On asymptotic stability for nonlinear ADRC based control system with application to the ball-beam problem

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.

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.

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.

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.

Aiming at the problem that the suspension force under disturbance of the permanent magnet slice rotor is difficult to be accurately detected, a new displacement controller based on the active disturbance rejection control is proposed. Firstly, the mathematic models of torque and suspension forces of the bearingless permanent magnet slice motor (BPMSM) are deduced. Secondly, the active disturbance rejection (ADR) controller is constructed. Thirdly, the BPMSM direct control system based on the ADR controller is built and the simulation is carried out, the correctness of the mathematic model and the control algorithm are verified. Finally, the displacement controller is used for a 4 kW prototype. Compared with the traditional PI controller, the floating stability time and the disturbed recovery time of the slice rotor are both decreased, the vibration displacement of rotor in stable state is reduced by 44%.

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.

This paper investigates the problem of stabilisation control of hydroelectric generating units. Firstly, the fully actuated system model of the linear hydraulic turbine is established by using the theory of fully actuated system. Then the control law is designed by using the direct parameterisation method, which can configure the closed-loop poles of the hydraulic turbine system expectation or region and ensure the stable operation of the hydraulic turbine regulating system with a small control gain. Finally, a nonlinear active disturbance rejection control method is proposed for the internal and external disturbances in the control of the fully actuated system. The simulation results demonstrate the effectiveness of the proposed control method.

ABSTRACTIn order to reduce the error and phase delay of the classical extended state observer (ESO) in estimating the system state and disturbance, in this paper, we combine ESO and tracking differentiator (TD) to construct a tracking differential extended state observer (TDESO). The observation error and observation speed of TDESO are also discussed. Then a nonlinear active disturbance rejection control system improved by TDESO for a linear plant is transformed into a Lurie system. Moreover, the circular criterion is used to analyse the absolute stability of the transformed Lurie system. Finally, TDESO is optimised and an improved linear state error feedback (PLSEF) is proposed to improve the rapidity of the system by using simulation and time domain analysis. And a second-order system is used to illustrate the performance of the proposed scheme. The simulation results show that our algorithm is effective.

The piezoelectric smart structures, which can be labeled as the cream of the crop of smart structures without overstatement, are strongly impacted by a large number of uncertainties and disturbances during operation. The present paper reviews active disturbance rejection control (ADRC) technologies developed for application in piezoelectric smart structures, focusing on measurement, analysis, estimation, and attenuation of uncertainties/disturbances in systems. It first explained vast categories of uncertainties/disturbances with their adverse influences. Then, after a brief introduction to the application of basic ADRC in smart structures, a thorough review of recently modified forms of ADRC is analyzed and classified in terms of their improvement objectives and structural characteristics. The universal advantages of ADRC in dealing with uncertainties and its improvement on the particularity of smart structures show its broad application prospects. These improved ADRC methods are reviewed by classifying them as modified ADRC for specific problems, modified ADRC by nonlinear functions, composite control based on ADRC, and ADRC based on other models. In addition, the application of other types of active anti-disturbances technologies in smart structures is reviewed to expand horizons. The main features of this review paper are summarized as follows: (1) it can provide profound understanding and flexible approaches for researchers and practitioners in designing ADRC in the field and (2) light up future directions and unsolved problems.

Linear active disturbance rejection control (ADRC) is known for its simplicity and its performance in disturbance attenuation. Currently, tuning of linear ADRC is via the bandwidth idea proposed in [1]. It is first shown that there are some limitations using only two bandwidths to tune the linear ADRC controllers. In this paper, tuning of linear ADRC with extra model dynamic information is investigated. It is shown that the available model dynamic information used in generalized ADRC (GADRC) can be realized by the observer gain and the controller gain of the conventional linear ADRC, thus extends the applicability of conventional linear ADRC. Simulation results show that with extra model dynamic information incorporated, by tuning the observer gain and controller gain, the performance of a conventional linear ADRC can indeed be improved, especially for non-minimum phase and time-delayed processes.

In this study, a closed-loop, 3-D path-following controller for steerable needles is presented. The control loop is closed via the feedback from FBG-inscribed MCFs embedded within the needle. The nonlinear guidance law, which is a well-known approach for path-following control of aerial vehicles, is used as the basis for the guidance method. To handle needle-tissue interactions, we propose using Active Disturbance Rejection Control (ADRC) because of its robustness within hard-to-model environments. We investigate both linear and nonlinear ADRC, and validate the approach with a Programmable Bevel-tip Steerable Needle (PBN) in both phantom tissue and ex vivo brain, with some of the experiments involving moving targets. The mean, standard deviation, and maximum absolute position errors are observed to be 1.79 mm, 1.04 mm, and 5.84 mm, respectively, for 3-D, 120 mm deep, path-following experiments. MCFs with FBGs are a promising technology for autonomous steerable needle navigation, as demonstrated here on PBNs. FBGs in MCFs can be used to provide effective feedback in path-following controllers for steerable needles.

Nowadays, Dynamic Positioning (DP) is applied to various tasks such as subsea pipeline laying and the requirements for the positioning performance in marine operations are higher and higher. The main objective of this paper is to design a DP controller based on the Active Disturbance Rejection Control (ADRC) to solve the problems of long response time, large overshoot and low positioning accuracy in ship positioning. Firstly, the mathematical models of the ship and environmental disturbances are established. Secondly, the basic principle of ADRC is described. Meanwhile, stability analysis of the control system is introduced. Thirdly, ADRC is improved by the fal function filter and phase prediction method which solve the problem of dither and phase delay in tracking differentiators. Finally, simulations are carried out to verify the performance of the designed ADRC and the improved ADRC. Several simulation results show that the designed ADRC can realize the fixed-point control of the ship, which effectively solves the problems of long response time, overshoot and positioning accuracy, and compared with the traditional ADRC, the improved ADRC can reduce the error of straight track control, which indicates that ADRC can meet the requirements for the positioning performance and has a strong application value.

Integrated electro-mechanical actuators (EMAs) are widely used in cooperative robots. Their control system has to be carefully designed to achieve a desirable performance. The proportional-integral (PI) control and the active disturbance rejection control (ADRC) are the two commonly used controllers. Compared with the PI, the ADRC shows better performance in terms of disturbance rejection, response speed and overshooting suppression. However, the ADRC utilises numerous parameters and the optimisation of these parameters is a challenge. In this study, the influence of the parameters of β 01 , β 02 , β 03 , β 1 , β 2 on the ADRC performance is deeply analysed. Considering the two non-linear factors of permanent magnet synchronous motor and harmonic transmission in the EMA, a simulation model of the EMA was established. An improved swarm optimisation algorithm was employed to optimise the parameters of the ADRC. A second-order ADRC in speed and position modes was designed. The parameters of the ADRC in these modes were adjusted using improved particle swarm optimisation. ADRC was applied to the EMA field-oriented control system instead of cascade PI, and the simulation and experimental results were compared using the cascade PI control method. When the target speed is to 15 rpm, the speed fluctuation range of the ADRC is about ±0.3 rpm, which is smaller than that of the PI controller’s ±0.5 rpm. Compared with the cascade PI control, ADRC affords a faster response speed, greater robustness and stronger disturbance resistance in the steady-state operation process.

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.