Active Disturbance Rejection Control Approach Research Articles

Event-triggered attitude tracking for rigid spacecraft

This study aims to investigate the problem of attitude control for a spacecraft with inertial uncertainties, external disturbances, and communication restrictions. An event-triggered active disturbance rejection control approach is proposed for attitude tracking of the spacecraft. An event-triggered mechanism is introduced together with an extended state observer to jointly monitor the system states and total disturbances. The observation error is proved to be uniformly bounded. Based on the proposed control scheme, the integrated tracking system is shown to be asymptotically stable, implying successful attitude tracking of the spacecraft for the desired motion. Numerical results illustrate the effectiveness of the control strategy in achieving satisfactory tracking performance with a reduced data-transmission cost.

Event-Triggered Sampled-Data Control: An Active Disturbance Rejection Approach

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.

A Robust Active and Reactive Power Control Scheme With Multiloop Disturbance Rejection for a Wind Energy Conversion System

In this paper, a new control scheme is proposed to regulate the active power and reactive power of a permanent magnet synchronous generator (PMSG) based wind energy conversion system (WECS). Due to uncertainties in the internal dynamics of PMSG, modeling error in WECS and external disturbances, such as wind speed variation, control of active power, and reactive power, of a WECS becomes a challenging task. To address the above-mentioned problem, we propose a multiloop active disturbance rejection control (MADRC) approach to achieve efficient control of active and reactive power flow between the WECS and grid. The performance of this proposed control scheme is verified first by simulation and then, through experimentation on a 1-kW PMSG-based WECS developed in our laboratory. From the obtained simulation and experimental results, it is observed that the proposed MADRC provides excellent active and reactive power controls in the face of parametric variations and disturbance with satisfactory steady-state and dynamic performances. Further, on comparing its performance with that of a single-loop active disturbance rejection control and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller, it is found that MADRC exhibits superior active and reactive power control performances amongst aforesaid controllers.

On vibration suppression and trajectory tracking in largely uncertain torsional system: An error-based ADRC approach

Abstract In this work, a practically relevant control problem of compensating harmonic uncertainties is tackled. The problem is formulated and solved here using an active disturbance rejection control (ADRC) methodology. A novel, custom ADRC structure is proposed that utilizes an innovative resonant extended state observer (RESO), dedicated to systems subjected to harmonic interferences. In order to make the introduced solution more industry-friendly, the entire observer-centered control topology is additionally restructured into one degree-of-freedom, compact, feedback error-based form (similar to ubiquitous in practice PID controller). Such reorganization enables a straightforward implementation and commission of the proposed technique in wide range of industrial control platforms, thus potentially increasing its outreach. In order to verify the efficiency of the introduced method, a multi-criteria experimental case study using a torsional plant is conducted in a trajectory tracking task, showing satisfactory performance in vibration suppression, without the often problem of noise amplification due to high observer/controller gains. Finally, a frequency analysis and a rigorous stability proof of the proposed control structure are given.

Mittag‐Leffler stabilization for an unstable time‐fractional anomalous diffusion equation with boundary control matched disturbance

SummaryThis paper addresses the Mittag‐Leffler stabilization for an unstable time‐fractional anomalous diffusion equation with boundary control subject to the control matched disturbance. The active disturbance rejection control (ADRC) approach is adopted for developing the control law. A state‐feedback scheme is designed to estimate the disturbance by constructing two auxiliary systems: One is to separate the disturbance from the original system to a Mittag‐Leffler stable system and the other is to estimate the disturbance finally. The proposed control law compensates the disturbance using its estimation and stabilizes system asymptotically. The closed‐loop system is shown to be Mittag‐Leffler stable and the constructed auxiliary systems in the closed loop are proved to be bounded. This is the first time for ADRC to be applied to a system described by the fractional partial differential system without using the high gain.

An algebraic version of the active disturbance rejection control for second-order flat systems

An algebra-based active disturbance rejection control approach for uncertain second-order flat systems, perturbed by a matching perturbation, is presented. This approach consists of proposing an online algebraic estimator for the uncertain system, together with an algebraic reconstructor for the unknown velocity. To assess the efficiency of the approach, numerical simulations to control an uncertain longitudinal vehicle system were carried out.

Stabilization of a constrained one-link flexible arm with boundary disturbance

We discuss the stabilisation problem of a constrained one-link flexible arm with boundary disturbance flowing to the control end. By the active disturbance rejection control (ADRC) approach, we first design a time varying high gain extended state observer to estimate the disturbance, and then give a feedback controller to eliminate the negative effect of the disturbance. The well-posedness of the closed-loop system is proved by the semigroup theory. Moreover, under different assumptions of the time varying high gain function, we obtain the asymptotical stability and the exponential stability of the closed-loop system, respectively. Finally, some numerical simulations are presented to support the theoretical results.

Hybrid disturbance rejection control of dynamic bipedal robots

This paper presents a disturbance rejection control strategy for hybrid dynamic systems exposed to model uncertainties and external disturbances. The focus of this work is the gait control of dynamic bipedal robots. The proposed control strategy integrates continuous and discrete control actions. The continuous control action uses a novel model-based active disturbance rejection control (ADRC) approach to track gait trajectory references. The discrete control action resets the gait trajectory references after the impact produced by the robot’s support-leg exchange to maintain a zero tracking error. A Poincare return map is used to search asymptotic stable periodic orbits in an extended hybrid zero dynamics (EHZD). The EHZD reflects a lower-dimensional representation of the full hybrid dynamics with uncertainties and disturbances. A physical bipedal robot testbed, referred to as Saurian, is fabricated for validation purposes. Numerical simulation and physical experiments show the robustness of the proposed control strategy against external disturbances and model uncertainties that affect both the swing motion phase and the support-leg exchange.

Output Regulation for a Class of MIMO Uncertain Stochastic Nonlinear Systems by Active Disturbance Rejection Control Approach

In this paper, the active disturbance rejection control (ADRC) approach is applied to a class of multi-input multioutput (MIMO) uncertain stochastic nonlinear systems. An extended state observer (ESO) is first designed for estimation of both unmeasured states and stochastic total disturbance of each subsystem which represents the total effects of internal unmodeled stochastic dynamics and external stochastic disturbance with unknown statistical property. The ADRC controller based on the states of ESO is further designed to achieve the closed-loop system’s output regulation performance including practical mean square reference signals tracking, disturbance attenuation, and practical mean square stability when the reference signals are zero avoiding solving any partial differential equations in the conventional output regulation theory. Some numerical simulations are presented to demonstrate the effectiveness of the proposed ADRC approach.

Comparative analysis of Backstepping and ADRC Approach used in PV System connected to the Grid

The aim of this paper is to ensure high performances of grid connected photovoltaic power system using DC-AC power inverters. It is susceptible to power grid disturbance, sudden environment changes and parameters uncertainties. Based in this characteristic, comparison between robust Backstepping controller and active disturbance rejection control (ADRC) strategy are developed. The two control algorithms are required to extract the maximum power of the solar energy, to maintain constant the DC-bus voltage, and to inject a suitable current into the grid with power factor near unity. Therefore, the Analysis and simulation of the ADRC and Backstepping controllers are validated with MATLAB/ Simulink software. It is showed the superiority of the backstepping technique through simulation results. Otherwise, The ADRC has only two parameters design, which make it easy to implement.

High-Order Sliding Mode-Based Fixed-Time Active Disturbance Rejection Control for Quadrotor Attitude System

This article presents a fixed-time active disturbance rejection control approach for the attitude control problem of quadrotor unmanned aerial vehicle in the presence of dynamic wind, mass eccentricity and an actuator fault. The control scheme applies the feedback linearization technique and enhances the performance of the traditional active disturbance rejection control (ADRC) based on the fixed-time high-order sliding mode method. A switching-type uniformly convergent differentiator is used to improve the extended state observer for estimating and attenuating the lumped disturbance more accurately. A multivariable high-order sliding mode feedback law is derived to achieve fixed time convergence. The timely convergence of the designed extended state observer and the feedback law is proved theoretically. Mathematical simulations with detailed actuator models and real time experiments are performed to demonstrate the robustness and practicability of the proposed control scheme.

Performance optimization of linear active disturbance rejection control approach by modified bat inspired algorithm for single area load frequency control concerning high wind power penetration

The linear active disturbance approach is employed to deal with the load frequency control issue of a single area wind power system based on doubly fed induction generator, and the performance of the control law is optimized by using the bat-inspired algorithm. The load frequency control issue has become more challenging in a complex power system based on wind energy conversion system due to the varying feature of the wind penetration, and sustaining the balance between the power generation and demand by rejecting the internal uncertainties in the process model and the external disturbances simultaneously. In the framework of the presented linear active disturbance rejection control approach, by constructing an extended state observer, the total disturbance, including all the unmodelled dynamics in the process model and the external disturbances, can be estimated in real time and then compensated by a simple linear PD control law. The controller parameters tuning is then simplified into the optimization of the two bandwidths: observer bandwidth, and the controller bandwidth. Then, this issue can be achieved by employing the heuristic modified bat inspired algorithm based on the optimization of the proposed performance index. The effectiveness of the proposed approach is validated by the extensive simulation examples of the load frequency control issue involved in the single area power system, taking into account different wind penetration, as well as the external disturbances. The performance robustness of the proposed approach against the parameters perturbation in the process model is also demonstrated via the Monte-Carlo method. The performance superiority of the proposed approach over the conventional Proportional Integral and Fuzzy-Proportional Integral based controller even in the presence of external disturbances and uncertainty in power system parameters under different cases of high wind penetration is also validated from the simulation results.

Stabilisation of an anti-stable joint string with boundary disturbance

ABSTRACTIn this paper, we consider the boundary stabilisation for a one-dimensional joint anti-stable string equation with input disturbance entering the control end. A backstepping transformation is used to design a suitable boundary controller so that the system is equivalent to a target system which is exponentially stable when the disturbance is absent. The active disturbance rejection control approach (ADRC) is adopted to estimate and eliminate the external disturbance. The well-posedness and stability of the target system are presented. Some numerical stimulations indicate the effectiveness of the control law.

Robust Active Disturbance Rejection Control for LVRT capability enhancement of DFIG-based wind turbines

This article presents the development of a strategy to enhance the Low-Voltage Ride-Through capability (LVRT) of Doubly Fed Induction Generator (DFIG)-based Wind Turbines (WTs). The developed control scheme proposes a trajectory generation system and a high-performance rotor current controller. First, the rotor current trajectories are obtained according to the grid codes requirements. These codes introduce suitable values for the electromagnetic torque and the active and reactive power during operation in normal and fault modes. A detailed analysis of controllability and stability aims to find out how to pair the control inputs and the controlled outputs according to the suggested operation conditions. As a result, a comprehensive study of the required rotor current trajectories to enhance the LVRT capability is developed. Second, the design of the rotor current controller is based on Active Disturbance Rejection Control (ADRC) approach. This controller accomplishes two main objectives: (1) it guarantees a robust tracking of the proposed trajectories, despite uncertainties, disturbances and symmetrical and asymmetrical faults in the grid; and (2) it keeps the rotor voltages and currents in their allowed ratings. Finally, the proposed scheme and the theoretical analysis are validated with simulation studies and laboratory tests.

Exponential regulation of the anti-collocatedly disturbed cage in a wave PDE-modeled ascending cable elevator

In cable elevators, large axial vibrations appear when a cage subject to disturbance is lifted up via a compliant cable. The axial vibration dynamics can be described by a wave partial differential equation (PDE) on a time-varying spatial interval with an unknown boundary disturbance. In this paper, we design an output feedback controller actuating at the boundary anti-collocated with the disturbance to regulate the state on the uncontrolled boundary of the wave PDE based on the backstepping idea and the active disturbance rejection control (ADRC) approach. The control law uses the state and disturbance information recovered from the state observer and the disturbance estimator, respectively, which are constructed via limited boundary measurements. The exponential convergence of the state on the uncontrolled boundary and uniform boundedness of all states in the closed-loop system are proved by Lyapunov analysis. Effective vibration suppression in the cable elevator with the designed controller is verified via numerical simulation.

An ADRC-Based Control Strategy for FRT Improvement of Wind Power Generation with a Doubly-Fed Induction Generator

This paper proposes a second-order active disturbance rejection control (ADRC)-based control strategy with an integrated design of the flux damping method, for the fault ride-through (FRT) improvement in wind power generation systems with a doubly-fed induction generator (DFIG). First, a first principles model of the rotor and grid side converter of DFIG is developed, which is then used to theoretically analyze the system characteristics and show the damage caused to the DFIG system by a grid voltage fault. Then, the flux damping method is used to suppress the rotor current during a fault ride-through. In order to enhance the robustness and effectiveness of the flux damping method under complex working conditions, an ADRC approach is proposed for disturbance attenuation of the DFIG systems. Finally, a comparison of the proposed method with three other control approaches on a 1.5-MV DFIG system benchmark is performed. It is shown that the proposed method can adaptively and effectively improve the system performance during an FRT.

Approximate decoupling and output tracking for MIMO nonlinear systems with mismatched uncertainties via ADRC approach

In this paper, we consider output tracking for a class of MIMO nonlinear systems which are composed of coupled subsystems with vast mismatched uncertainties. First, all uncertainties influencing the performance of controlled outputs, which include internal unmodelled dynamics, external disturbances, and uncertain nonlinear interactions between subsystems, are refined into the total disturbance in the control channels of subsystems. The total disturbance is shown to be sufficiently reflected in the measured output of each subsystem so that it can be estimated in real time by an extended state observer (ESO) in terms of the measured outputs. Second, we decouple approximately the MIMO systems by cancelling the total disturbance based on ESO estimation so that each subsystem becomes approximately independent linear time invariant one without uncertainty and interaction with other subsystems. Finally, we design an ESO based output feedback for each subsystem separately to ensure that the closed-loop state is bounded, and the closed-loop output of each subsystem tracks practically a given reference signal. This is completely in comply with the spirit of active disturbance rejection control (ADRC). Some numerical simulations are presented to demonstrate the effectiveness of the proposed output feedback control scheme.

Optimized Active Disturbance Rejection Control for DC-DC Buck Converters With Uncertainties Using a Reduced-Order GPI Observer

The output voltage regulation problem of a PWM-based dc-dc buck converter under various sources of uncertainties and disturbances is investigated in this paper via an optimized active disturbance rejection control (ADRC) approach. Aiming to practical implementation, a new reduced-order generalized proportional integral (GPI) observer is first designed to estimate the lumped (possibly time-varying) disturbances within the dc-dc circuit. By integrating the disturbance estimation information raised by the reduced-order GPI observer into the output prediction, an optimized ADRC method is developed to achieve optimized tracking performance even in the presence of disturbances and uncertainties. It is shown that the proposed controller will guarantee the rigorous stability of the closed-loop system, for any bounded uncertainties of the circuit, by appropriately choosing the observer gains and the bandwidth factor. Experimental results illustrate that the proposed control solution is characterized by improved robustness performance against various disturbances and uncertainties compared with traditional ADRC and integral model predictive control (MPC) approaches.

Active disturbance rejection control for small unmanned helicopters via Levy flight-based pigeon-inspired optimization

PurposeThe purpose of this paper is to propose a control approach for small unmanned helicopters, and a novel swarm intelligence algorithm is used to optimize the parameters of the proposed controller.Design/methodology/approachSmall unmanned helicopters have many advantages over other unmanned aerial vehicles. However, the manual operation process is difficult because the model is always instable and coupling. In this paper, a novel optimized active disturbance rejection control (ADRC) approach is presented for small unmanned helicopters. First, a linear attitude model is built in hovering condition according to small perturbation linearization. To realize decoupling, this model is divided into two parts, and each part is equipped with an ADRC controller. Finally, a novel Levy flight-based pigeon-inspired optimization (LFPIO) algorithm is developed to find the optimal ADRC parameters and enhance the performance of controller.FindingsThis paper applies ADRC method to the attitude control of small unmanned helicopters so that it can be implemented in practical flight under complex environments. Besides, a novel LFPIO algorithm is proposed to optimize the parameters of ADRC and is proved to be more efficient than other homogenous methods.Research limitations/implicationsThe model of proposed controller is built in the hovering action, whereas it cannot be used in other flight modes.Practical implicationsThe optimized ADRC method can be implemented in actual flight, and the proposed LFPIO algorithm can be developed in other practical optimization problems.Originality/valueADRC method can enhance the response and robustness of unmanned helicopters which make it valuable in actual environments. The proposed LFPIO algorithm is proved to be an effective swarm intelligence optimizer, and it is convenient and valuable to apply it in other optimized systems.

Event-Triggered Active Disturbance Rejection Control of DC Torque Motors

Physical servo systems are affected by disturbances, uncertainties, and resource restrictions. In this paper, an event-triggered active disturbance rejection control approach is proposed to achieve position tracking of dc torque motors. An event-based sampler together with an extended state observer is introduced, which allows the joint observation of the system state, and the total disturbance induced by model uncertainty and intermittent sampling. Based on the observation results, closed-loop control is achieved with guaranteed stable tracking performance. To quantify the effect of event-based sampling, a quantitative relationship between the asymptotic upper bound of tracking error and the parameters in the event-based sampler is developed. The control strategy is applied to a dc torque motor system, and comparative experimental results indicate that for different reference signals, the proposed event-based control strategy can achieve satisfactory tracking performance with reduced sampling cost.