Active disturbance rejection control of pressurized water reactor

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.

An anti-windup compensate algorithm for active disturbance rejection mechanism is proposed in this paper. This paradigm extends the traditional anti-windup scheme to the Active Disturbance Rejection Control (ADRC) mechanism, to deal with the input saturation nonlinearity and meanwhile reject the disturbance automatically by using Extended State Observer (ESO) . The output of anti-windup compensator is treated as a part of unknown disturbances and is introduced into the ESO, which can online observe both internal and external disturbances (parameter uncertainties and model mismatches). The controller input is yielded by using a nonlinear feedback combination, and it is used to compensate the integrator windup caused by the saturation nonlinearity element. On the other hand, in order to determine the parameters of the ESO and the anti-windup compensator feedback gain, the ℒ 2 gain is adopted. The effectiveness and the robustness against model and parameter uncertainties of the proposed method is verified by an example of the seeker platform.

In the permanent magnetic synchronous motor (PMSM) system with active disturbance rejection controller (ADRC), the estimation accuracy of extended state observer (ESO) will decrease when the ADRC does not depend on the system model completely. In order to improve the estimation accuracy, this paper proposes an improved ADRC approach by adding a model compensation term. Furthermore, the rotor inertia and viscous friction coefficient in the model compensation term is identified by the model reference adaptive identification (MRAI) algorithm. The load torque is estimated according to the mechanical equation of PMSM system. Then the identification values of rotor inertia, viscous friction coefficient, and load torque make up the compensation term of the ESO. Simulation results indicate that this improved ADRC approach has the better parameter robustness and anti-load-disturbance performance.

In permanent magnetic synchronous motor (PMSM) speed regulation system, the tracking performance and disturbance rejection property of the system are coupled when using conventional active disturbance rejection control (ADRC) controller, which complicates the parameter setting of the controller. A decoupled ADRC controller with position feedback is proposed in this paper. Extended state observer (ESO) is modified to make disturbance rejection property of the system independent of the proportional coefficient, which affects both the tracking performance and the disturbance rejection property in the conventional ADRC control system. Using the modified ESO, the tracking performance and disturbance rejection property can be adjusted by the proportional coefficient and the bandwidth of ESO respectively, thus simplifies the parameter setting of the controller. Extensive experiments are performed on dSPACE DS1103 to verify the validity and practicality of the proposed algorithm.

A generalized active disturbance rejection control (ADRC) approach is proposed for general linear systems. The method follows the idea of the conventional ADRC by using extended state observer (ESO) to estimate the generalized disturbance and using it in the feedback control to attenuate it quickly. It is observed that the idea is appropriate under a matching condition assumption. The generalized ADRC method makes it possible to incorporate any known information of the plant in the control instead of just using the order and the gain information, thus better performance can be achieved, especially for nonminimum-phase processes and unstable processes. Moreover, the generalized ADRC structure is transferred to the well-known two-degree-of-freedom internal-model-control (IMC) structure, thus the stability analysis and parameter tuning can be done in the IMC framework.

Multivariable active disturbance rejection control for compression liquid chiller system

This paper presents an in-depth study of the application of Active Disturbance Rejection Control (ADRC) in the high-precision motion control system of the “WeHoST” 2.5-meter large-aperture telescope using a Programmable Multi-Axis Controller (PMAC). The goal is to enhance the telescope's tracking accuracy and stability under complex environmental conditions. In response to disturbances encountered during the telescope's observation process, an optimized solution based on ADRC was designed and implemented. At first, based on ADRC theory, a controller architecture was constructed, incorporating an Extended State Observer (ESO) and a Nonlinear State Error Feedback (NLSEF) control law. Subsequently, the key parameters of the controller were determined according to the specific parameters and performance requirements of the “WeHoST” telescope to ensure the controller's fast response and stability. The ADRC was then implemented in the PMAC control system, and the telescope's position was monitored in real-time using high-precision encoders. Experimental data show that the positioning accuracy of the “WeHoST” telescope was significantly improved after the introduction of ADRC. In dynamic tracking tests, the tracking error decreased from 0.01817” to 0.01261”, a reduction of approximately 30.59%. The PP(Peak to Peak) value decreased from 0.04585” to 0.03201”, a reduction of approximately 30.18%, significantly enhancing the telescope's tracking accuracy and stability. The study successfully applied ADRC to the main axes of the “WeHoST” telescope. demonstrating its effectiveness in improving the tracking accuracy and stability of the telescope. It provides valuable insights and references for instruments requiring high-precision motion control.

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.

This paper presents a sliding mode synchronization controller (SMSC) based on extended state observer (ESO) for the dual-drive system in gantry-type machine tools (GTMT). This controller achieves not only excellent tracking accuracy but also high synchronization performance. Firstly, a sliding mode synchronization controller is designed for the dual-drive system based on a simplified mode. Then, in order to handle the difficulties associated with the parameter uncertainties, external disturbances and coupling effects of the dual-drive system, a linear extended state observer (LESO) is designed. In this active disturbance rejection control (ADRC) technology, the total disturbances are treated as an extended state of the system and compensated with the disturbance observed value. Moreover, Rigorous theoretical analysis is performed to show that the proposed control method is able to achieve asymptotical tracking and synchronization performance for the dual-drive system in GTMT. Finally, Simulation studies are carried out and the results show that the proposed control strategy performs an improved tracking and synchronization motion control in comparison to the independent axis P-PI control approach.

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.

PurposeThis paper aims to study a disturbance rejection controller to improve the anti-interference capability and the position tracking performance of airborne radar stabilized platform that ensures the stability and clarity of synthetic aperture radar imaging.Design/methodology/approachThis study proposes a disturbance rejection control scheme for an airborne radar stabilized platform based on the active disturbance rejection control (ADRC) inverse estimation algorithm. Exploiting the extended state observer (ESO) characteristic, an inversely ESO is developed to inverse estimate the unmodeled state and extended state of the platform system known as total disturbances, which greatly improves the estimation performance of the disturbance. Then, based on the inverse ESO result, feedback the difference between the output of the tracking differentiator and the inverse ESO result to the nonlinear state error feedback controller (NLSEF) to eliminate the effects of total disturbance and ensure the stability of the airborne radar stabilized platform.FindingsSimulation experiments are adopted to compare the performance of the ADRC inverse estimation algorithm with that of the proportional integral derivative controller which is one of the mostly applied control schemes in platform systems. In addition, classical ADRC is compared as well. The results have shown that the ADRC inverse estimation algorithm has a better disturbance rejection performance when disturbance acts in airborne radar stabilized platform, especially disturbed by continuous airflow under some harsh air conditions.Originality/valueThe originality of this paper is exploiting the ESO characteristic to develop an inverse ESO, which greatly improves the estimation performance of the disturbance. And the ADRC inverse estimation algorithm is applied to ameliorate the anti-interference ability of the airborne radar stabilization platform, especially the ability to suppress continuous interference under complex air conditions.

Uncertain friction is a key factor that influences the accuracy of servo system in CNC machine. In this paper, based on the principle of Active Disturbance Rejection Control (ADRC), a control method is proposed, where both the extended state observer (ESO) and the reduced order extended state observer (RESO) are used to estimate and compensate for the disturbance. The authors prove that both approaches ensure high accuracy in theory, and give the criterion for parameters selection. The authors also prove that ADRC with RESO performs better than that with ESO both in disturbance estimation and tracking error. The simulation results on CNC machine show the effectiveness and feasibility of our control approaches.

Usually, the order of active disturbance rejection control (ADRC) is equal to the relative order of the plant. To improve the control performance, a robust reduced-order method for ADRC is investigated in this paper. Firstly, frequency domain analysis shows that the lower-order extended state observer (ESO) has a smaller disturbance estimation error, so disturbance attenuation capability can be improved by reducing the order of ADRC. However, using only reduced-order ADRC will worsen the robustness of closed-loop systems. Therefore, a robust ADRC method based on a modified noise reduction disturbance observer (MNRDOB) is proposed. The main role of the MNRDOB is to improve the control performance of the closed-loop system by modifying the structure of the controlled object. In addition, the robust stability of the closed-loop control system based on the MNRDOB is discussed. Moreover, some simulations are used to demonstrate the robustness and noise suppression effects of the compound control method reduced-order ADRC with MNRDOB, and the parameter tuning method for the MNRDOB to improve the robustness of the system is given. Finally, some experiments on speed control of a one-dimensional gimbal are performed, and the results show that the proposed method is excellent in overshoot, tracking accuracy, and disturbance attenuation.

This paper develops a nonsingular terminal sliding mode controller (NTSMC) based on extended state observer (ESO) for a buck converter subject to load disturbances and input voltage variations. First, a novel modeling method is developed to transform the matched and mismatched disturbances caused by load resistance and input voltage variations into a uniform matched total disturbance. Second, an ESO is established to estimate the differential of the output voltage and the total disturbance. Third, a NTSMC based on ESO is designed to achieve faster tracking speed and better tracking accuracy around the expected voltage. In addition, the theoretical stability of the proposed controller is analyzed by a Lyapunov stability criterion. Finally, both simulation and experimental results show that the proposed NTSMC-ESO controller with the novel modeling method can attenuate the input voltage variation effectively and has a better load disturbance rejection ability than the reduced-order ESO based sliding mode controller. Abbreviations: ADRC: active disturbance rejection control; ESO: extended state observer; NTSMC: nonsingular terminal sliding mode control; RESO: reduced-order extended state observer; SMC: sliding mode control;

In this technical note, the active disturbance rejection control (ADRC) is generalized to uncertain nonaffine-in-control nonlinear systems. The proposed controller incorporates both an extended state observer (ESO) as well as a dynamic inversion. The ESO is designed to estimate system state and total uncertainty, which includes the uncertain internal dynamics and the external disturbance, and is nonaffine-in-control. Based on the output of the ESO, the dynamic inversion is used to deal with the nonaffine-in-control problem. The proposed control has a multi-time-scale structure, in which the ESO is the fastest time scale; the dynamic inversion is the second; and the considered nonlinear system is the slowest. The practical convergence of the resulting closed-loop system is obtained. An example is presented to illustrate the efficiency of the proposed method.