A new state observer for active disturbance rejection control with measurement noise and output delay using the PDE-backstepping predictor

This paper proposes a new type of extended state observer (ESO) for state observation of nonlinear system with measurement noise. ESO can observe the inner and outer disturbance of uncertain system and it is the foundation of active disturbance-rejection controller, while the measurement noise degrades the performance of the normal ESO. In this paper, fal function feedback structure is used to deal with measurement noise, then ESO is applied, thus their combination can eliminate the effect of measure noise on ESO. Comparing with the method of extending a rank state to ESO and the method of extending the filter equation to ESO, this new method does not need to extend the rank of ESO. So the tracking error increasing problem and the parameter tuning problem which are brought by the rank increase of ESO can be avoided. The simulation results shows that this method can satisfactorily track states for system with measurement noise.

This paper presents an active disturbance rejection adaptive control scheme via full state feedback for motion control of hydraulic servo systems subjected to both parametric uncertainties and uncertain nonlinearities. The proposed controller is derived by effectively integrating adaptive control with extended state observer via backstepping method. The adaptive law is synthesized to handle parametric uncertainties and the remaining uncertainties are estimated by the extended state observer and then compensated in a feedforward way. The unique features of the proposed controller are that not only the matched uncertainties but also unmatched uncertainties are estimated by constructing two extended state observers, and the parameter adaptation law is driven by both tracking errors and state estimation errors. Since the majority of parametric uncertainties can be reduced by the parameter adaptation, the task of the extended state observer is much alleviated. Consequently, high-gain feedback is avoided and improved tracking performance can be expected. The proposed controller theoretically achieves an asymptotic tracking performance in the presence of parametric uncertainties and constant disturbances. In addition, prescribed transient tracking performance and final tracking accuracy can also be guaranteed when existing time-variant uncertain nonlinearities. Comparative experimental results are obtained to verify the high tracking performance nature of the proposed control strategy.

Metal additive manufacturing (AM) has been intensively advanced due to numerous industrial applications such as automobiles, aerospace, consumer electronics, and medical devices. The dynamics of the melt pool via laser sintering for metal AM has been studied by means of the thermodynamic phase change model known as Stefan problem. In this paper, we develop a control design for the laser power to drive the depth of the melt pool to a desired setpoint. The governing equation is described by a partial differential equation (PDE) defined on a time-varying spatial domain which is dependent on the PDE state, and the optical penetration of the laser energy affects the PDE dynamics in domain as well as at surface boundary. The control design is derived via the backstepping method for moving boundary PDEs. The closed loop system is proven to satisfy some conditions to validate the physical model, and its origin is shown to be exponentially stable using Lyapunov method. Numerical simulation illustrates a desired performance of the proposed control law.

In this paper, we consider boundary stabilization for a multi-dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables. The active disturbance rejection control (ADRC) approach is adopted in investigation. An extended state observer is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multi-dimensional system by infinitely many test functions. The disturbance is canceled in the feedback loop together with a collocated stabilizing controller. All subsystems in the closed-loop are shown to be asymptotically stable. In particular, the time varying high gain is first time applied to a system described by the partial differential equation for complete disturbance rejection purpose and the peaking value reduction caused by the constant high gain in literature. The overall picture of the ADRC in dealing with the disturbance for multi-dimensional partial differential equation is presented through this system. The numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction.

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.

Integrated flight-propulsion control (IFPC) in cruise mode is under study for ramjet powered supersonic vehicle. The longitudinal flight control and propulsion control model are built with system disturbance and measurement noise. We propose a decoupling active disturbance rejection control (ADRC) scheme for IFPC design. For velocity control loop, a second-order linear extended state observer (ESO) is used. The altitude control loop includes inner pitch angle control and outer altitude control. Two third-order linear ESOs are applied in the altitude control loop. These ESOs estimate the disturbances on altitude and pitch angle, and their parameters are determined by their bandwidth. Two tracking-differentiators (TD) ensure the transient process of velocity and altitude. The linear combinations of state error feedback are applied. The control design eliminates coupling effects between altitude and velocity and attenuates measurement noise.

The active disturbance rejection control is used to design the control scheme for the vertical inverted pendulum system. Based on the original active disturbance rejection control algorithm, a linear/nonlinear switched extended state observer is proposed for such an unstable system with single input and double output, strong nonlinear and strong coupling. Firstly, the reason of the limited ability of nonlinear extended state observer to estimate large perturbations is analyzed, then a linear extended state observer is proposed to make up for the defects of NLESO, and the feasibility of the proposed linear/nonlinear auto disturbance rejection switching control is verified by numerical simulation.

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;

The direct drive of the permanent magnet linear synchronous motor (PMLSM) requires excellent disturbance rejection capability to achieve precise position control. This article proposes an improved adaptive linear active disturbance rejection control (IALADRC) to improve trajectory tracking and disturbance rejection capability. First, we explain the difference between proportional–integral–derivative (PID) control and LADRC in terms of trajectory tracking and disturbance rejection. Unlike PID, which uses the integral controller to reject disturbances, LADRC uses the extended state observer (ESO) to decouple reference tracking and disturbance rejection. This simplifies the PMLSM control system to a second-order system, which in turn inspired the proposal of the improved LADRC (ILADRC). ILADRC reconstructs the disturbance from the position error using the inverse closed-loop model and injects it into the control output, resulting in better control performance. Due to the complex disturbance existing in the motion process of PMLSM, an improved adaptive ESO (AESO) is proposed to strike a balance between disturbance estimation and noise reduction. The ILADRC and the improved AESO are combined to form the IALADRC. Comparative experiments show that the IALADRC has excellent disturbance rejection capability and significantly improves the position control accuracy of the PMLSM system.

This study addresses the limitations inherent in the traditional Extended State Observer (ESO) within the Active Disturbance Rejection Control (ADRC) framework, specifically targeting issues such as large observation errors, low accuracy, and significant overshoot in estimating the total angular velocity perturbation of torque motors. To overcome these challenges, a Fractional-Order Extended State Observer (FOESO) is proposed. This observer utilizes a novel nonlinear function with improved smoothness and continuity near the origin to enhance observation precision. Furthermore, Repetitive Control (RC), based on the internal model principle, is introduced to mitigate periodic errors and further refine accuracy. By integrating the high-precision estimation of the FOESO with the periodic disturbance rejection of the RC, a composite strategy termed Repetitive Control and Fractional-Order Active Disturbance Rejection Control (RC-FOADRC) is developed. This strategy upgrades the conventional ADRC architecture to achieve stable, high-precision system state observation with minimal error. Experimental analysis targeting the angular velocity of a torque motor validates the effectiveness and feasibility of the proposed RC-FOADRC strategy compared to traditional methods.

Observing the state of totally unknown nonlinear systems is a problem that is addressed in the ADRC framework which relies on Extended State Observers (ESO). A weak point of available ESO designs is that they do not take into account explicitly the statistical knowledge on the measurement noise when this one is available. This paper introduces a generic approach that replaces the ESO observer by a Linear Kalman filter, taking into account the variance of any Gaussian measurement noise. This approach can be applied on a specific class of unknown nonlinear SISO systems. Despite the fact that a linear Kalman filtering is a model-based estimation, the proposed approach makes possible the observation of nonlinear and time-varying systems when no information exists on their structure, time-varying parameters and potential disturbances. The process noise associated to this linear observation approach is also provided.

To provide high output force and to reduce the installation space, the electro-hydrostatic actuator (EHA) usually adopts asymmetric cylinder. However, comprehensive effects produced by its asymmetric flow, parameter uncertainties and unknown disturbance make it difficult to achieve high-accuracy position control. This paper proposed an integral sliding mode backstepping control (ISMBC) based on extended state observer for the asymmetric EHA. Firstly, the principle of the EHA was analyzed and an EHA model was built. Furthermore, the state space equation of the EHA was established based on flow distribution analysis. Two extended state observers (ESO) were designed to achieve real-time estimation of the unmeasured system states, unmatched and matched disturbances. The backstepping method was used to compensate the matched and unmatched disturbance, and an integrated sliding mode controller was developed to eliminate the static error and to improve the response ability. Theoretical analysis indicates that the controller can guarantee the desired tracking performance for the actuator under time-varying unmatched disturbances, and can make the tracking error asymptotically converge to zero under constant matched disturbances. Finally, simulations were performed with the designed controller, backstepping controller and proportional–integral–derivative (PID) controller, respectively. Thereafter, detailed comparisons of the control performances were provided. The results show that the proposed controller can achieve better position tracking and stronger robustness in parameter changing compared with the backstepping controller and PID controller.

A practical data-based third-order linear extended state observer (ESO) filter is proposed based on state estimated by ESO. The filter is simple to use with only one parameter to tune. Then its transfer function, parameters tuning method and discrete simulation realization are given respectively. The proposed ESO filter is applied to the tracking of sine signal and square signal, the filter of signal with white Gaussian noise, and the filter of the width data for hot strip rolling mill in real time with measurement noise. Simulation results show the proposed ESO filter is practical without signal model, noise model and statistical characteristic of the measurement noise. Only according to present moment of the measurement data, it could meet the requirement with appropriate parameter.

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.

Robust internal model control based on a novel generalized extended state observer and its application on a two-inertia system