Second-order Active Disturbance Rejection Control Research Articles

Research on a Sensorless ADRC Vector Control Method for a Permanent Magnet Synchronous Motor Based on the Luenberger Observer

A sensorless vector active disturbance rejection control (ADRC) method for permanent magnet synchronous motors (PMSM) utilizing a Luenberger observer is presented. This method aims to address the challenges associated with weak active disturbances, substantial steady-state speed amplitude fluctuations, and difficulty in achieving a balance between overshoot and speed control in the sensorless PMSM control system. Mathematical models of the Luenberger observer and the ADRC were analyzed, leading to the proposal of a second-order ADRC control method based on the Luenberger observer. A mathematical model of the permanent PMSM has been introduced. Additionally, the necessary conditions for the convergence of the Luenberger observer were derived and examined. The allowable range of error feedback gain values was determined, and rotor position data were acquired using a phase-locked loop. The principle of the ADRC was analyzed, and the ADRC simulation results, along with the PI simulation results, were detailed. When the target speed is 1000 r/min, the steady-state error and load disturbance resistance of the ADRC control method outperform those of the PI control method. Finally, the control method was experimentally tested on an STM32F4 chip, demonstrating the advantages of small steady-state error and strong active disturbance ability.

Research on the Control Method of a Brushless DC Motor Based on Second-Order Active Disturbance Rejection Control

This research addresses the issues of weak anti-disturbance ability, fast response, and incompatibility of overshoot in the control process of brushless DC motors (BLDCs). A six-step commutation control method based on second-order active disturbance rejection control (ADRC) is derived following the analysis of the BLDC model and the mathematical model of ADRC. A control model of the BLDC using both PI and ADRC is constructed. Detailed comparative and quantitative analyses of the simulation results using PI and ADRC are conducted, focusing on the anti-load disturbance capabilities using the integrated square error (ISE), integrated time square error (ITSE), integrated absolute error (IAE), and integrated time absolute error (ITAE). Experimental testing on the STM32F4 controller is also carried out, analyzing four error integral criteria in depth. The results indicate that both the ADRC and PI control modes can track the target signal without overshooting, demonstrating strong anti-load disturbance ability and robustness at varying working speeds. In the BLDC control system, using the ADRC control method can achieve fast and non-overshoot tracking of target signals compared to the PI control method, and ADRC has stronger resistance to load disturbances.

Active Disturbance Rejection Control Algorithm for the Driven Branch Chain of a Polishing Robot

To overcome poor error suppression performance and low control accuracy in the polishing robot-driven branch chain control system, this paper proposes an improved active disturbance rejection control (ADRC) from the design of the derived nonlinear function. Subsequently, the tracking differentiator (TD), extended state observer (ESO) and nonlinear state error feedback (SEF) are designed in the ADRC, and the driven branch’s ADRC servo-control system is established based on the permanent magnet synchronous motor (PMSM) with each driven branch. Meantime, by establishing first-order and second-order ADRC, current-loop control, and speed-and-position-loop control are realized, respectively. Finally, this study analysed differences in the speed and motor rotor error performance between the proportional-integral-derivative (PID)control and ADRC control strategy by using Simulink. Furthermore, an experiment platform, including hardware and software, is built to validate some inclusions. The results show that the ADRC not only realises high-precision trajectory tracking control but also ensures the rapid response performance of the system.

Control strategy for the anode gas supply system in a proton exchange membrane fuel cell system

Stable pressure control can improve the lifespan, efficiency, and stability of proton exchange membrane fuel cell system (PEMFCs). We successfully implemented a feedforward-based proportion-integral controller (FPIC) to control the anode pressure of a 100 kW fuel cell system. The bench experimental results demonstrate that the fuel cell stack achieves a maximum efficiency of 62.3 %, while the fuel cell power generation system achieve a maximum efficiency of 53.5 %. Under the steady-state and dynamic conditions, the strategy achieves a pressure tracking control accuracy of 98.93 % and 94.47 %, respectively. To address the large overshoot phenomenon and slow response speed of the FPIC when controlling the anode pressure, we further design a second order active disturbance rejection controller (SOADRC). The simulation results show that the SOADRC exhibits higher control stability and lower overshoot than FPIC. Moreover, it demonstrates a 51.3 % increase in response speed and an 80.7 % improvement in control stability under steady-state conditions compared to FPIC. The evaluation metrics for the error integral criterion (eISE = 0.023, eITSE = 2.58, eIAE = 0.35, and eIEAE = 36.76) are lower than FPIC, which demonstrates that the SOADRC provides more precise control of anode pressure, and enhances the stability of PEMFCs.

Research on flywheel energy storage control strategy based on active disturbance rejection controller

Based on nonlinear busbar voltage in flywheel energy storage systems and frequent discharge characteristics, in order to improve the dynamic control derived from the analysis of a permanent magnet synchronous motor and its inverter set up model of DC bus and the active disturbance rejection principle and use the active disturbance rejection control (ADRC) technique to design the DC bus voltage adaptive controller, the first- and second-order ADRC controllers are compared with the traditional PI controller in MATLAB. In this work, we demonstrate that the voltage controller designed with the first- and second-order ADRCs was superior to a traditional PI in terms of dynamic performance control.

Tracking and Synchronization Control Strategy of Vehicle Dual-Motor Steer-by-Wire System via Active Disturbance Rejection Control

A novel vehicle dual-motor steer-by-wire (SBW) system is proposed to improve the reliability and safety of traditional SBW system. However, the biggest challenge of dual-motor SBW is its tracking and synchronization control issues. In order to solve the problems of poor tracking and synchronization of the vehicle dual-motor SBW system caused by load disturbance, parameter perturbation, and model mismatch, a tracking and synchronization control strategy of the vehicle dual-motor SBW system via the active disturbance rejection control is proposed. First, the driving mechanism of dual-motor SBW system is analyzed, and the system dynamics model is established. Then, considering the system disturbance and parameter uncertainty, a second-order active disturbance rejection controller is designed for the position loop of the steering motor, which is composed of a third-order extended state observer and a state error feedback control law. Next, in order to simplify the adjustment difficulty of the controller, the bandwidth method is introduced to greatly reduce the number of controller parameters and the difficulty of parameter adjustment. Based on this, the disturbance rejection performance and stability of the designed active disturbance rejection controller are proved. Furthermore, the cross-coupling control structure is employed to enhance the synchronization performance of the dual-motor system. Finally, the performance of the controller to suppress the external disturbance and internal parameter perturbation is analyzed in step condition and double lane change condition, respectively, and the effectiveness of the proposed control strategy is verified on the dual-motor experimental platform.

A second-order ADRC for Synchronized Frequency-Voltage Mitigation of EV Integrated Power System

ABSTRACT The present paper proposes a novel disturbance rejection-based scheme applied to a power system for concurrent control of system voltage, frequency, and tie-line power. The generating units in the power system comprise varied generating sources, such as thermal, diesel, solar-thermal, and wind sources. Owing to the present rigid limitations on energy assets and environmental alarms, electric vehicles are integrated with the power system in both areas. The complex power system needs a robust controller for stable operation. In response to this challenge, a novel second-order Active Disturbance-Rejection-Control (ADRC) is modeled as a secondary controller for performance studies. An extended state observer is designed for the estimation of system disturbance and uncertainties assisting ADRC in compensating for the impact through disturbance rejection. The magnetotactic bacteria-optimization approach is utilized to optimize the controller gains by reducing the errors in the objective function. Detailed case studies are carried out on two-area and three-area hybrid power-system incorporating different renewable energy plants to test the performance of the proposed controller. The dominance of the developed second-order-ADRC is verified based on system performance improvement concerning testified controllers available in the literature. The developed second-order-ADRC validates the robustness under different system-changed conditions. The fact that electric vehicles assist in system dynamic regulation is studied thoroughly.

Active control of combustion oscillation with active disturbance rejection control (ADRC) method

This research aims to develop a novel method for the active control of combustion oscillation based on active disturbance rejection control (ADRC). The effectiveness of parameter tuning and the controller in suppressing combustion oscillation was studied by simulation and experiments. The control performance was verified using a Rijke tube and turbulent premixed swirling flame within a model combustor. For the former, the results show that the first-order ADRC can rapidly mitigate the limit cycle oscillation and maintain the effectiveness of the control when the oscillation frequency changes. For the latter, a system identification method based on an acoustic network was adopted. Combining the identification results with a thermoacoustic network, the formation process of the limit cycle oscillation and the effectiveness of the first-order ADRC were simulated by SIMULINK. The experimental results show that the first-order ADRC performs better than the proportional–integral–derivative (PID) controller. At the same time, the first-order ADRC and second-order ADRC achieve good outcomes when the equivalence ratio changes. However, the second-order ADRC exhibits a better pressure-suppression effect and smaller controller output voltage.

Comprehensive Engineering Frequency Domain Analysis and Vibration Suppression of Flexible Aircraft Based on Active Disturbance Rejection Controller.

The crash of an aircraft with an almost vertical attitude in Wuzhou, Guangxi, China, on 21 March 2022, has caused a robust discussion in the civil aviation community. We propose an active disturbance rejection controller (ADRC) for suppressing aeroelastic vibrations of a flexible aircraft at the simulation level. The ADRC has a relatively simple structure and it has been proved in several fields to provide better control than the classical proportional-integral-derivative (PID) control theory and is easier to translate from theory to practice compared with other modern control theories. In this paper, the vibration model of the flexible aircraft was built, based on the first elastic vibration mode of the aircraft. In addition, the principle of ADRC is explained in detail, a second-order ADRC was designed to control the vibration model, and the system’s closed-loop frequency domain characteristics, tracking effect and sensitivity were comprehensively analyzed. The estimation error of the extended state observer (ESO) and the anti-disturbance effect were analyzed, while the robustness of the closed-loop system was verified using the Monte Carlo method, which was used for the first time in this field. Simulation results showed that the ADRC suppressed aircraft elastic vibration better than PID controllers and that the closed-loop system was robust in the face of dynamic parameters.

A Novel Control Algorithm of the Air Supply Subsystem: Based on Dynamic Modeling of Proton Exchange Membrane Fuel Cell

In this paper, a novel second-order active disturbance rejection control (2-ADRC) algorithm is proposed to optimize the control of the air supply subsystem for Proton Exchange Membrane Fuel Cell (PEMFC). To improve the optimal control effect of the air supply subsystem for PEMFC, the modeling theory of the air supply subsystem considering dynamic characteristics of the PEMFC system is first studied, and the dynamic Simulink model of the PEMFC system is established and verified. Then, the optimal oxygen excess ratio (OER) parameters under different load currents are obtained, and the optimal OER parameters are also used as the OER control reference for the designed algorithms. In addition, a 2-ADRC algorithm is designed and proposed to make the actual OER parameters close to the optimal OER in real time. Furthermore, compared with PID and MPC algorithms, the 2-ADRC algorithm can comprehensively consider the two parameters of mass flow and pressure ratio to make the compressor work in the high-efficiency zone and improve the net power and efficiency of the PEMFC system.

High performance control method of electro-mechanical actuator based on active disturbance rejection control

Integrated electro-mechanical actuators (EMAs) are widely used in cooperative robots. Their control system has to be carefully designed to achieve a desirable performance. The proportional-integral (PI) control and the active disturbance rejection control (ADRC) are the two commonly used controllers. Compared with the PI, the ADRC shows better performance in terms of disturbance rejection, response speed and overshooting suppression. However, the ADRC utilises numerous parameters and the optimisation of these parameters is a challenge. In this study, the influence of the parameters of β01, β02, β03, β1, β2on the ADRC performance is deeply analysed. Considering the two non-linear factors of permanent magnet synchronous motor and harmonic transmission in the EMA, a simulation model of the EMA was established. An improved swarm optimisation algorithm was employed to optimise the parameters of the ADRC. A second-order ADRC in speed and position modes was designed. The parameters of the ADRC in these modes were adjusted using improved particle swarm optimisation. ADRC was applied to the EMA field-oriented control system instead of cascade PI, and the simulation and experimental results were compared using the cascade PI control method. When the target speed is to 15 rpm, the speed fluctuation range of the ADRC is about ±0.3 rpm, which is smaller than that of the PI controller’s ±0.5 rpm. Compared with the cascade PI control, ADRC affords a faster response speed, greater robustness and stronger disturbance resistance in the steady-state operation process.

High-speed train speed tracking control based on active disturbance rejection control strategy

The speed tracking control of high-speed trains has the characteristics of nonlinearity, time delay, and multi-factor interference. Aiming at this, a train speed tracking algorithm based on active disturbance rejection control strategy is proposed. First, establish a train control model based on the train dynamics model. Secondly, design a second-order active disturbance rejection controller to set and compensate for unknown disturbances, and then convert the known train parameters to the controlled object for system simulation, the target speed curve is tracked, which proves the feasibility of the auto disturbance rejection control algorithm. Finally, compare traditional PD control algorithms in terms of anti-jamming performance and tracking error. The results show that the high-speed train speed controller based on active disturbance rejection control has greatly improved the tracking speed accuracy and the robustness of the control system.

An Active Disturbance Rejection Control Strategy for a Three-Phase Isolated Matrix Rectifier

Single-stage three-phase isolated matrix rectifiers (TIMRs) have high efficiency and compact configurations and are very suitable for electric vehicle (EV) chargers. However, external and internal disturbances challenge the robustness and tracking performance of EV chargers, and conventional proportional integral (PI) controllers cannot solve the unmodeled dynamics and the uncertainty of model parameters in the system, so other feedback controllers, which have disturbance rejection performance, need to be designed. Therefore, this article proposes a dual-loop control strategy based on active disturbance rejection control (ADRC) to guarantee high-speed dynamic response and strong robustness against disturbances. First, the dynamic model of the TIMR is established and divided into two parts to facilitate the controller design. Second, the extended state observer (ESO) is designed to estimate and compensate for the disturbances of the system, and the inner current loop and the outer current loop are designed based on the second-order ADRC. In addition, a simplified parameter-tuning method of the proposed control scheme is presented in detail. Finally, a frequency-domain analysis is given to explain the robust performance of the proposed control scheme. The effectiveness and feasibility of the proposed controller are verified by simulation and experimental results.

Study on Active Disturbance Rejection Control of a Bearingless Induction Motor Based on an Improved Particle Swarm Optimization–Genetic Algorithm

To overcome the limitations that active disturbance rejection control (ADRC) system of a bearingless induction motor (BIM) has difficulty in tuning parameters depending on experience to select parameters, an ADRC strategy based on improved particle swarm optimization-genetic algorithm (IPSO-GA) is proposed. Based on the orientation of the air-gap magnetic field, the first-order and the second-order ADRC are, respectively, designed for the BIM rotation and suspension parts according to the different order of the BIM system. Then, the parameters of the basic particle swarm optimization algorithm are optimized by considering the characteristics of the basic particle swarm algorithm parameters, and the crossover and mutation operations are introduced to enhance global search capability. Meanwhile, through the performance test based on the test function, the performance of IPSO-GA is verified, and the parameters of ADRC are adjusted by IPSO-GA. In addition, this strategy is analyzed with simulation in MATLAB/Simulink and verified on an experimental prototype. Both simulation and experimental results show that the proposed strategy not only effectively improves the starting performance and antidisturbance ability of the BIM but also reduces the maximum radial offset of the rotor and improves the suspension precision of the motor.

Synthesis of Active Disturbance Rejection Control

Synthesis of Active Disturbance Rejection Control (ADRC) has been discussed in this work. Two main approaches have been presented for the second-order ADRC: Linear ADRC and nonlinear ADRC. A design procedure for the three main components of ADRC: controller, estimator, and disturbance rejection scheme has been presented in each approach. Parameters of the linear approach are tuned using the desired closed loop system bandwidth. Parameters of the nonlinear approach are selected by categorizing them first into usual parameters and key parameters. After that, the key parameters are optimized using Genetic Algorithm (GA). The two approaches have been tested on a quarter-car system that deals with the passenger comfort problem. Simulation results show a good performance and a good compensation for external disturbances and dynamic uncertainties

Tidal stream turbine control: An active disturbance rejection control approach

As an emerging technology to harness the marine current energy, tidal stream turbine (TST) systems have been developed due to high predictability and energy density in tidal current resources. However, considering that various challenges such as swell disturbances, unknown disturbances, or parameter uncertainties may deteriorate the system performance, it is interesting to investigate alternative control strategies to the conventional proportional-integral (PI) controls. In this paper, the active disturbance rejection control (ADRC) approach is proposed to replace PI controllers in the conventional generator-side control scheme. In this approach, two ADRC schemes (cascaded and second-order ADRC strategies) are respectively applied and compared to achieve MPPT under current velocity and turbine torque disturbances. Performances of the proposed ADRC approaches are compared to PI and sliding mode control strategies. Energy production during swell wave disturbance is also evaluated under these control strategies. The comparisons show that the cascaded ADRC has better performance than the second-order approach. Moreover, the cascaded ADRC is tested under parameter variations to evaluate its robustness. The carried out simulation-based comparative study shows the effectiveness and advantages of the cascaded ADRC strategy over conventional PI controller in terms of fast convergence, overshoots elimination, and improved robustness under disturbances and parameter uncertainties.

Active Disturbance Rejection Control for Steering System of Unmanned Vehicle

A method of intelligent steering control of unmanned vehicle wheel using Active Disturbance Rejection Control (ADRC) is proposed. The steering system of unmanned vehicles is composed of active disturbance rejection controller, angle sensor, motor driver and steering bridge mechanism. When ADRC of front wheels is realized by active disturbance rejection controller, the dynamic equation of the vehicle needs to be normalized first to ensure the dynamic equation of vehicle degree of freedom that can accurately reflect the lateral dynamic characteristics of the vehicle and then the accurately control the tracking of the ideal yaw rate of the vehicle by second-order ADRC. The unmanned vehicle controlled by the proposed method did not overshoot. At the initial stage of yaw disturbance, the response speed of the front wheel’s angle controlled by the proposed method is faster than that of the PID control and the present time is about 0.02s. The vehicle path deviation controlled by the proposed control method is only 60% of the vehicle path deviation controlled by the PID control method. The proposed method makes the vehicle to have stronger anti-yaw disturbance ability and further enhances the vehicle’s path-keeping ability.

Improved Linear Active Disturbance Rejection Controller Control Considering Bus Voltage Filtering in Permanent Magnet Synchronous Generator

In the permanent magnet direct drive wind power generation system, the direct current (DC) bus voltage signal of the converter is usually used as the feedback of the voltage outer loop. Because of the existence of random white noise and the measurement error when the sensor collects the DC bus voltage signal, it is necessary to filter the bus voltage signal through the first-order inertial link. The time constant of the first order inertial link is usually 10ms-15ms. In the traditional voltage external loop second-order active disturbance rejection controller (ADRC) system, the influence of the bus voltage filter is not considered in the design of ADRC, which results in the phase lag and amplitude offset between the feedback of the controller and the real bus voltage. This will make the performance of the system affected by the time constant of the first-order inertial link. In this paper, an improved ADRC considering the bus voltage filter is proposed. The filtered bus voltage is expanded into a new state variable. The voltage before the filter is estimated by using the fourth-order linear expansion state observer (LESO) and used as the feedback. The simulation results show that the improved ADRC system has better control performance.

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.

The Research on Second-Order ADRC Algorithm of Using Wind Turbine Virtual Inertia to Participate in Primary Frequency Regulation in a Small Stand-Alone Microgrid

In order to improve the transient stability of frequency in a small stand-alone microgrid (SSM), this paper takes a SSM composed of a direct-drive permanent magnet synchronous generator (D-PMSG) and a micro gas turbine (MGT) as the background and uses wind turbine generator (WTG) virtual inertia (VI) to participate in the primary (short-term) system frequency regulation. First of all, this paper constructs a grid-connected model composed of a WTG and a MGT, analyzes the WTG virtual inertia frequency regulation mechanism, and explains the principle of proportional-differentiation (PD) virtual inertia control (VIC) and its shortcomings. Secondly, the paper introduces the structure principle of n-order active disturbance rejection control (ADRC) and deduces the design process of second-order ADRC-VIC. Finally, through the simulation and experimental verification, comparing the frequency perturbation of without-VIC, PD-VIC, and ADRC-VIC, it is concluded that PD-VIC and ADRC-VIC both can use the WTG virtual inertia to participate in the primary frequency regulation. The frequency regulation effect of ADRC-VIC is better than PD-VIC, ADRC-VIC can extend the rotor speed recovery time and avoid overshoot, and its frequency fluctuation amplitude and settling time are obviously improved, and ADRC-VIC can effectively avoid the overshoot phenomenon of the MGT output power.