Electric Propulsion System: Modeling, Analysis, and Validation

The electric propulsion system is composed of permanent magnet synchronous motor (PMSM) equipped with propeller load. Due to the strong coupling of propeller speed and load torque, they considerably characterize dynamic response and disturbance suppression capabilities of the speed controller. Traditional nonlinear active disturbance rejection control (NADRC) is less effective in dealing with a step change of command speed and large disturbance. In order to provide faster response and stronger disturbance rejection potential, an enhanced NADRC strategy is proposed in this paper. Initially, a linear extended state observer (LESO) is applied to preliminary estimate the total disturbance. Then, using the designed weight regular function, this estimation is introduced into the nonlinear extended state observer (NESO) with a cascade structure. The convergence, stability and disturbance estimation performance of the proposed strategy are then analyzed. Finally, experimental validation is performed based on a constructed experimental platform. The results show that the proposed method reasonably enhances the speed response and anti-disturbance performances.