Disturbance Rejection Control Approach Research Articles

Boundary disturbance rejection for Caputo-Hadamard fractional heat equations via ADRC approach

This paper focuses on the boundary control matched disturbance rejection problem for Caputo-Hadamard fractional heat equations with time delay. By utilizing the novel idea of the active disturbance rejection control (ADRC) approach, two infinite-dimensional systems are constructed. One separates the disturbance from the control input, and the other estimates the unknown disturbance without high gain. By employing the backstepping method, together with the disturbance-compensator, a desired stabilizing controller is designed, and the asymptotical stability is achieved for the original system.

Active disturbance rejection control for four-wire inverters in standalone renewable resources-based microgrid — islanded microgrids ADRC-based control

This paper presents an active disturbance rejection control (ADRC) approach for three-phase four-legs voltage source inverters (FL-VSIs) in a standalone renewable energy resources (RES)-based islanded microgrid. The key purpose of the proposed approach is to improve the control robustness against load-side disturbances, power supply parameters uncertainties, and faulty operating conditions. Indeed, a notable benefit of ADRC is its ability to operate effectively without the need for precise knowledge of disturbance characteristics or accurate modeling and FL-VSI parameters. As compared with conventional PI controllers, this advanced control strategy allows improving the voltage waveforms quality and conforming to existing power quality standards and metrics while using only output voltage sensors. Extensive simulations on Matlab/Simulink software have been conducted to assess the effectiveness of the proposed approach.

A Modified ADRC Scheme Based on Model Information for Maglev Train

During the operation of maglev trains, they are subjected to various disturbances. The presence of these disturbances presents a significant challenge for attaining high-performance control and even poses the risk of system instability. To further enhance the anti-disturbance capability of maglev trains, this paper proposes a model information-assisted modified active disturbance rejection control (MADRC) approach. A mathematical model of the single-point suspension system of maglev trains is constructed for the design of the extended state observer (ESO), which is a modified extended state observer (MESO), and a nonlinear mechanism is incorporated to boost the performance of the ESO. Owing to the introduction of model information, the estimated quantity of disturbances by MESO no longer considers the system model deviation as a disturbance. Hence, the linear feedback control law is modified accordingly. The MESO is regarded as an ESO with time-varying gain using the equivalent gain method, and its stability is proven using the Lyapunov method. The tracking and anti-disturbance performances of different controllers are compared via simulation experiments. Suspension and anti-disturbance experiments are conducted on the single-point suspension experimental platform, verifying that the proposed MADRC has a more potent suppression ability for load disturbances in the suspension system.

An active disturbance rejection control approach to vibration control on flexible systems based on frequency response

AbstractActive disturbance rejection control (ADRC) is considerably applied due to its advantage of focusing on merely dominant parameters. Research on flexible systems frequently confronting perplexing disturbances can utilize this method to simplify irrelevant items as a single variable. In this paper, we focused on vibration control problems in flexible systems with the application of ADRC and constructed a second‐order system model under the guideline of fundamental principles of ADRC and an innovative algorithm for tuning feedforward compensation ADRC. During the simulation, we discussed three cases in which each solely one parameter varies while others are kept invariant. Time, open‐loop frequency, and close‐loop frequency responses were respectively analyzed in all cases as to determine the stability of the system. According to the simulation results, we arrived at the conclusion: we should choose the specification of a flexible system within an intermediate range and evade from critical system parameters to procure stability and efficiency.

Sliding mode active disturbance rejection control for manipulator considering actuator saturation

<p style="text-align: justify;">Considering the issue of low control accuracy in joint trajectory tracking control for manipulator systems with actuator saturation due to external disturbances, modelling inaccuracies, and joint friction, a sliding mode active disturbance rejection control approach was proposed. An improved extended state observer is employed to observe and estimate the lumped disturbances affecting the system, providing feedback compensation. A variable gain reaching law is devised, coupled with a fast non-singular terminal sliding mode to design the system control law, which mitigates chattering inherent and ensuring precision control. Additionally, a novel output error compensation-based anti-windup scheme is introduced to compensate for the detrimental impacts caused by actuator saturation. Simulation results collectively demonstrate that the proposed tracking control algorithm exhibits better control performance and robustness against disturbances.</p>

A fractional‐order active disturbance rejection control for permanent magnet synchronous motor position servo system

AbstractThis paper introduces a novel control scheme for the permanent magnet synchronous motor (PMSM) position servo system using a fractional‐order active disturbance rejection control (ADRC) approach. Specifically, a first‐order ADRC is employed in the current loop, while a fractional‐order ADRC is designed for the position loop. In the latter, a linear extended state observer (LESO) is utilized to estimate and compensate for disturbances, while a fractional‐order proportional derivative (FO[PD]) feedback controller is employed to enhance the control performance. Moreover, a parameter tuning method is presented based on frequency domain specifications. This technique utilizes the flat phase constraint as a design constraint to ensure that the phase is flat near the gain crossover frequency, thus ensuring that the closed‐loop system remains robust to loop gain variations. Simulation and experimental results demonstrate that the proposed fractional‐order ADRC control scheme yields improved dynamic response, disturbance rejection, and robustness to loop gain variations.

Active disturbance rejection control approach to the output tracking of PDEs with general disturbances: A new perspective

In recent years, significant progress has been made in output regulation for systems described by partial differential equations (PDEs) through the active disturbance rejection control approach (ADRC). However, in all these studies, the disturbance typically manifests in a single channel and requires estimation, often necessitating additional measured signals. This is because the disturbance must be identified through the output. In this paper, we approach this problem from a novel perspective: disturbances occur in all channels, yet few measured signals are required. In most cases, only the tracking error is utilized as the measured signal. This marks a significant advancement in the application of ADRC to PDEs. We primarily demonstrate this approach by addressing the output tracking problem for a multi-dimensional heat equation, considering general disturbances across all possible channels. Additionally, we briefly discuss some other one-dimensional problems studied in the literature, such as the one-dimensional wave equation.

The active disturbance rejection control approach to output feedback stabilization of an anti-stable wave equation with corrupted boundary observation

In this paper, we are concerned with the boundary output feedback stabilization for an anti-stable wave equation where the boundary observation is corrupted by a general disturbance. We cope with the disturbance by the approach of active disturbance rejection control. In contrast with the existing results, the assumptions on the derivative of the disturbance are removed. It is necessary to assume that the disturbance is Lipschitz continuous. A state observer together with a disturbance estimator is designed by using the corrupted output. Both the well-posedness and the stability of the closed-loop system are proved. The theoretical results are validated visually by some numerical simulations.

Output tracking for nonlinear stochastic systems driven by bounded and colored noises

In this paper, we consider practical tracking problem for a class of nonlinear stochastic systems driven by bounded and colored noises by means of active disturbance rejection control approach. The nonlinear extended state observer with homogeneous weighted functions is constructed to estimate in real time the unmeasurable state and the total stochastic disturbance that affects system performance. An observer-based output feedback is designed to guarantee the almost surely practical convergence of the tracking errors. The existence of the global weak solution of the closed-loop system is proved and the tracking convergence accuracy is shown to be higher than that of linear one under the same tuning parameters. Some numerical simulations are carried out to validate the effectiveness of the proposed controller.

Trajectory Tracking Control of Pneumatic Servo System: A Variable Gain ADRC Approach.

In this article, a novel error-driven variable gain active disturbance rejection control (ADRC) approach is developed for pneumatic servo system, and the desired performance of trajectory tracking and the disturbance rejection can be guaranteed. The proposed variable gain ADRC includes three parts: 1) variable gain tracking differentiator (TD); 2) variable gain extended state observer (ESO); and 3) variable gain error feedback controller (EFC). The proposed variable gain TD is noise tolerant and possesses a variable gain, which can be dynamically adjusted according to the tracking error, and the performance for tracking the reference signal and extracting its derivative is improved. The variable gain ESO is also equipped with a variable gain driven by estimation errors to improve the estimation performance. Then, the variable gain EFC is further designed to improve control accuracy. Finally, simulations and experimental results are presented to verify the efficiency of the proposed methods.

Output feedback stabilization for a wave–ODE cascaded system subject to uncertain disturbance

AbstractIn this paper, we consider output feedback stabilization for a wave–ODE cascaded system with uncertain disturbance flowing the control end. Firstly, a disturbance estimator is designed by the new active disturbance rejection control (ADRC) approach that we propose two auxiliary systems. Then, we design an observer for the coupled system based on the idea that copy of the original system plus injection of the output estimation error. Finally, by the backstepping method, we design an output feedback control and obtain the exponential stabilization of the closed‐loop system, which consists of the original coupled system, the observer, two new auxiliary systems, and the control. Due to the existence of the in‐domain anti‐damping in wave equation, the proposed two auxiliary systems are different from those in the previous literature. And their designs are inspired by the design idea of the observer. Some numerical simulations are given to illustrate the effectiveness of the control.

The Design of a Reaction Flywheel Speed Control System Based on ADRC

The reaction flywheel is a crucial operational component within a satellite’s attitude control system. Enhancing the performance of the reaction flywheel speed control system holds significant importance for satellite attitude control. In this paper, an active disturbance rejection control (ADRC) approach is introduced to mitigate the impact of uncertain disturbances on reaction flywheel speed control precision. The reaction flywheel speed control system is designed as an ADRC controller due to the current challenge of measuring unknown disturbances accurately in the reaction flywheel system. To derive the rotor’s speed observation value and the estimated total disturbances value, the sampled data of the reaction flywheel rotor position and torque control signal are fed into the extended state observer. The estimated total disturbances value is compensated on feedforward control, which could mitigate significantly the effects of various nonlinear disturbances. The paper initially establishes the rationale behind the reaction flywheel ADRC controller through theoretical analysis, followed by analysis of the differences of performance of reaction flywheel control by the ADRC controller and the PID controller in MATLAB/SIMULINK. Simulation results demonstrate the evident advantages of the ADRC controller over the PID controller in terms of speed command tracking capability and disturbances suppression ability. Subsequently, the ADRC controller program and the PID controller program are implemented on the reaction flywheel control circuit, and experiments are conducted to contrast speed command tracking and disturbance suppression. Importantly, the experimental outcomes align with the simulation results.

Robust Model Predictive Control Based on Active Disturbance Rejection Control for a Robotic Autonomous Underwater Vehicle

This work aims to develop a robust model predictive control (MPC) based on the active disturbance rejection control (ADRC) approach by using a discrete extended disturbance observer (ESO). The proposed technique uses the ADRC approach to lump disturbances and uncertainties into a total disturbance, which is estimated with a discrete ESO and rejected through feedback control. Thus, the effects of the disturbances are attenuated, and a model predictive control is designed based on a canonical model free of uncertainties and disturbances. The proposed control technique is tested through simulation into a robotic autonomous underwater vehicle (AUV). The AUV’s dynamic model is used to compare the performance of a classical MPC and the combined MPC-ADRC. The evaluation results show evidence of the superiority of the MPC-ADRC over the classical MPC under tests of reference tracking, external disturbances rejection, and model uncertainties attenuation.

Anti-disturbance control for a nonlinear flexible beam with velocity disturbance at the boundary

This paper deals with the output feedback stabilization for a nonlinear flexible beam system with a general disturbance at the boundary. An extended state observer is designed to reject the uncertain disturbance estimated by a relatively independent estimator in the feedback loop via the active disturbance rejection control approach. The existence and uniqueness of the solution to the closed-loop beam system are investigated by means of the Galerkin approximation. The asymptotic stability of the closed-loop beam system is shown by utilizing the energy perturbation method. To demonstrate the control performance, numerical simulations are provided by the finite element method.

Active Vibration Control of a Rotating Mechanical System with a Rigid Coupling using Active Disturbance Rejection Control

The work aims to develop an active control method for mitigating torsional vibration of a rotating mechanical system with a rigid coupling, driven by an electric motor, particularly for suppressing vibration associated with its mechanical resonances. It is commonly known that torsional oscillations in a rotating system, which is normally used for various power transmission systems, can generate significant levels of vibration and noise. In this work, therefore, an active control system that was based on the Active Disturbance Rejection Control approach was utilized to develop an active control system that was robust against uncertainties associated with the internal dynamics and external disturbances affecting the system. The dynamic interactions between the inertias of the electric motor and the load, which were connected through elastic shafts and a rigid coupling, were investigated. The Extended State Observer was used to estimate the generalized disturbance consisting of not only the external disturbances but also the disturbances associated with internal dynamics of the rotating system. The effectiveness of the developed controller was demonstrated, which showed that in the case of the varying load inertia, the control system could still perform well in mitigating the torsional vibration.

Variable gain based composite trajectory tracking control for 4-wheel skid-steering mobile robots with unknown disturbances

This paper investigates the trajectory tracking problem for 4-wheel skid-steering mobile robots (SSMRs) with unknown disturbances. A novel variable gain based composite disturbance rejection control approach is proposed. By designing a variable gain disturbance observer, the unknown uncertainty and external disturbance are estimated. Then, a novel time-varying sliding surface and nonsingular terminal sliding mode controller (NTSMC) are proposed, and the estimation of disturbance is incorporated in the controller to achieve the active disturbance rejection. It is shown that, with the proposed disturbance observer and controller, the tracking error is guaranteed to converge within a predefined time. Moreover, the control allocation for motors is also considered, which can allocate the virtual driving force to obtain the motor driving torque commands for the four wheels. Finally, the stability and the tracking performance of the proposed control scheme are verified respectively by theoretical analysis and comparative experiments.

Clinical Trajectory control for lower Knee rehabilitation using ADRC method

The design and study of the Active Disturbance Rejection Control (ADRC) approach for control and disturbance rejection for lower knee rehabilitation utilizing a residential exoskeleton system are provided in this paper. Linear ADRC (LADRC) and Nonlinear ADRC (NADRC) are two controllers that are considered for control purposes based on the structure of ADRC. The contrasts between them are thoroughly discussed in this work. The LADRC is made up of a tracking differential (TD), a linear proportional derivative (LPD) controller, and a linear extended state observer (LESO), whereas the NADRC is made up of the same LESO but with a nonlinear PD (NPD) and a modified optimized TD (MTD). In terms of robustness against the ability to reject applied disturbances, a comparison of LADRC and NADRC has been done. The fundamental challenge with ADRC is that its constituent parameters must be fine-tuned. Grey Wolf Optimizer (GWO) has been proposed for tuning the parameters of ADRC to have the least amount of error variation in order to improve the controlled system's dynamic performance. When a prescribed disturbing torque is applied, the results of a MATLAB simulation show that the LADRC has greater disturbance rejection capabilities than the NADRC.

Active Disturbance Rejection Control Approach for Double Pendulum Cranes with Variable Rope Lengths

The overhead crane is a typical underactuated system with complicated dynamics and strong couplings. It is widely employed to transport heavy cargoes in many industrial fields. Due to the complexity of working environments, however, cranes often encounter various unfavorable factors, which may degrade the transportation efficiency. To enhance control performance and anti-disturbance ability, this paper proposes an active disturbance rejection control approach based on differential flatness for double pendulum cranes with variable rope lengths. The proposed approach can position the trolley accurately, regulate rope length, and suppress the swing angles of the payload and the hook simultaneously. During the controller design, flat outputs were constructed based on differential flatness technique to deal with system couplings, and the results prove that double pendulum crane system is differentially flat. After that, model uncertainties and external disturbances were estimated by the designed extended state observer. On this basis, a controller was developed based on the feedback control technique. Finally, a series of simulations were carried out to show that the control scheme is effective and robust.

DC Motor Drive Powered by Solar Photovoltaic Energy: An FPGA-Based Active Disturbance Rejection Control Approach

This paper presents an experimental platform for regulating the DC motor angular speed powered by photovoltaic cells. The experimental platform comprises an Eco Green Energy EGE-260P-60 solar panel, DC/DC SEPIC converter, DC bus, DC/DC buck converter, DC motor and Nexys 4 board with an Artix-7 100T FPGA. The DC/DC SEPIC converter is used for harvesting the maximum amount of energy from the PV cells using the perturb and observe algorithm to track the maximum power point. The DC/DC buck converter is used as the motor drive using the active disturbance rejection control to regulate the angular speed of the DC motor. In addition, the FPGA architecture design is presented using a hierarchical top-down methodology with the VHDL hardware description language and Xilinx System Generator tool. The software takes advantage of the FPGA’s concurrency to simultaneously evaluate the different processes, which is the main reason for choosing this digital device. Several tests were performed on the platform such as irradiance changes, DC bus variations, DC motor connection and load torque variations applied in the motor shaft. The results indicate that the maximum power is obtained from the photovoltaic cells, establishing the minimum operating conditions. In addition, the control approach estimates and cancels the effects of disturbances caused by variations in the environmental conditions, photovoltaic system, DC bus, and load changes in order to regulate DC motor speed.

Stabilization of a uniform rotating disk-beam-mass system with boundary input disturbance

In this paper, we study the stabilization problem of a disk beam structure with disturbance. Specifically, the structure consists of a beam clamped at one end to the center of a rotating rigid disk, while the other end is attached to a tip mass subject to a non-uniform bounded disturbance. We start the investigation by designing the controller via the Active disturbance rejection control (ADRC) approach. The high gain extended state observer (ESO) is first designed to estimate the disturbance, then the feedback observer-based controller is designed to employ the estimation to cancel the disturbance effect. Furthermore, the well-posedeness of the controlled system is proved using the semigroup theory. Using the Lyapunov method, the exponential stability is proved. Finally, the performance of the control method is illustrated by simulation results.