Nonlinear State Error Feedback Research Articles

Rotor position angle control of permanent magnet synchronous motor based on sliding mode extended state observer

ABSTRACT To achieve fast, accurate control of the position angle of the rotor of permanent magnet synchronous motor (PMSM), traditional auto disturbance rejection control often has many adjustable parameters and complex tuning problems. Sliding mode control technology is introduced into the extended state observer (ESO) part of the auto disturbance rejection controller, and a new sliding mode approach law is designed based on several typical sliding mode approaches, which simplifies parameter tuning while retaining the original anti-interference performance of auto disturbance. In addition, the nonlinear state error feedback control law in active disturbance rejection control is enhanced to improve the component order PID control law, which can improve the response speed and robustness of the system, and prove the stability of the controller. Finally, the simulation of the PMSM rotor position control system based on the sliding mode ESO is carried out, and the results verify the validity of the method.

Cascade ADRC with neural network-based ESO for hypersonic vehicle

In this paper, active disturbance rejection control (ADRC) based on a neural network has been investigated for the attitude control of the hypersonic vehicle (HV) with uncertain disturbances, which are regarded as a strongly time-varying, nonlinear, and coupled system. The structure of nonlinear state error feedback (NLSEF) with an Extended State Observer (NLSEF+ESO) utilized in ADRC is considered to have good disturbance resistance ability in engineering applications with less dependence on the mathematical model of the system. However, the strong coupling of the HV makes it complicated to separately design ADRC for each channel. In addition, the bandwidth and parameters of the ESO can seriously affect the performance of the ADRC, while jitter occurs when they are not well matched. A cascade active-rejection control scheme is designed by introducing the Radial Basis Function (RBF) Neural Network to substitute the ESO in ADRC, which mitigates the shortcoming of ADRC in addressing the control problems of the MIMO system with coupling disturbances. The NNESO can adapt well to disturbance characteristics through online training and fitting and can effectively reduce the jitter of the control. The stability of the NNESO is proved by Lyapunov stability theory, and the numerical simulations are presented to demonstrate the effectiveness of our theoretical results. In summary, the proposed NNESO-based cascade ADRC is an effective method for solving the problem of HV control with better disturbance resistance.

Active disturbance rejection control for optoelectronic stabilized platform based on model-assisted double extended state observers

PurposeThis study aims to promote the anti-disturbance and tracking accuracy of optoelectronic stabilized platforms, which ensure that optical detectors accurately track targets and acquire high-quality images.Design/methodology/approachAn improved active disturbance rejection control (ADRC) strategy based on model-assisted double extended state observers (MDESOs) is proposed in this paper. First, by establishing an auxiliary model, the total disturbances are separated into two parts: inner and external disturbances. Then, MDESOs are designed to estimate the two parts by separately using two parallel ESOs, by which the controlled plant is adjusted to the ideal pure integral series. Simultaneously, combined with the nonlinear state error feedback, an overall control strategy is established.FindingsCompared with the conventional ADRC and proportional derivative, the improved ADRC (IADRC) has stronger robustness and adaptability and effectively reduces the requirements for model accuracy and the gain of the ESO. The error of the auxiliary model is tolerated to exceed 50%, and the parameter values of the MDESOs are reduced by 90%.Originality/valueThe total disturbance rejection rate of the proposed strategy is only 3.11% under multiple disturbances, which indicates that the IADRC strategy significantly promotes anti-disturbance performance.

Mathematical Modeling and Control of COVID-19 Using Super Twisting Sliding Mode and Nonlinear Techniques.

Since the outbreak of the COVID-19 epidemic, several control strategies have been proposed. The rapid spread of COVID-19 globally, allied with the fact that COVID-19 is a serious threat to people's health and life, motivated many researchers around the world to investigate new methods and techniques to control its spread and offer treatment. Currently, the most effective approach to containing SARS-CoV-2 (COVID-19) and minimizing its impact on education and the economy remains a vaccination control strategy, however. In this paper, a modified version of the susceptible, exposed, infectious, and recovered (SEIR) model using vaccination control with a novel construct of active disturbance rejection control (ADRC) is thus used to generate a proper vaccination control scheme by rejecting those disturbances that might possibly affect the system. For the COVID-19 system, which has a unit relative degree, a new structure for the ADRC has been introduced by embedding the tracking differentiator (TD) in the control unit to obtain an error signal and its derivative. Two further novel nonlinear controllers, the nonlinear PID and a super twisting sliding mode (STC-SM) were also used with the TD to develop a new version of the nonlinear state error feedback (NLSEF), while a new nonlinear extended state observer (NLESO) was introduced to estimate the system state and total disturbance. The final simulation results show that the proposed methods achieve excellent performance compared to conventional active disturbance rejection controls.

A relative degree one modified active disturbance rejection control for four-tank level control system

Abstract This paper deals with the disturbance rejection, parameter uncertainty cancelation, and the closed-loop stabilization of the water level of the four-tank nonlinear system. For the four-tank system with relative degree one, a new structure of the active disturbance rejection control (ADRC) has been presented by incorporating a tracking differentiator (TD) in the control unit to obtain the derivate of the tracking error. Thus, the nonlinear-PD control together with the TD serves as a new nonlinear state error feedback. Moreover, a sliding mode extended state observer is presented in the feedback loop to estimate the system's state and the total disturbance. The proposed scheme has been compared with several control schemes including linear and nonlinear versions of ADRC techniques. Finally, the simulation results show that the proposed scheme achieves excellent results in terms of disturbance elimination and output tracking as compared to other conventional schemes. It was able to control the water levels in the two lower tanks to their desired value and exhibits excellent performance in terms of Integral Time Absolute Error (ITAE) and Objective Performance Index (OPI).

ADRC Control System of PMLSM Based on Novel Non-Singular Terminal Sliding Mode Observer

In an attempt to solve the problem of the many parameters of the traditional active disturbance rejection controller (ADRC) and to accurately estimate the mover position and speed required by a permanent magnet synchronous linear motor (PMLSM) system, an improved ADRC and a novel nonsingular fast terminal sliding mode observer (NFTSMO) are proposed. Firstly, the traditional first-order ADRC is simplified, the tracking differentiator (TD) module is removed, and the direct error is used to replace the nonlinear function in the extended state observer (ESO) and nonlinear state error feedback (NLSEF) module. Based on the traditional NFTSMO, the smooth back electromotive force (EMF) is obtained by adding the TD to reduce the phase delay caused by the low-pass filter in the traditional sliding mode observer (SMO), and the actuator position and speed information are modulated from the observed back EMF based on the principle of a phase-locked loop (PLL). Simulation and experiments show that this method not only simplifies the system structure of PMLSM but also optimizes many parameters in ADRC while retaining the original excellent performance. Compared with the traditional NFTSMO, the improved NFTSMO enhances the observation accuracy, reduces the chattering phenomenon of the system, and improves the robustness of the system.

DISTURBANCE REJECTION DIFFERENTIAL TRACKING VARIABLE STRUCTURE CONTROLLER, 1-8.

In view of the shortcomings of the traditional proportional, integral,and derivative controller, the active disturbance rejection controlmethod is put forward, which extracts the differential and arrangesthe transition process reasonably through the “tracking differentia-tor” (TD) and the nonlinear state error feedback (NLSEF) con-troller.

Active disturbance rejection attitude control of unmanned quadrotor via paired coevolution pigeon-inspired optimization

PurposeThe purpose of this paper is to develop a novel active disturbance rejection attitude controller for quadrotors and propose a controller parameters identification approach to obtain better control results.Design/methodology/approachAiming at the problem that quadrotor is susceptible to disturbance in outdoor flight, the improved active disturbance rejection control (IADRC) is applied to design attitude controller. To overcome the difficulty that adjusting the parameters of IADRC controller manually is complex, paired coevolution pigeon-inspired optimization (PCPIO) algorithm is used to optimize the control parameters.FindingsThe IADRC, where nonlinear state error feedback control law is replaced by non-singular fast terminal sliding mode control law and a third-order tracking differentiator is designed for second derivative of the state, has higher control accuracy and better robustness than ADRC. The improved PIO algorithm based on evolutionary mechanism, named PCPIO, is proposed. The optimal parameters of ADRC controller are found by PCPIO with the optimization criterion of integral of time-weighted absolute value of the error. The effectiveness of the proposed method is verified by a series of simulation experiments.Practical implicationsIADRC can improve the accuracy of attitude control of quadrotor and resist external interference more effectively. The proposed PCPIO algorithm can be easily applied to practice and can help the design of the quadrotor control system.Originality/valueAn improved active disturbance rejection controller is designed for quadrotor attitude control, and a hybrid model of PIO and evolution mechanism is proposed for parameters identification of the controller.

Dynamic Landing Control of a Quadrotor on the Wave Glider

Aiming at the problems of difficult attitude stabilization, low landing accuracy, large external disturbance and slow dynamic response during the quadrotor dynamic landing on the wave glider, an improved series active disturbance rejection control method for the quadrotor is proposed. The quadrotor controller with inner-loop attitude angular velocity control and outer-loop position control based on the active disturbance rejection controller (ADRC) is designed by analyzing the dynamic model of the quadrotor. A tracking differentiator (TD) is adopted to track the input signal, and an expansive state observer (ESO) is used to estimate the total disturbance. Moreover, a nonlinear law state error feedback (NLSEF) is used to generate the virtual control volume of the system to realize the control of the quadrotor, and the stability of the cascaded self-turbulent controller is verified by Lyapunov’s theory. The simulation verifies that the proposed controller can accurately control the attitude and the position with better anti-interference capability and faster tracking speed. According to the final sea trial, a combination of an active disturbance rejection controller optimized with improved crow search algorithm (ICADRC) and April Tag visual reference system is used to land the quadrotor efficiently and successfully even under the surface float attitude uncertainty.

Adaptive Fuzzy Active-Disturbance Rejection Control-Based Reconfiguration Controller Design for Aircraft Anti-Skid Braking System

The aircraft anti-skid braking system (AABS) is an essential aero electromechanical system to ensure safe take-off, landing, and taxiing of aircraft. In addition to the strong nonlinearity, strong coupling, and time-varying parameters in aircraft dynamics, the faults of actuators, sensors, and other components can also seriously affect the safety and reliability of AABS. In this paper, a reconfiguration controller-based adaptive fuzzy active-disturbance rejection control (AFADRC) is proposed for AABS to meet increased performance demands in fault-perturbed conditions as well as those concerning reliability and safety requirements. The developed controller takes component faults, external disturbance, and measurement noise as the total perturbations, which are estimated by an adaptive extended state observer (AESO). The nonlinear state error feedback (NLSEF) combined with fuzzy logic can compensate for the adverse effects and ensure that the faulty AABS maintains acceptable performance. Numerical simulations are carried out in different runway environments. The results validate the robustness and reconfiguration control capability of the proposed method, which improves AABS safety as well as braking efficiency.

Azimuth Control for Large Aperture Telescope Based on Segmented Arc Permanent Magnet Synchronous Motors

A tracking control algorithm based on active disturbance rejection controller (ADRC) is proposed to overcome the telescope’s mount fluctuation. The fluctuations are caused by internal and external disturbance when the large aperture telescope runs at ultra-low speed with direct drive. According to the high-precision and high-stability requirements of a large aperture telescope, the ADRC position controller is designed based on segmented arc Permanent Magnet Synchronous Motors (arc PMSMs). The tracking differentiator of ADRC is designed to undergo a transition process to avoid overshoot in the position loop. The speed of target tracking process is observed by the extended state observer and the position information in the system is estimated in real time. The current control variable of the segmented arc PMSM is generated by implementing a non-linear state error feedback control law. The simulation results demonstrate that the proposed control strategy can not only accurately estimate the position and speed of the tracking target, but also estimate the disturbance to compensate the control variables. Experiments showed that the speed error is less than 0.05′ s−1 when using the ADRC, and it can realize high tracking performance when compared with PID controller, which improves the robustness of a large aperture telescope control system.

Disturbance rejection control of airborne radar stabilized platform based on active disturbance rejection control inverse estimation algorithm

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

Smith control of SCR system based on sliding mode control

The reaction process of selective catalytic reduction (SCR) denitrification system is complex, which has the characteristics of large inertia, large delay, strong interference and uncertainty. Traditional PID control can’t achieve accurate control of ammonia injection. Based on linear active disturbance rejection control (LADRC), Smith predictor is used to eliminate the delay output variables before entering extended state observer. The nonlinear state error feedback control law of ADRC structure is designed by using sliding mode control law, which improves the fast response and stability of the system. To solve the problem that the selective catalytic reduction denitrification system is difficult to achieve accurate modeling and large delay, Smith-SMC linear extended state observer (Smith-SMC-LESO) is designed. The simulation results of tracking characteristics, anti-jamming characteristics and robustness show that the set-point tracking performance and anti-jamming ability of Smith-LADRC and Smith-SMC-LESO are significantly improved.

Low-speed control of PMSM based on ADRC + FOPID

ABSTRACT In this study, a new low-speed control strategy based on active disturbance rejection control (ADRC) + fractional-order proportion integration differentiation (FOPID) is proposed to realize fast and accurate control of permanent magnet synchronous motor (PMSM) at low speed. First, a new nonlinear function with enhanced smoothness and continuity around the origin is designed. On the basis of the above nonlinear function, an improved extended state observer (ESO) is developed. Then, the parameters of ESO are adjusted online by the designed fuzzy rules. Considering the improved dynamic performance of the FOPID controller, the nonlinear state error feedback control law module of ADRC is replaced by FOPID to calculate the proportion, differential, and integral of the error signal. Finally, the simulation analysis of the new low-speed control system based on ADRC + FOPID is carried out. The results show that the proposed algorithm has faster response speed and better anti-interference ability in the low-speed control of PMSM than the traditional ADRC.

Design and Control of a Deformable Trees-Pruning Aerial Robot

Tree branches near the electric power transmission lines are of great threat to the electricity supply. Nowadays, the tasks of clearing threatening tree branches are still mostly operated by hand and simple tools. Traditional structures of the multirotor aerial robot have the problem of fixed structure and limited performance, which affects the stability and efficiency of pruning operation. In this article, in order to obtain better environmental adaptability, an active deformable trees-pruning aerial robot is presented. The deformation of the aerial robot is implemented through two ways, arm telescopic and folding. In order to suppress the influence of internal and external disturbances on the system, Active Disturbance Rejection Control (ADRC) technology is adopted to build the flight controller. Firstly, active deformation aerial robot structure is given, followed by system dynamic model establishment under wind disturbance using the Newton–Euler method. Also, the analysis of the gusts influence on the system is considered. Then, the active deformation aerial robot system is decoupled into a combination of six SISO systems, so that a disturbance rejection controller is designed. Finally, the expanded state observer and the nonlinear state error feedback law are used to inspect and compensate the disturbance. Simulation results of attitude and position tracking as well as the antidisturbance capability show that the active deformation aerial robot with the ADRC flight controller designed in this paper has excellent attitude control capabilities during flight and trees-pruning operation.

Research on improved active disturbance rejection control of continuous rotary motor electro-hydraulic servo system

In order to meet the precision requirements and tracking performance of the continuous rotary motor electro-hydraulic servo system under unknown strong non-linear and uncertain strong disturbance factors, such as dynamic uncertainty and parameter perturbation, an improved active disturbance rejection control (ADRC) strategy was proposed. The state space model of the fifth order closed-loop system was established based on the principle of valve-controlled hydraulic motor. Then the three parts of ADRC were improved by parameter perturbation and external disturbance; the fast tracking differentiator was introduced into linear and non-linear combinations; the nonlinear state error feedback was proposed using synovial control; the extended state observer was determined by nonlinear compensation. In addition, the grey wolf algorithm was used to set the parameters of the three parts. The simulation and experimental results show that the improved ADRC can realize the system frequency 12 Hz when the tracking accuracy and response speed meet the requirements of double ten indexes, which lay foundation for the motor application.

Improved active disturbance rejection heading control for unmanned wave glider

The Unmanned Wave Glider (UWG) captures wave energy in the ocean and mechanically converts it into propulsion. This unique propulsion mode makes the speed of UWG uncontrollable and changeable, which leads to the unique heading control problem. The large model perturbation brought by the speed change of UWG makes it difficult for traditional controllers to maintain consistent heading control effect. In this paper, the Improved Active Disturbance Rejection Control (IADRC) method was proposed for UWG heading control. The Improved Linear Extended State Observer (ILESO) was proposed to dynamically modify the second-order series integral system transformed from LESO based on similarity principle. Falfunction filter was utilized in ILESO to reduce the influence of speed sensor noise. The Improved S-surface control strategy was proposed as the error feedback of IADRC. Compared with Non-Linear State Error Feedback (NLSEF), the parameters of the controller are greatly reduced and can be adjusted adaptively according to the speed of UWG. Numerical simulation experiments and sea trail were performed. The results showed that the proposed IADRC can significantly improve heading control performance for UWG at both steady and unsteady speeds.

Control of a Tilting Hexacopter under Wind Disturbance

Multicopters are well suited for executing fast maneuvers with high velocity, but they are still affected by the external atmospheric environment because attitude and position cannot be independently controlled. In this paper, we present a novel hexacopter which improves the wind resistance and strong coupling between attitude control and position control. The copter is designed such that the rotor sections can tilt around their respective arm axes. We present the aerodynamic methods to analyze the system dynamics model in windy environments. The entire system is decomposed into six loops based on the model, and the presented flight controller uses the ADRC method to consider both the attitude and the position. The controller introduces the extended state observer to estimate the white noise and wind disturbance. We use the nonlinear state error feedback law to control the output with disturbance compensation. Finally, we linearize the control allocation matrix that the controllers output directly mapped to the rotor velocities and tilting angles. The new theoretical results are thoroughly validated through comparative experiments.

Non-linear active disturbance rejection control for upper limb rehabilitation exoskeleton

Trajectory tracking in upper limb rehabilitation exercises is utilized for repeatability of joint movement to improve the patient’s recovery in the early stages of rehabilitation. In this article, non-linear active disturbance rejection control as a combination of non-linear extended-state observer and non-linear state error feedback is used for the sinusoidal trajectory tracking control of the two-link model of an upper limb rehabilitation exoskeleton. The two links represent movements like flexion/extension for both the shoulder joint and the elbow joint in the sagittal plane. The Euler–Lagrange method was employed to acquire a dynamic model of an upper limb rehabilitation exoskeleton. To examine the efficacy and robustness of the proposed method, four disturbances cases in simulation studies with 20% parameter variation were applied. It was found that the non-linear active disturbance rejection control is robust against disturbances and achieves better tracking as compared to proportional–integral–derivative and existing conventional active disturbance rejection control method.

An Active Disturbance Rejection Control-Based Voltage Control Strategy of Single-Phase Cascaded H-Bridge Rectifiers

In the traditional control strategy for single-phase PWM converter applications, the proportional-integral (PI) controller has the role of voltage tracking in the outer loop voltage controller, which has limited capability to provide acceptable dynamic performance and disturbance rejection. With regard to this, this article proposes a voltage control strategy based on the active disturbance rejection control (ADRC) for single-phase cascaded H-bridge rectifiers, aiming at achieving satisfactory dynamic performance and strong robustness to the disturbances. First, the extended state observer is used for the state and disturbance estimations. Then, the nonlinear state error feedback deals with the system error and makes the dynamic compensation to the disturbances. More specifically, an improved continuous nonlinear function is adopted to mitigate the jitter behavior of the traditional ADRC and provide immunity to large disturbance errors. Furthermore, the performance and stability analysis of the proposed strategy are implemented. A parameter tuning guideline of the proposed strategy is detailed. The effectiveness of the proposed ADRC-based voltage control strategy is verified through extensive experimental tests and is compared to that of the conventional PI-based voltage control strategy.