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This article presents a new method that employs the active disturbance rejection control (ADRC) paradigm to handle the control problem for a class of nonlinear systems with unknown disturbances and measurement noise. An improved extended state observer (ESO) is devised to separate disturbance estimation from state reconstruction and a new parameter is used to adjust disturbance-rejection performance independently. This increases the flexibility of system design and makes the gain of the improved ESO (IESO) small compared to that of a conventional ESO in the ADRC. A low-pass filter is added to the IESO. This changes the slope of the magnitude curve of the Bode diagram from $-20$ dB/dec to $-40$ dB/dec at high frequencies for measurement noise, which improves the noise-suppression performance. Comparison with a conventional ESO reveals the superiority of the IESO in disturbance rejection and noise suppression. The presented method is validated by simulation and experimental results. [ABSTRACT FROM AUTHOR]

In this article, an active disturbance rejection controller (ADRC) based on deep reinforcement learning (DRL) algorithm is proposed to be used in the flux weakening control (FWC) system of motors for more electric aircraft. Artificial intelligence algorithm is introduced into ADRC motor control system for the first time, and DRL is designed as the automatic tuning for the parameters optimization of ADRC. The interface module scheme is proposed to realize the conversion between the relevant quantities of the control system and the DRL Agent according to the characteristics of ADRC. The parameters are optimized in the form of parameter modification, and a new DRL-ADRC control framework is proposed which can avoid being trapped into local optimum. The ADRC model designed for the speed loop of FWC system are first introduced. An interface module is subsequently built to enable DRL to interact with the FWC system automatically. DRL agent is trained to optimize the internal parameters of ADRC, which have the characteristics of large quantities, weak sensitivity and strong coupling. Deep deterministic policy gradient is used as the strategy of DRL, which can quickly determine the descent gradient and converge the multiobjective optimization problem. Simulation and comparison with classical heuristic algorithms and disturbance rejection methods are carried out to show the superiority of DRL. The feasibility and effectiveness of the proposed control method are verified by experiments on an aerospace motor for MEA. [ABSTRACT FROM AUTHOR]

High-gain nature of extended state observer (ESO), which forms an integral part of active disturbance rejection control (ADRC) technique, results in the following limitations: 1) Sensitivity to high-frequency measurement noise which limits closed-loop performance in practical applications. 2) Escalation of observer gains up to a power $\boldsymbol{n+1}$ of observer bandwidth, which complicates numerical implementation when system order $(\boldsymbol{n})$ or observer bandwidth is large. To overcome these limitations, a low-power higher order ESO is proposed in the present work for practical application of ADRC scheme in noisy environment. Moreover, a recently proposed cascade ESO (CESO), designed for noise suppression, is analyzed in the frequency-domain to reveal an underlying similarity with higher-order ESO, which is not reported in literature. Presented analysis justifies the performance improvement obtained over conventional ESO and provides a guideline for selecting the number of cascade levels based on the expected nature of disturbance. Case study performed on a dc–dc boost converter illustrates the practical advantages of proposed scheme over CESO in terms of improved immunity to high-frequency measurement noise, precise regulation in presence of time-varying disturbance, low observer gains that facilitate numerical implementation, and ease of tuning due to a single observer parameter. [ABSTRACT FROM AUTHOR]

As the higher order or generalized extended state observer (ESO), generalized proportional-integral (GPI) observer (GPIO) haves been proposed to enhance the active disturbance rejection (ADR) control (ADRC) system's disturbance rejection ability. However, different ADR controllers can be deduced based on the same order GPIO, resulting in different dynamic performances. In this article, ten different ADR controllers based on the fourth order GPIO are present. In order to reveal the relationship between these ADR controllers and the conventional ADR controllers based on the third order ESO, six different third-order-ESO-based ADR controllers are present and compared with the fourth-order-ESO-based ADR controllers. To ease the comparison between different ADRC systems, a common expression is built for different ADR controllers. A novel frequency-domain analysis method is also introduced to reveal how the observer and feedback control law affects the closed-loop control system's dynamic performance. The effectiveness of the proposed method is verified on the test bench based on dSPACE DS1103. [ABSTRACT FROM AUTHOR]

Active disturbance rejection control (ADRC) shows great potential in mitigating various uncertainties of both motion and process control. However, the controller tuning is generally time-consuming, and the resulting performance highly depends on the individual experience. This brief aims to develop a standard robust tuning rule for a time-delayed ADRC structure based on a class of time-delay systems represented by a second-order plus time delay (SOPTD) model. The bandwidth parameters of the controller and the observer are, respectively, scaled in terms of SOPTD parameters. The resulting dimensionless parameters enable exhaustive evaluation of the robustness. Compared to the traditional metrics, it reveals that delay margin is the dominant robustness index for the controller tuning. A dominated form of the robust tuning rule is recommended, and the stability condition of a closed-loop system is given. Simulations and experiments are conducted on a factual electrostatic precipitator in the coal-fired power plant to validate the efficacy of the proposed tuning rule. [ABSTRACT FROM AUTHOR]

Surge is one of the main factors affecting the stability of the centrifugal compressor. This article investigates surge disturbance suppression of active magnetic bearing (AMB)-rotor systems in magnetically suspension centrifugal compressors. An active disturbance control method is adopted to make the rotor stably levitate under surge disturbance. First, the dynamic model of the magnetic bearing rotor is established and simplified into a single-channel model. Second, a third-order linear extended state observer (LESO) and a linear active disturbance rejection controller are designed. The performance analysis of the controller shows that the estimation error accumulation of the observer is bounded and the estimation errors decrease with the increase of the observer bandwidth. Furthermore, the variable differential parameter added in the differential link of the controller can flexibly adjust the system damping. A method of tuning parameters for linear active disturbance rejection control (LADRC) is proposed to suppress surge disturbance while satisfying the stability of the system. Finally, the results of the experiment demonstrate that the proposed scheme is effective in suppressing the large-scale vibration effect of the surge disturbance on the rotor, and the magnetically suspended centrifugal compressor (MSCC) can run stably with low amplitude under the modified surge and mild surge. [ABSTRACT FROM AUTHOR]

This article presents an optimal direct torque control (DTC) strategy with variable flux for a switched reluctance motor using the improved linear active disturbance rejection control (LADRC) plus the hybrid optimization algorithm (HOA). First, the constant flux amplitude is substituted by the variable flux DTC (VF-DTC) to reduce the torque ripple. Then, the LADRC with the improved extended state observer applied in speed controller is utilized instead of the conventional PI control to improve the speed of the observer, antidisturbance ability, and robustness. Moreover, the HOA is employed to search for the optimal control parameters and acquire satisfactory dynamic performances. Finally, the optimal VF-DTC system is implemented on a 12/8 SRM. Simulation and experimental results are carried out to compare the performances of the conventional DTC, the VF-DTC with LADRC, the VF-DTC with PI using HOA, and the proposed optimal VF-DTC using HOA. The results show that the proposed control method has a faster speed response, superior antidisturbance ability, and lower torque ripples. [ABSTRACT FROM AUTHOR]

Hybrid energy storage microgrid represents the future direction of distributed energy development. However, under the influence of interference, the dynamic performance of the output side interface will be severely deteriorated. In this article, a linear active disturbance rejection controller with reference differential feedforward and cascade linear extended state observer (ADRC-RDCO) is proposed to deal with unknown modeling error and the unknown dynamics of the interface converter. In this strategy, a cascaded linear extended state observer is introduced to cope with the steady-state offset in the disturbance estimation error, so as to implement the accurate reconstruction of the disturbance state. Furthermore, a control law with RDF is applied to offset a portion of the tracking error of the given signal to achieve the purpose of optimizing the tracking accuracy of the given signal. Then, the tracking performance and stability of ADRC-RDCO are analyzed theoretically. On the basis of discussing the relationship between dynamic characteristics and control parameters, a parameter configuration method is proposed. Finally, the proposed ADRC-RDCO technology was verified on the 40 kW microgrid platform. [ABSTRACT FROM AUTHOR]

In this article, we apply the active disturbance rejection control (ADRC) to the output tracking of a class of lower triangular nonlinear systems subject to mismatched bounded stochastic disturbances of unknown statistic characteristics and nonvanishing at the origin. A major obstacle is that the paths of the stochastic disturbances are nowhere differentiable almost surely which causes that the stochastic disturbances cannot be refined into the control input channel by the usual way of state transformation. To overcome this obstacle, a set of second-order extended state observers is first designed to estimate, in real time, the disturbance in each channel, and then a backstepping ADRC based on feedforward compensation and a constructive backstepping procedure is developed, guaranteeing that the closed-loop output tracks a time-varying reference signal in practically mean square and the closed-loop states are practically bounded in probability first defined in this article. Finally, some numerical simulations are presented to validate the effectiveness of the proposed backstepping ADRC approach. [ABSTRACT FROM AUTHOR]

Active disturbance rejection control using extended state observer (ESO) is less dependent on the knowledge of the system. It has proved to be an excellent scheme for speed control of electrical drives. However, for time-varying disturbance, the observation precision of conventional ESO is undesired, which limits the speed tracking accuracy. Accordingly, this article proposes an enhanced speed controller for electrical drives based on adaptive switching high-order ESO (ASHESO). First, the critical parameters affecting the steady-state performance of ASHESO are determined according to frequency analytical results. Then, optimized observer gain is obtained by modifying a part of pole locations, which weakens the influence of noise on estimated state. Finally, an adaptive switching gain mechanism is proposed according to the closed-loop tracking error and the swiftness of dynamic response is maintained. The proposed speed controller has achieved high estimation accuracy for disturbance and strong immunity to measurement noise. The feasibility and effectiveness of the strategy is verified on a laboratory permanent magnet synchronous motor (PMSM) drive system. [ABSTRACT FROM AUTHOR]

This article proposes a two-degree-of-freedom fractional-order proportional derivative (FOPD) controller with a general extended state observer (GESO) to achieve both optimal set-speed tracking and disturbance rejection performance for a typical permanent magnet synchronous motor servo system. The GESO simplifies the control plant, estimates and actively rejects total disturbances. The FOPD controller achieves fast speed tracking with almost no overshoot. Furthermore, it is verified that the control system with the proposed FOPD-GESO controller design meets the separation principle through mathematical derivation and simulation illustration. It shows that the proposed controller breaks the inherent tradeoff on tracking performance and disturbance robustness of the typical traditional proportional–integral–derivative (PID) control. Meanwhile, a systematic scheme for designing the FOPD-GESO controller to satisfy both frequency-domain and time-domain specifications is proposed in this article. Simulation illustration and experimental validation are performed to demonstrate that the proposed FOPD-GESO controller is superior to the typical integer-order PID controller, integer-order active disturbance rejection control with a typical extended state observer, and fractional-order PID controller in terms of speed tracking, antiload disturbance, and robustness to internal uncertainties. [ABSTRACT FROM AUTHOR]

In the permanent magnet synchronous motor speed regulation system, the dynamic performance of the conventional active disturbance rejection control (ADRC) system will be deteriorated by using a low bandwidth speed filter. To solve this problem, two ADRC controllers considering the speed measurement noise are proposed in this article. One proposed ADRC system is based on the extended state observer (ESO), the other proposed ADRC system is based on phase-locking loop observer (PLLO). In the proposed two ADRC systems, an integrator is employed as the speed filter so that the measured position can be directly used for observing the speed and disturbance without speed calculation. Meanwhile, by using an integrator as the speed filter, the dynamic performance of the proposed ESO-based ADRC system is not affected since it is independent of the speed filter, and the proposed PLLO-based ADRC system has a better rejection ability for the low-frequency disturbance. Experimental results validate the proposed methods. [ABSTRACT FROM AUTHOR]

In this article, a global finite-time active disturbance rejection control (ADRC) scheme is proposed for tracking control of redundant parallel manipulators with unknown bounded uncertainties. This approach combines an ADRC and a global finite-time control for high accuracy trajectory tracking control. Based on the nonsingular fast terminal sliding mode control, the proposed approach can remove the condition in the original ADRC that the derivative of the uncertainties is required to be bounded. The extended state observer is employed to handle the real-time estimation of the total uncertainty. It can be found that the proposed scheme not only can converge fast to the semi-global finite-time stable equilibrium but also can have superior tracking control performance. In summary, compared to existing approaches, the proposed scheme can have several advantages, such as uncertainty rejection, easy implementation, robustness, chattering-free, high precision, and no need for prior knowledge of bounded uncertainties. The simulation results validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article is concerned with the fixed-time active disturbance rejection control approach for nonlinear systems subject to uncertainties and disturbances. First, a new type of extended state observer (ESO) which can attain fixed-time convergence is established to estimate the states and the total disturbance. Then a fixed-time controller based on the above ESO is developed to achieve high precision control performance. Finally, the proposed method is utilized for the wheeled mobile robot where the experiment validates the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

A robust optimized active disturbance rejection control (ADRC) based grid voltage sensorless current controller is developed for an LCL-filtered grid-connected inverter (GCI) via a predictive control approach under various sources of disturbance, including the model uncertainties, the LCL inherent resonance phenomenon, and nonideal grid environment. Aiming to improve the sinusoidal reference tracking performance as well as to reject lumped sinusoidal disturbances in the control practice, a resonant extended state observer is integrated into the ADRC structure, which guarantees a rigorous stable operation of inverter for bounded filter parameter uncertainties and adverse grid voltage conditions. The grid frequency adaptability is thoroughly considered in the controller design process and synchronization technique, offering an extra capability for GCI to operate under different grid voltage frequency levels or even the frequency deviation caused by grid fault events. Robustness against parameter uncertainty and system stability is analyzed through the discrete-time frequency analysis and pole-zero map approaches. The simulation and hardware experiments are conducted for GCI with LCL filter parameters designed for two typical regions (i.e., the resonance frequency is less and greater than one-sixth of switching frequency) to validate the theoretical analysis and the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

Multiactive bridge (MAB) converter is a promising solution for integrating multiple renewable sources, storage, and loads for various applications. However, the MAB converter is challenging to control due to the inherent coupling between the port power flows. To that end, this article presents a decoupling control strategy based on linear active disturbance rejection control. The proposed controller observes the coupling disturbance using a linear extended state observer and subsequently rejects the observed disturbance resulting in dynamic decoupling. Experiments conducted on a 2-kW 100-kHz Si-C-based four-port MAB converter laboratory prototype illustrate the decoupling performance of the proposed control strategy. Compared to the traditional decoupling control strategy, the proposed approach is decentralized and model independent, only requiring information regarding its order. [ABSTRACT FROM AUTHOR]

Formation tracking is a critical issue in the consensus control of multiagent systems (MASs). This article presents a time-varying formation tracking strategy with predefined performance for a class of uncertain nonaffine nonlinear MASs connected through a directed topology. The nonaffine nonlinear MASs are transformed into affine nonlinear ones with uncertainties via the idea of active disturbance rejection control (ADRC). The uncertainties in the MASs are approximated and compensated by extended state observers (ESOs) in real time. Tracking differentiators (TDs) are introduced to reduce the complexity in the computation of the derivatives of virtual control variables. Employing funnel variables, our strategy guarantees the formation of tracking errors to stay within the desired ranges, thus improving the control performance of the closed-loop system. It is proved that all signals of the system are bounded and the formation errors can be made arbitrarily small within a residue around the origin by appropriate choices of control parameters. Case studies are carried out to demonstrate the effectiveness of the proposed control strategy. Note to Practitioners—The motivation of this article is to present a time-varying formation tracking strategy with predefined performance for a class of uncertain nonaffine nonlinear MASs within a directed topology. To simplify the process of solving the formation tracking problem, the presented strategy incorporates ADRC with the backstepping technique. Employing ADRC, our strategy approximates the uncertainties of the MAS followers via ESOs. The uncertainties are then compensated through real-time estimations of extended states. Moreover, with ADRC, TDs are used to estimate the derivatives of complex nonlinear functions, eliminating the requirement of the operations of higher order derivatives of virtual control variables. It provides a feasible strategy for industrial applications. [ABSTRACT FROM AUTHOR]

A novel active disturbance rejection based repetitive learning control scheme, including three channels, namely, feedforward, feedback, and disturbance rejection channels, is investigated. The goal of this work is to achieve a high-quality output voltage and robustness to disturbances and uncertainties in the inverter system. The mathematics model of the inverter is replaced by a chain of two integrators to avoid model identification and time-varying parameter estimation when designing the controller. The ignored system dynamics, the uncertainties, and the nonrepetitive factors caused by nonrepetitive disturbances are all defined as part of the total disturbance to be estimated and compensated for, which decreases the controller sensitivity for the system parameters and operating environment. The stability conditions of the control system scheme along the periods are analyzed, and the mitigation of different frequency-band disturbances using the combination control scheme is demonstrated on the frequency spectrum. Finally, the algorithm is validated on a hardware platform, and the tolerability of varying parameters is tested. [ABSTRACT FROM AUTHOR]

In the context of disturbance-estimation (DE)-based control, it is reported that including desired dynamics into the nominal model yields a simple and compact control law that is easier to implement. The resulting control structure unifies the nominal feedback controller and feed-forward disturbance compensator to formulate an overall feed-forward disturbance compensation problem. Based on this, two popular DE-based techniques, namely active disturbance rejection control (ADRC) and uncertainty and disturbance estimator (UDE)-based control, are restructured into a unified form. By reformulating the controllers in the frequency domain, it is shown that the two structures are equivalent provided the UDE filter is selected based on the observer designed for ADRC. For an easier understanding of practitioners who are familiar with the conventional control structures, the designed controllers are reinterpreted in the framework of two-degree-of-freedom (2DoF) internal model control and 2DoF proportional-integral-derivative (PID) controller to show the equivalence among them. Tuning rules for PID controllers in terms of unified ADRC parameters are also presented to aid practical implementation in industry. Performance of the unified control scheme is evaluated on a non-minimum phase dc–dc boost converter that is operating under line and load disturbances using simulation and experimental study. [ABSTRACT FROM AUTHOR]

Parkinson’s disease (PD) is one of the most common diseases that its main complications are hand and head tremors and inflexibility of muscles. One of the prevalent treatments that employ for reducing the symptoms of that is deep brain stimulation (DBS). In practice, a sensor is located in the patient’s finger for detecting and evaluating the tremor values in PD. Using an open-loop control structure for stimulating one area of basal ganglia (BG) is the common approach, but in this work, two areas of BG, named subthalamic nucleus (STN) and globus pallidus internal (GPi) are stimulated in a closed-loop manner separately for i) reducing the intensity of electric field and consequently disappearing the side effects of DBS ii) decreasing hand tremor. In particular, an adaptive Active Disturbance Rejection Control (ADRC) based on a deep deterministic policy gradient (DDPG) and a conventional feedback controller are presented for simultaneous stimulating STN and GPi, respectively. In this way, the control coefficients of the ADRC are considered as the control objective parameters that are designed by the actor and critic neural networks (NNs) of DDPG. The suggested scheme is applied to a BG system model which is frequently studied in the literature. The comprehensive simulation studies are accomplished to confirm the supremacy of the ADRC based DDPG scheme over the state-of-the-art strategies. Moreover, hardware-in-the-loop (HiL) simulations are performed to verify the efficiency of the proposed scheme from real-time perspective. [ABSTRACT FROM AUTHOR]

In some servo applications, restricted by the measurement noise and the stiffness of the mechanical system, the bandwidth of the disturbance observer cannot be high enough to realize a good robust control to parameters uncertainties, it is essential to identify the mechanical parameters. In the existing mechanical parameter identification methods, the viscous and Coulomb friction torque coefficients are usually identified using two different constant speeds, and the moment of inertia can be identified with various methods. However, no one method can identify these three parameters at the same time using only one speed. The contribution of this article is to propose a method that can identify the three mechanical parameters simultaneously using only one speed. A low-pass filter is used to suppress the measurement noise in the speed feedback, thus parameters are identified with high precision. A unidirectional sine-wave speed is used to decouple the viscous friction torque and the Coulomb friction torque, two speeds with different amplitudes and the detection of the speed amplitude are no more required. Adaptive extended state observer (ESO) is designed based on the Lyapunov's stability theory, can be easily changed to the normal ESO used in active disturbance rejection control. The proposed method is easy to understand and implement. The effectiveness of the method is verified by both the simulation and experimental results. [ABSTRACT FROM AUTHOR]

An observer-based containment control issue is addressed for a class of uncertain nonlinear multiagent systems with a directed topology via the active disturbance rejection control and backstepping techniques. A kind of nonlinear extended state observers (ESOs) based on fractional power functions is developed, and the estimations of extended states are utilized to compensate uncertain dynamics in real time. Compared with linear ESOs, the advantages of the ESOs in this paper lie in peaking reduction and better tolerance of measurement noise for the closed-loop system. Moreover, tracking differentiators are employed to avoid the explosion of complexity caused by repeated differentiations of nonlinear functions. It is proven that the containment errors of the followers converge to small neighborhoods of the origin and they are adjustable by suitable choice of parameters. Finally, two simulation examples, both practical and numerical ones, are shown to demonstrate the effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

An energy balance active disturbance rejection control (EB-ADRC) is proposed in this letter, which advances fast dynamics and enlarged stability region, suitable for the stability enhancement of converters cascaded with constant power loads. A unified converter energy control is employed to simplify the converter dynamic model to a first order, which is easy for dynamic design. Takagi-Sugeno (TS) fuzzy models are constructed and linear matrix inequalities (LMI) solving method is utilized to not only evaluate the upper limit of controller gain, but also make stability comparisons between EB-ADRC and classical proportional integral (PI) control. In the same main circuit inductor and capacitor values and approximate dynamic response precondition, the results illustrate that EB-ADRC enables a larger stability region. Experimental results are provided to validate the effectiveness and superiority of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The conversion and utilization of renewable energy generations often require grid-tied inverters. When an LCL filter is applied to attenuate the high switching frequency harmonics, it is complex to design a controller with proper parameters due to the characteristics of the LCL filter and system uncertainties. In this article, with LCCL filter, the order of the inverter system is degraded from third order to first order, and an active disturbance rejection control-based current control strategy for LCCL-type grid-tied inverters is proposed. The proposed strategy is able to treat the unknown dynamics and the external disturbance of the inverter system as overall disturbance through a single structure, and the closed-loop system is regulated by an improved control law with reference differential feedforward. Moreover, with parameter uncertainties considered, the robustness of the proposed strategy is studied through an internal model control structure. A 2-kW experimental prototype has been tested to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

We explore the equivalence among flat filters, dirty derivative-based proportional integral derivative (PID) controllers, active disturbance rejection control, and integral reconstructor-based sliding mode control, in the context of SISO second-order, perturbed, pure integration systems. This is the prevailing paradigmatic class of differentially flat systems or feedback linearizable systems. The equivalence is valid beyond the second-order pure integration systems. However, PID controllers of such plants do not make much sense without imposing assumptions that will move the considerations out of the pure integration systems case. The equivalence among the rest of the controllers is valid for any finite order pure integration system. [ABSTRACT FROM AUTHOR]

This paper aims to propose a quantitative tuning method for active disturbance rejection control (ADRC) that controls the K/(Ts + 1)n-type high-order processes. An asymptote in the Nyquist curve has been observed for the first time and its mathematical expression has been deduced. An asymptote condition is provided in order to derive a parameter tuning rule under the sensitivity constraint. Although this proposed tuning rule is originally designed for a certain type of high-order processes, it can be extended to other types processes that can be approximated into the form of K/(Ts + 1)n. Comparisons with different PID control strategies have been conducted for a range of cases to demonstrate the efficiency of the proposed tuning method. Finally, the effectiveness of the proposed tuning rule is experimentally verified on water tank system that exhibits high-order dynamics. Field tests on the superheater steam temperature control of a circulating fluidized bed power plant further demonstrate its potential for applications in complex industrial processes. [ABSTRACT FROM AUTHOR]

The problem of event-triggered sampled-data control for networked systems is considered in this article. A nonlinear continuous-time system with uncertainty and disturbance is introduced, for which an event-triggered control problem based on an active disturbance rejection control approach is formulated. We first present the framework of the closed-loop system in which the control signal is transmitted at each event instant while the output measurements are transmitted in real time. Based on this framework, an easy-to-implement event-triggering strategy that relies on the state observation generated by an extended state observer is proposed, so that the asymptotic boundedness of the observation error is obtained and the stability of the closed-loop system can be guaranteed. Then, with some mild restrictions on initial values of the observer and plant, the boundedness of observation error can be maintained at any time. Finally, we extend the obtained results to a more general case in which the transmission of the measurements and control inputs are determined by separate event-triggering strategies. The performance of the proposed method is verified through experimental results on a direct current motor loading platform. [ABSTRACT FROM AUTHOR]

In this paper, an active disturbance rejection control scheme with a nonlinear sampled-data extended state observer (NSESO) is proposed for a pneumatic muscle actuator (PMA) system. The phenomenon of the actuator saturation is taken into account in the design procedure. The NSESO is utilized to estimate the so-called total disturbance that reflects the aggregated impacts of unmodeled nonlinearities and disturbances. Then, an NSESO-based composite control strategy is designed, where the estimates provided by the designed NSESO serve as the compensation to eliminate the total disturbance. Finally, a number of practical experiments on the PMA systems are conducted to verify the validity and applicability of the proposed design method. [ABSTRACT FROM AUTHOR]

An active disturbance rejection control (ADRC) controller using phase-locking loop observer (PLLO) is proposed in this paper to improve the disturbance rejection property of speed control system. First, to simplify the comparison with other controllers, a universal speed controller design method based on disturbance estimation is employed, and a unified expression for different controllers is presented. Then, several common speed controllers are compared with each other, and two PLLO-based ADRC controllers are presented. After that, considering the variations of load inertia, robustness of the proposed ADRC system to inertia variation is analyzed. Finally, to improve the tracking performance for sinusoidal speed reference, an adaptive speed control system using identified inertia is presented. Simulation and experimental results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, important issues that could come up in practice of active disturbance rejection control (ADRC) due to a common assumption and some inevitable practical restrictions are investigated. The main idea behind ADRC is modeling effects of both internal uncertainties and external disturbances as an extra state called the total disturbance which is timely estimated. In the majority of recent works, it is assumed that time derivative of total disturbance is bounded. First we prove that, beside the system characteristics, the validity of this assumption strongly depends on the tuning parameters, even in the case of simple classes of linear second-order systems. Thus, one should be careful upon making this common assumption independent from the tuning parameters. Then, the effect of imperfections imposed by sensor dynamics, measurement noise, actuator saturation, and discrete implementation are thoroughly studied. It is shown that these imperfections could crucially affect the control performance. Furthermore, a tuning method, with a higher degree of freedom, is proposed involving the stability considerations in its design procedure. The given theoretical analyses are supported via both simulation and experimental results. The discussed issues are recommended to be carefully considered by experts and practitioners of ADRC. [ABSTRACT FROM AUTHOR]

In order to improve the tracking accuracy of the fine tracking system of free-space optical communications, a proposed active disturbance rejection control (ADRC) with iterative learning control (ILC) strategy is designed to regulate the fast steering mirror (FSM) system. First, based on the open-loop frequency response results of the system, we can approximately confirm the system transfer function and prepare for the design of the controller. Then, an improved ADRC that using sliding mode control instead of the traditional nonlinear state error feedback method is proposed to attenuate the influence of the unknown and unmolded parts. In addition, the ILC method is used to compensate the hysteresis of piezoelectric actuators and improve the overall system performance. The experimental results indicate that the tracking accuracy of the system is 1 μrad at 1k sampling frequency. In addition, the recommended method shows the better disturbance suppression performance than traditional ADRC in simulation and experimental investigations. This method has a very high application value in the field of visual axis stability, adaptive optics, and other fields. [ABSTRACT FROM AUTHOR]

In this brief, attitude control is investigated for a quadrotor under gust wind via a dual closed-loop control framework. In the dual closed-loop framework, active disturbance rejection control and proportional–derivative control are used in the inner and outer loops, respectively. The perturbations of gust wind are considered as dynamic disturbances, which are estimated by an extended state observer in the inner loop. Both convergence and stabilization are given for the extended state observer and the closed-loop system, respectively. Experimental results are given to show the effectiveness of the proposed method for quadrotors. [ABSTRACT FROM AUTHOR]

Active disturbance rejection control (ADRC) as a standalone motion solution has been made available in recent years on various industrial platforms. The idea of ADRC, however, can be integrated with the existing control technologies seamlessly, as shown in this paper. A modularized ADRC design is proposed in this particular work for set-point tracking task in motion control, such that better uncertainty rejection can be obtained without any change in the existing proportional-derivative control with a linear observer. It is proven that a certain extended state of the observer, i.e., the integration of the observer error, can serve as an estimation for the “total disturbance” in low-frequency range by only tuning the augmented gain. This enables the estimation and cancellation of the “total disturbance” to be incorporated into the existing control loop. Also, a comparison between the methods with and without such “module” is discussed. The proposed ADRC is implemented and validated experimentally using a laboratory manipulator, where the desired set-point tracking performance in position control is achieved under unknown mass variations and sudden external disturbances. [ABSTRACT FROM AUTHOR]

Superconducting cavities are widely used in linear accelerator facilities all over the world. It is challenging for the low level RF (LLRF) system to stabilize the RF field inside the cavities working in pulsed mode with heavy beam loading and strong Lorenz force detuning. Feedback loops are implemented in LLRF system which should have fast responses to the disturbances on cavities. To enhance the feedback performance, active compensation of Lorenz force detuning with Piezo tuners and the compensation of beam loading with feed forward control are strongly needed. They all require the knowledge of cavity parameters, such as the quality factor, time varying detuning and the amplitude and phase of the beam. A disturbance observer based on the active disturbance rejection control (ADRC) was designed for superconducting cavities counting the Lorenz force detuning and beam loading as disturbances to the cavities. The ADRC disturbance observer can be integrated into LLRF feedback loops to speed up the responses to disturbances and the outputs of the observer are interpreted furtherly to identify the cavity parameters. This paper presents the algorithm and architecture of the ADRC disturbance observer, the simulation of the LLRF feedback loop with disturbance rejection and the cavity parameter identification applied on the archived data of superconducting cavities in operation. [ABSTRACT FROM AUTHOR]

Active disturbance rejection control (ADRC) was originally given in a nonlinear gain structure to better accommodate the dynamic uncertainties and disturbances. However, the resulting complexity in a theoretical analysis and in the parameter tuning inhibits the applications of an ADRC. ADRC was linearized and parameterized for a practical convenience. Since linear ADRC (LADRC) and nonlinear ADRC (NLADRC) each has its own advantages and disadvantages, choosing between LADRC and NLADRC is rather difficult. As a matter of fact, there is a lack of quantitative analysis and comparison between LADRC and NLADRC. This paper first gives an easy solution in the parameter tuning of the nonlinear extended state observer, followed by a quantitative analysis and comparison study on LADRC and NLADRC; then, an LADRC/NLADRC switching control (SADRC) scheme is proposed and its stability is analyzed; finally, the SADRC scheme is verified by experiment using the ball–beam platform. The proposed SADRC takes the advantage of the additional performance improvement associated with the NLADRC, but make it easier to use. [ABSTRACT FROM AUTHOR]

Finding simple and reliable mathematical models for describing a complex process is a difficult task. In deriving a reasonably model, we frequently find necessary to ignore certain properties of the system. Active Disturbance Rejection Control (ADRC) is a method that does not require a detailed mathematical description of the system, it supposes that the unmodeled elements of the dynamics and external disturbances can be estimated trough an Extended State Observer (ESO), and then rejected online by adding the estimate in the control law. In this work, the input-output behavior of a coupled tanks system is approximated by a second order uncertain model. This allows employing the Linear Quadratic Regulator (LQR) approach to design a Proportional-Integral-Derivative (PID) controller into the ADRC framework. It is proposed a criterion for selecting the weighting matrices in LQR in order to have a desired percentage overshoot and settling time of the closed loop system response. [ABSTRACT FROM PUBLISHER]

Practical applications of controllers often impose further requirements on the implementation beyond the actual control performance, such as the ability to switch between manual and automatic control or between different control laws or controller parameter settings, known as bumpless transfer. Another common requirement is to limit the control signal in magnitude and/or rate. This paper examines and extends several discrete-time variants of active disturbance rejection control (ADRC), which is increasingly being applied especially in the field of power electronics and drives, in this regard. Detailed guidelines for practical ADRC implementations with these abilities are presented, and all features are being demonstrated with the help of simulation examples. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel class of adaptive extended state observers (AESOs) that significantly expand the applications of extended state observers (ESOs) to nonlinear disturbed systems. An AESO is designed as a linear time-varying form that, as a result, combines both the advantages of theoretical completeness in a conventional linear ESO (LESO) and good practical performance in a conventional nonlinear ESO (NESO). To tune the time-varying observer gains, AESO error dynamics is first transformed into a canonical (phase-variable) form. Then, time-varying PD-eigenvalues are assigned for the canonical system based on differential algebraic spectral theory. Theorems for stability and estimate error bounds of the AESO are given in the presence of unknown disturbances. These theorems also offer some important guidelines for assigning the PD-eigenvalues. To demonstrate the effectiveness of this new observer, two representative applications, including a numerical single-input–single-output example and a practical multiple-input–multiple-output hypersonic vehicle application, are exemplified, and comparison simulations are conducted among AESO, LESO, and NESO. Future work is pointed out in the end. [ABSTRACT FROM PUBLISHER]

This paper describes the adaptive control design to solve the trajectory tracking problem of a Delta robot with uncertain dynamical model. This robot is a fully actuated, parallel closed-chain device. The output-based adaptive control was designed within the active disturbance rejection framework. An adaptive nonparametric representation for the uncertain section of the robot model was obtained using an adaptive least mean squares procedure. The adaptive algorithm was designed without considering the velocity measurements of the robot joints. Therefore, a simultaneous observer–identifier scheme was the core of the control design. A set of experimental tests were developed to prove the performance of the algorithm presented in this paper. Some reference trajectories were proposed which were successfully tracked by the robot. In all the experiments, the adaptive scheme showed a better performance than the regular proportional-integral-derivative (PID) controller with feed-forward actions as well as a nonadaptive active disturbance rejection controller. A set of numerical simulations was developed to show that even under five times faster reference trajectories, the adaptive controller showed better results than the PID controller. [ABSTRACT FROM PUBLISHER]

This brief presents an active disturbance rejection control scheme for the angular velocity trajectory tracking task on a substantially perturbed, uncertain, and permanent magnet synchronous motor. The presence of unknown, time varying, and load-torque inputs, unknown system parameters, and the lack of knowledge of the initial shaft's angular position, prompts a high-gain generalized proportional integral (GPI) observer-based active disturbance rejection (ADR) controller. This controller is synthesized on the basis of the differential flatness of the system and the direct measurability of the system's flat outputs, constituted by the motor's angular displacement and the $d$ -axis current. As a departure from many previous treatments, the d\-q -axis currents model is here computed on the basis of the measured displacement and not on the basis of the unknown position. The proposed high-gain GPI observer-based ADR controller is justified in terms of a singular perturbation approach. The validity and robustness of the scheme are verified by means of realistic computer simulations, using the MATLAB/SIMULINK-PSIM package. [ABSTRACT FROM PUBLISHER]

Active disturbance rejection control (ADRC) is a new design concept that shows promising power in dealing with the uncertainties of control systems. However, most of the previous work has been numerical time-domain development and frequency-domain analysis for the linear framework. This paper focuses on the frequency-domain analysis of the nonlinear ADRC behavior using the describing function method and characterizes the effect of the fal nonlinearity parameter on the performance of the closed-loop system. Both the describing function of the nonlinearity and the transfer function description of the system's linear portion are derived. The stability, dynamic stiffness, and tracking performance are analyzed for a second-order single-input single-output plant. The analysis results show that the nonlinearity parameter plays a crucial role in the system performance. The nonlinear ADRC has higher control efficiency than the linear ADRC but reduces the stability margin of the system. Using the fast tool servo case, simulations and hardware experiments are conducted, and the results further support the analysis. [ABSTRACT FROM PUBLISHER]