Nonlinear State Error Feedback Research Articles

Optimal power tracking control of a hydraulic wind turbine based on active disturbance rejection control methodology

Power point tracking (PPT) is one of the necessary functions of the wind turbine to optimize the use of wind energy. PPT is a condition that needs to be completed after the grid is connected, which can be achieved by tracking the optimal rotation speed of the output of the wind turbine and the optimum torque and power output of the hydraulic system. Based on a fixed displacement pump speed control, an optimal PPT strategy with the active disturbance rejection control (ADRC) method is proposed, and the control objective is to maximize the energy conversion of the system. This paper sets out to (i) establish a hydraulic wind turbine grid-connected affine nonlinear mathematical model, based on the ADRC method and a fixed displacement pump speed output control, (ii) design a nonlinear tracking differentiator and extended state observer and nonlinear state error feedback control law, and (iii) achieve optimal PPT under different wind speeds. Simulations were model by MATLAB/Simulink, where the system inputs signals of different wind speeds and analyses control system stability and robustness. Simulation results show that the input power was greater with a fixed displacement pump speed .

Control system of the six-axis serial manipulator based on active disturbance rejection control

This study considers the problems of manipulators with high coupling, parameter uncertainties, and external disturbances. A six-axis serial manipulator control system based on active disturbance rejection control strategy is proposed without the requirement of the exact dynamic model. First, the operating circuit of the manipulator joint motor is analyzed, and the mathematical model of the direct-current torque motor is established. Second, the components of active disturbance rejection control are designed, and a new nonlinear function is selected to construct the extended state observer and nonlinear state error feedback control law. Then, Kalman filter is introduced into an extended state observer to estimate the disturbance efficiently. Finally, the proportion–integration–differentiation control, traditional active disturbance rejection control, and improved active disturbance rejection control are simulated and compared under the same input signal. The results show that the proposed control strategy has good dynamic performance and uncertain disturbance robustness, which proves the effectiveness of the proposed method.

Improved Active Disturbance Rejection Control for Trajectory Tracking Control of Lower Limb Robotic Rehabilitation Exoskeleton.

Neurological disorders such as cerebral paralysis, spinal cord injuries, and strokes, result in the impairment of motor control and induce functional difficulties to human beings like walking, standing, etc. Physical injuries due to accidents and muscular weaknesses caused by aging affect people and can cause them to lose their ability to perform daily routine functions. In order to help people recover or improve their dysfunctional activities and quality of life after accidents or strokes, assistive devices like exoskeletons and orthoses are developed. Control strategies for control of exoskeletons are developed with the desired intention of improving the quality of treatment. Amongst recent control strategies used for rehabilitation robots, active disturbance rejection control (ADRC) strategy is a systematic way out from a robust control paradox with possibilities and promises. In this modern era, we always try to find the solution in order to have minimum resources and maximum output, and in robotics-control, to approach the same condition observer-based control strategies is an added advantage where it uses a state estimation method which reduces the requirement of sensors that is used for measuring every state. This paper introduces improved active disturbance rejection control (I-ADRC) controllers as a combination of linear extended state observer (LESO), tracking differentiator (TD), and nonlinear state error feedback (NLSEF). The proposed controllers were evaluated through simulation by investigating the sagittal plane gait trajectory tracking performance of two degrees of freedom, Lower Limb Robotic Rehabilitation Exoskeleton (LLRRE). This multiple input multiple output (MIMO) LLRRE has two joints, one at the hip and other at the knee. In the simulation study, the proposed controllers show reduced trajectory tracking error, elimination of random, constant, and harmonic disturbances, robustness against parameter variations, and under the influence of noise, with improvement in performance indices, indicates its enhanced tracking performance. These promising simulation results would be validated experimentally in the next phase of research.

A Novel Compound Nonlinear State Error Feedback Super-Twisting Fractional-Order Sliding Mode Control of PMSM Speed Regulation System Based on Extended State Observer

In this article, a novel compound nonlinear state error feedback super-twisting fractional-order sliding mode control (NLSEF-STFOSMC) is proposed for the control of the permanent magnet synchronous motor (PMSM) speed regulation system. Firstly, a novel fractional-order proportion integration differentiation (FOPID) switching manifold is designed. A modified sliding mode control (SMC) is constructed by a super-twisting reaching law and the novel FOPID sliding surface. Secondly, the nonlinear state error feedback control law (NLSEF) has been widely used because of high control accuracy, fast convergence, and flexible operation. Therefore, combining the modified SMC with the NLSEF, the compound NLSEF-STFOSMC is proposed, which has an excellent performance. At the same time, the external disturbance of the system is observed by a novel extended state observer. Finally, the performance of the corresponding control law to the speed operation of the PMSM is fully investigated compared with other related algorithms to demonstrate the effectiveness. The comparison results show that the proposed compound control strategy has excellent dynamic and static performance and strong robustness.

Model-free active input–output feedback linearization of a single-link flexible joint manipulator: An improved active disturbance rejection control approach

Traditional input–output feedback linearization requires full knowledge of system dynamics and assumes no disturbance at the input channel and no system’s uncertainties. In this paper, a model-free active input–output feedback linearization technique based on an improved active disturbance rejection control paradigm is proposed to design feedback linearization control law for a generalized nonlinear system with a known relative degree. The linearization control law is composed of a scaled generalized disturbance estimated by an improved nonlinear extended state observer with saturation-like behavior and the nominal control signal produced by an improved nonlinear state error feedback. The proposed active input–output feedback linearization cancels in real-time fashion the generalized disturbances which represent all the unwanted dynamics, exogenous disturbances, and system uncertainties and transforms the system into a chain of integrators up to the relative degree of the system, which is the only information required about the nonlinear system. Stability analysis has been conducted based on the Lyapunov functions and revealed the convergence of the improved nonlinear extended state observer and the asymptotic stability of the closed-loop system. Verification of the outcomes has been achieved by applying the proposed active input–output feedback linearization technique on the single-link flexible joint manipulator. The simulations results validated the effectiveness of the proposed active input–output feedback linearization tool based on improved active disturbance rejection control as compared to the conventional active disturbance rejection control–based active input–output feedback linearization and the traditional input–output feedback linearization techniques.

Active disturbance rejection control strategy for airborne radar stabilization platform based on cascade extended state observer

PurposeThis paper aims to improve the anti-interference ability of the airborne radar stabilization platform, especially the ability to suppress continuous disturbance under complex air conditions to ensure the clarity and stability of airborne radar imaging.Design/methodology/approachThis paper proposes a new active disturbance rejection control (ADRC) strategy based on the cascade extended state observer (ESO) for airborne radar stabilization platform, which adopts two first-order ESOs to estimate the angular velocity value and the angular position value of the stabilized platform. Then makes the error signal which subtracts the estimated value of ESO from the output signal of the tracking-differentiator as the input signal of the nonlinear state error feedback (NLSEF), and according to the output signal of the NLSEF and the value which dynamically compensated the total disturbances estimated by the two ESO to produce the final control signal.FindingsThe simulation results show that, compared with the classical ADRC, the ADRC based on the cascade ESO not only estimates the unknown disturbance more accurately but also improves the delay of disturbance observation effectively due to the increase of the order of the observer. In addition, compared with the classical PID control and the classical ADRC, it has made great progress in response performance and anti-interference ability, especially in the complex air conditions.Originality/valueThe originality of the paper is the adoption of a new ADRC control strategy based on the cascade ESO to ameliorate the anti-interference ability of the airborne radar stabilization platform, especially the ability to suppress continuous interference under complex air conditions.

Speed Control for the Pitching Axis of a Remote Sensing Camera Using an Improved Active Disturbance Rejection Controller

This paper proposes the theoretical framework and the experimental application of an improved active disturbance rejection controller (ADRC) to speed control for the pitching axis of a remote sensing camera. Mechanical model of the pitching axis, mechatronics model of the speed control system for the pitching axis, and speed algorithm model of a permanent magnet synchronous motor are established. Control rates of the extended state observer (ESO) and the nonlinear state error feedback (NSEF) of the traditional ADRC are improved using a new nonlinear function. The nonlinear dynamics, model uncertainty, and external disturbances of the speed control system are extended to a new state, and the improved ESO is implemented to observe this state. The overtime variation of the speed control system is predicted and compensated for in real time using the improved ESO. The nonlinear integration method is adopted to nonlinearly combine the differential and the error differential by the improved NSEF. Subsequently, high-quality control is provided to the system. Simulation and experimental verification for the speed control system for the pitching axis of a remote sensing camera are conducted. Results show the effectiveness of the proposed controller.

Application of improved active disturbance rejection control algorithm in tilt quad rotor

The Tilt Quad Rotor (TQR) has complex dynamics characteristics, especially in conversion mode. It is difficult to build the dynamic model of the TQR and the environmental factors have a great influence on it. To solve the problem of control in conversion mode of TQR, this paper carries out the design of the controller based on improved Active Disturbance Rejection Control (ADRC). According to the characteristics of flight in conversion mode, Tracking Differentiator (TD) with explicit model is used to solve the problem of multiple integrals when the system is high-order system. Extended State Observer (ESO) with Radial Basis Function (RBF) neural network is used to estimate and compensate for internal and external uncertainties, and the adaptive sliding mode control in Nonlinear State Error Feedback (NLSEF) is used to improve the response speed of the controller and reduce the parameters which should be tuned. Through the flight control simulation of the TQR, the validity and rationality of the control system are verified.

A Novel Active Disturbance Rejection Control for the Quad Tilt Rotor in Conversion Process

The quad tilt rotor (QTR) has complex dynamics characteristics, especially in conversion mode. It is difficult to model the QTR dynamics and the environmental factors have a great influence on it. To solve the problem of control in conversion mode of QTR, this paper carries out the design of the controller based on improved active disturbance rejection control (ADRC). According to the characteristics of flight in conversion mode, tracking differentiator (TD) is used to solve the problem of multiple integral when the system is high-order system. Extended state observer (ESO) with radial basis function (RBF) neural network is used to estimate and compensate for internal and external uncertainties, and the adaptive sliding model control in nonlinear state error feedback (NLSEF) is used to improve response speed of the controller and reduce the parameters which should be tuned. Through the flight control simulation of the QTR, the validity and rationality of the control system are verified.

Observer-Based Nonlinear Decoupling Control for Two-Joint Manipulator Systems Driven by Pneumatic Artificial Muscles

Abstract Pneumatic artificial muscles (PAMs) are an important type of bionic actuators for high power-to-weight ratio and good flexibility. However, nonlinearities always exist in systems driven by PAMs, which should be dealt with to obtain good performances during position control. In this paper, a nonlinear state error feedback controller (NSEFC) is presented to obtain good position accuracy for a two-joint manipulator system driven by PAMs. The two-joint manipulator system has nonlinearities, which come from friction, hysteresis, uncertainties of model, loss of piping pressure, coupling between two joints, and so on. A nonlinear extended state observer (ESO) is designed to estimate the nonlinearities in the two-joint manipulator system. Both the effectiveness of the nonlinear ESO and stability of the two-joint manipulator system are given by Lyapunov approaches. Experimental results are obtained to show that the position accuracy of the two-joint manipulator system is improved based on the proposed method in this paper.

Variable Pitch Active Disturbance Rejection Control of Wind Turbines Based on BP Neural Network PID

When wind speeds are above the rated speed of variable speed variable pitch wind turbines, pitch angles are changed to keep output powers and rotor speeds at their rated values. For wind turbines with nonlinear and complex structure, conventional PID variable pitch controller is difficult to achieve precise control. In this paper, a variable pitch controller combining back-propagation(BP) neural network with PID (BP-PID) is proposed. By real-time detecting the deviation of the rotor speeds, the BP neural network with self-learning and weighting coefficient correction capability is used to adjust the PID parameters online and further to achieve the optimal combination of the PID parameters. Considering various uncertain disturbances and parameter changes on the mechanical components of the wind turbines, an active disturbance rejection pitch controller of the wind turbines is designed based on BP-PID algorithm. Combined with a tracking differentiator, an extended state observer (ESO) is employed to observe the state and disturbance of the system. In addition, in order to compensate the BP-PID variable pitch controller, nonlinear state error feedback control laws are designed by configuring nonlinear structures according to the state deviation between the extended state observer and the tracking differentiator. The simulation results show that the variable pitch active disturbance rejection control (ADRC) based on BP-PID can effectively estimate the system states and disturbances. And the proposed controller has good dynamic performance and strong robustness.

Active disturbance rejection attitude control for the dove flapping wing micro air vehicle in intermittent flapping and gliding flight

This paper proposes an attitude control scheme for the Dove flapping wing micro air vehicle in intermittent flapping and gliding flight. The Dove flapping wing micro air vehicle adopts intermittent flapping and gliding flight to make the wing movements more natural; this strategy also has the potential to reduce energy consumption. To implement this specific flight mode, this paper proposes a closed-loop active disturbance rejection control strategy to stabilize the attitude during the processes of flapping flight, transition and gliding flight. The active disturbance rejection control controller is composed of three parts: a tracking differentiator, a linear extended state observer and a nonlinear state error feedback controller. The tracking differentiator estimates the given target signal and the differential signal in real time. The extended state observer estimates the system states and system nonlinearity. Moreover, the bandwidth parameterization method is applied to determine the observer gains. The stability of the closed-loop system is verified using Lyapunov’s theorem. Several outdoor flight experiments have been conducted to verify the effectiveness of the proposed control method, and the results show that the proposed method can guarantee the stability of intermittent flapping and gliding flight.

Autonomous underwater vehicle depth control based on an improved active disturbance rejection controller

Large fluctuation, large overshoot, and uncertain external disturbance that occur when an autonomous underwater vehicle is in deep motion are difficult to address using the traditional control method. An optimal control strategy based on an improved active disturbance rejection control technology is proposed to enhance the trajectory tracking accuracy of autonomous underwater vehicles in actual bathymetric operations and resist external and internal disturbances. First, the depth motion and mathematical models of an autonomous underwater vehicle and propeller are established, respectively. Second, the control rate of the extended state observer and the nonlinear error feedback of the traditional active disturbance rejection control are improved by using a new nonlinear function. The nonlinearity, model uncertainty, and external disturbance of the autonomous underwater vehicle depth control system are extended to a new state, which is realized by an improved extended state observer. Third, the improved nonlinear state error feedback is used to suppress residual errors and provide high-quality control for the system. Simulation and experimental results show that under the same parameters, the traditional active disturbance rejection control has a small overshoot, fast tracking ability, and strong anti-interference ability. The optimized active disturbance rejection control and traditional active disturbance rejection control are applied to the deep-variation motion of autonomous underwater vehicles. Results show that the proposed optimal control strategy is not only simple and feasible but also demonstrates good control performance.

Manipulation strategy of tilt quad rotor based on active disturbance rejection control

To solve the problem of manipulation redundancy and coupling in transition mode of tilt quad rotor, this paper studied the manipulation strategy in transition mode, and carried out the design of the attitude controller based on active disturbance rejection control (ADRC) with sliding mode control in nonlinear state error feedback (NLSEF). According to the characteristics of flight in transition mode, the rudders and propellers were assigned different control rights. The differential output of the tracking differentiator was used as the attitude angular rate instruction to simplify the structure of the attitude controller. Extended state observer was used to estimate and compensate internal and external uncertainties. The sliding mode control in NLSEF was used to improve response speed of the controller. Through the flight control simulation and flight test of the tilt quad rotor, the validity of the control system and the rationality of the manipulation strategy were verified.

Controller Design for Different Electric Tail Rotor Operating Modes in Helicopters

The nonlinear aerodynamics and new kinds of operation associated with helicopter electric tail rotors (ETRs) make accurate speed tracking control under complex flight conditions a key challenge confronting designers. In this paper, we present an electric propulsion system for tail rotors that uses a high-power-density permanent magnet motor. The management of aerodynamic disturbance rejection and accurate speed control are aspects of ETR design that require particularly close attention. To this end, we have developed a speed controller that is based on an active disturbance rejection control (ADRC) technique that can handle fixed speed and adjustable pitch-angle modes. We have also applied a linear extended state observer (LESO) with a self-tuning bandwidth to estimate fluctuations in the drive system. For variable speeds, a simple controller combined with an adaptive radial basis function (RBF) observer and nonlinear state error feedback using ADRC was designed to replace LESO while avoiding any dependence on the system parameters. The stability of the controllers was analyzed and their effectiveness was verified using a simulation platform. Test results showed that the propulsion system is able to achieve fast dynamic response and aerodynamic disturbance rejection.

Speed Control of PMSM Based on an Optimized ADRC Controller

Permanent‐magnet synchronous motor (PMSM) is a nonlinear, multivariate, strongly coupled system with uncertain external interference. A general control method cannot meet system requirements. This study proposes an optimal control strategy based on active disturbance rejection control (ADRC) to achieve high‐precision control of PMSM. First, interpolation fitting is used to construct a nonlinear function with improved continuity and derivative near the origin and segment points. Second, various components of active disturbance rejection control are constructed based on the new nonlinear function, which mainly improves the extended state observer and nonlinear state error feedback. Simulation results show that under similar parameters, the improved active disturbance rejection control has smaller overshoot, faster tracking capacity, and stronger anti‐interference capability compared with traditional active disturbance rejection control. Finally, the optimized active disturbance rejection control is used in the motion control system of PMSM. Experimental results show that the proposed optimal control strategy is simple and has good control performance.

搭载光谱遥感载荷的多旋翼无人机控制系统设计与试验

As a new low -cost remote sensing platform, rotor UAV has been paid much attention by researchers and applications. Rotor UAV equipped with commercial remote sensing has many advantages, such as high ground resolution, quick response and easy maintenance, which make up for the shortcomings of traditional remote sensing, in practical use the anti-interference ability has become an important part of the remote sensing system of the rotor. In order to make up for the lack of conventional multi rotor torque heading control, firstly, six axis twelve -rotor UAV structure was designed and its dynamic model was established, then according to the anti disturbance capability of agricultural remote sensing platform requirements, the special algorithm of active disturbance rejection controller (ADRC) was designed with differential tracker, extended state observer and nonlinear state error feedback control law. Secondly, the stability and effectiveness of the controller was verified by simulation. The real wind disturbance test shows that the control algorithm maintains good trajectory tracking characteristics under the influence of instantaneous wind disturbance of 11.2 m/s. Finally, the UAV equipped with self -developed commercial high micro spectrometer MNS2001 and two axis stabilized in six axis twelve tilt rotor, fixed spectral remote sensing measurements in a particular area of rice over 300 -900 nm in the spectral range, spectral reflectance hovering over the region of multiple measurement relative error was less than 5%. The test results show that the rotor has a good platform for remote sensing stability and reliability can be further applied in the field of agricultural remote sensing and auxiliary production management. 2019, Editorial Board of Journal of Infrared and Laser Engineering. All right reserved.

Position control for ball and beam system based on active disturbance rejection control

ABSTRACTThis paper proposes a new control strategy to the position control of the ball in the ball and beam system by adopting an active disturbance rejection control (ADRC). ADRC is composed of a tracking differentiator (TD), an extended state observer (ESO), a nonlinear state error feedback control law (NLSEF), and a disturbance compensation device (DCD). The ESO observes and tracks the position of the ball and the direct current (DC) servomotor in real time. The total disturbance of the system can be expanded and amplified, and can also be effectively compensated in real time to suppress interferences by the ESO. The procedures of research are as follows. First, the model of the ball and beam system, including the motion equation of the system and the DC servomotor, is established. Second, ADRC is designed and applied to the ball and beam system and the DC servomotor. Third, the control model of the ball and beam system is built on the basis of ADRC. Finally, the ball position of ADRC is simulated and verified. The results show that the ball and beam system based on ADRC exhibits better performance than the proportion integration differentiation controller.

A Sliding Mode Control with Nonlinear Fractional Order PID Sliding Surface for the Speed Operation of Surface‐Mounted PMSM Drives Based on an Extended State Observer

A novel sliding mode controller (SMC) with nonlinear fractional order PID sliding surface based on a novel extended state observer for the speed operation of a surface‐mounted permanent magnet synchronous motor (SPMSM) is proposed in this paper. First, a new smooth and derivable nonlinear function with improved continuity and derivative is designed to replace the traditional nonderivable nonlinear function of the nonlinear state error feedback control law. Then, a nonlinear fractional order PID sliding mode controller is proposed on the basis of the fractional order PID sliding surface with the combination of the novel nonlinear state error feedback control law to improve dynamic performance, static performance, and robustness of the system. Furthermore, a novel extended state observer is designed based on the new nonlinear function to achieve dynamic feedback compensation for external disturbances. Stability of the system is proved based on the Lyapunov stability theorem. The corresponding comparative simulation results demonstrate that the proposed composite control algorithm displays good stability, dynamic properties, and strong robustness against external disturbances.

Improved ADRC With ILC Control of a CCD-Based Tracking Loop for Fast Steering Mirror System

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.