An approach to improve active disturbance rejection control

Nonlinear active disturbance rejection control is much more effective than linear active disturbance rejection control in tolerance to uncertainties and disturbances. However, it brings a great challenge for theoretical analysis, especially the stability analysis. This article proposes a linear matrix inequality method to analyze the absolute stability of generalized nonlinear active disturbance rejection control form which contains multiple nonlinearities with different parameters in both extended state observer and control law for single-input single-output systems. The generalized nonlinear active disturbance rejection control algorithm and the single-input single-output system are transformed into a direct multiple-input multiple-output Lurie system. A sufficient condition to determine its absolute stability based on linear matrix inequality method is given. The Lyapunov function of the Lurie system exists when the group of linear matrix inequalities is feasible. The free parameters and coefficients in Lyapunov function are given by the solution of these linear matrix inequalities. The electromagnetic valve actuator system in camless engine is presented as an application to illustrate how to perform the proposed method for absolute stability analysis and the stable region of parameter perturbations is obtained via the method. Simulation results show that the linear matrix inequality–based method is convenient and effective to determine whether the closed-loop system is absolutely stable.

Two new active disturbance rejection control (ADRC) structures for nonlinear systems are introduced: a locally linearized variant and a fully nonlinear formulation. Both approaches incorporate model knowledge to enhance performance but differ in how nonlinear dynamics are integrated into the control and observer design. The first proposed structure employs a state-dependent local approximation of the nonlinear model to generate dynamic controller and observer gains, aiming to balance robustness and accuracy. In contrast, the second one directly embeds the full nonlinear dynamics into both the control law and extended state observer, tightly coupling performance to model fidelity. The proposed methods were experimentally validated on a magnetic levitation system, known for its strong nonlinearity, and compared with a classical linear ADRC (LADRC). Furthermore, stability analysis of the methods was conducted using Lyapunov theory. Results show that the linearized structure consistently improves regulation performance over LADRC and, in most cases, achieves similar results to nonlinear ADRC with lower computational effort. However, the performance of the nonlinear approach may degrade under modeling inaccuracies and limited observer bandwidth. This study highlights that the way model information is integrated–rather than its level of detail–has a decisive impact on control quality. Finally, practical design guidelines are provided to assist in selecting an appropriate ADRC structure for nonlinear applications where robustness, computational efficiency, and limited model knowledge must be balanced.

The control stability and accuracy of quad tiltrotor UAVs is improved when encountering external disturbances during automatic flight by an active disturbance rejection control (ADRC) parameter self-tuning control strategy based on a radial basis function (RBF) neural network. Firstly, a nonlinear flight dynamics model of the quad tiltrotor UAV is established based on the approach of component-based mechanistic modeling. Secondly, the effects of internal uncertainties and external disturbances on the model are eliminated, whilst the online adaptive parameter tuning problem for the nonlinear active disturbance rejection controller is addressed. The superior nonlinear function approximation capability of the RBF neural network is then utilized by taking both the control inputs computed by the controller and the system outputs of the quad tiltrotor model as neural network inputs to implement adaptive parameter adjustments for the Extended State Observer (ESO) component responsible for disturbance estimation and the Nonlinear State Error Feedback (NLSEF) control law of the active disturbance rejection controller. Finally, an adaptive attitude control system for the quad tiltrotor UAV is constructed, centered on the ADRC-RBF controller. Subsequently, the efficacy of the attitude control system is validated through simulation, encompassing a range of flight conditions. The simulation results demonstrate that the Integral of Absolute Error (IAE) of the pitch angle response controlled by the ADRC-RBF controller is reduced to 37.4° in comparison to the ADRC controller in the absence of external disturbance in the full-states mode state of the quad tiltrotor UAV, and the oscillation amplitude of the pitch angle response controlled by the ADRC-RBF controller is generally reduced by approximately 50% in comparison to the ADRC controller in the presence of external disturbance. In comparison with the conventional ADRC controller, the proposed ADRC-RBF controller demonstrates superior performance with regard to anti-disturbance capability, adaptability, and tracking accuracy.

In order to improve the effect of electrical automation control, this paper combines the intelligent computer technology to construct the electrical automation control system, explores the principle of the active disturbance rejection controller, and applies it to the induction motor vector control system. The active disturbance rejection controller estimates the state variables of the system and their changing trends in real time through the extended state observer, compensates them by nonlinear feedback method, and provides appropriate control signals. In addition, this paper builds the induction motor active disturbance rejection control system based on ant colony algorithm and conducts a lot of simulation analysis. The research shows that the electrical automatic control system based on the intelligent computer algorithm proposed in this paper has a good electrical automatic control effect.

In this paper, a novel nonlinear active disturbance rejection (ADR) controller is proposed for the speed control of electric drives so that a better robustness to parameter variations can be achieved. The nonlinear observer is designed by using the sliding mode techniques. When the nonlinear observer is simplified as a linear one, it is equivalent to a phase-locked loop observer (PLLO). However, compared with the existing PLLO, the proposed observer has two gains with specific physical interpretation, which simplifies the gain tuning process, especially for the nonlinear observer. To alleviate the chattering problem, the fraction power function is employed in the observer and the guideline for parameter setting is present. An experimental comparative study of the linear PLLO and the proposed nonlinear PLLO is provided to show the effectiveness.

Nonlinear characteristics are very common in marine steam turbine, such as control input constraints and external disturbances. Based on the active disturbance rejection control (ADRC), an anti-windup scheme is proposed to eliminate the undesired effects of nonlinear characteristics in the control system. In this scheme, firstly, a method of setting parameter is designed for nonlinear active disturbance rejection control (NLADRC). Then, two kinds of anti-windup schemes are proposed in this paper for NLADRC in the presence of control input constraints and external disturbances. Finally, simulation study is carried out for a first order delay object with actuator constraints, simulation results show that both schemes can achieve good anti-windup performance. The method is further extended to marine steam turbine control, with simulation results demonstrating that both methods have their own advantages.

Vibration is a common problem in rotating machine. Active Magnetic Bearing (AMB) produces controllable magnetic force to levitate rotor and the control algorithm contributes to reduce vibration. This paper proposes a vibration suppression strategy based on active disturbance rejection control (ADRC). ADRC applies extend state observer (ESO) to estimate generalized disturbance. However, in AMB system, disturbance is mainly caused by centrifugal force, whose frequency is rotating frequency. For sinusoidal disturbance, ESO cannot estimate it absolutely. To estimate sinusoidal disturbance in AMB system, generalized integrator ESO (GI-ESO) is applied in ADRC. The resonant frequency of GI is set as rotating frequency. Transfer function of error of GI-ESO is analyzed and notch feature at resonant frequency is displayed. The transfer function of third-order of ADRC applied GI-ESO is obtained. Stability of proposed vibration suppressing strategy is analyzed by root locus. Results of simulations show better effect for sinusoidal disturbance estimation of GI-ESO. After applying ADRC based on GI-ESO, vibration of displacement in AMB system is reduced effectively, which shows the effectiveness of proposed vibration suppressing strategy.

The active disturbance rejection control technology was designed to solve the problem of formation maintenance in UAV cooperative formation flight, so that the response process had good dynamic quality and small static error. This paper first established a UAV formation flying model based on relative error in a two-dimensional plane. On this basis, the tracking differentiator, the extended state observer and the nonlinear state feedback controller were designed. The simulation results showed that the active disturbance rejection controller designed has good control performance and could realize the mission of maintaining the UAV with high precision.

This paper presents an improved active disturbance rejection controller to study the trajectory tracking problem of a pneumatic servo system. It is a challenging job to track a given trajectory for pneumatic system with strong nonlinearity. The designed active disturbance rejection controller consists of tracking differentiator, extended state observer and nonlinear controller. Tracking differentiator is designed to arrange a transition process for the given signal and get its corresponding differential signal. Extended state observer has advantages in observing states and estimating the nonlinear part of system. Moreover, a nonlinear controller is derived on the basis of backstepping approach. Finally, simulation results indicate the capabilities of the proposed method.

Active disturbance rejection control (ADRC) is a relatively new but very practical technology, which shows much promise in replacing PID as industry workhorse with unmistakable advantage in performance and practicality. This paper mainly concerns with a problem of fundamental nature: the asymptotic stability of nonlinear ADRC based control system, and applies ADRC to the ball-beam system to check the presented methods and the performance of ADRC. Firstly, the general nonlinear ADRC algorithm is introduced; then the asymptotical stability problem is transformed into that of determining whether a matrix or interval matrix is Hurwitz; finally the results of theoretical analysis are verified in simulations and experiments using the ball-beam platform, demonstrating the convenience and effectiveness of the proposed methods, in addition to the good performance of ADRC.

In this paper, a nonlinear active disturbance rejection control (ADRC) scheme is designed to control the pneumatic muscle actuator system. To reflect the impact of the sampling period, a continuous-discrete extended state observer (CDESO) is employed to estimate the so-called total disturbance, which describes the unmodeled complexities. Then, a nonlinear composite controller is used, where the estimates provided by the CDESO act as the feedforward term. The sufficient conditions to guarantee the stability of the CDESO and the overall controlled system are provided, respectively. Finally, a number of practical experiments are conducted on a pneumatic motion platform in order to verify the applicability of the proposed method.

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.

The electric propulsion system is composed of permanent magnet synchronous motor 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 article. Initially, a linear extended state observer 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 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 antidisturbance performances.

Although the structure of PI controller is simple, there are some flaws. In order to overcome the contradictions between the rapid response and overshoot for speed, the model of active disturbance rejection control (ADRC) was established in the paper. The transition process for a given speed was got by tracking - differentiator (TD). The sum of internal and external disturbance is estimated by the extended state observer (ESO). The capability of resisting disturbance is improved for the disturbance compensated timely. Permanent magnet synchronous motor (PMSM) direct torque control based on ADRC scheme is realized. The simulation results have shown its availability.

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.