Nonlinear State Error Feedback Control Research Articles

Design and Stability Analysis of Sliding Mode Controller for Non-Holonomic Differential Drive Mobile Robots

This paper presents a novel extended state observer (ESO) approach for a class of plants with nonlinear dynamics. The proposed observer estimates both the state variables and the total disturbance, which includes both exogenous and endogenous disturbance. The study’s changes can be summarized by developing a sliding mode higher-order extended state observer with a higher-order augmented state and a nonlinear function for the estimation error correction terms (SMHOESO). By including multiple enhanced states, the proposed observer can monitor total disturbances asymptotically, with the second derivative of the total disturbance serving as an upper constraint on the estimation error. This feature improves the observer’s ability to estimate higher-order disturbances and uncertainty. To extend the concept of the linear extended state observer (LESO), a nonlinear function can modify the estimation error in such a way that the proposed observer can provide faster and more accurate estimations of the state and total disturbance. The proposed nonlinearity also reduces the chattering issue with LESOs. This research thoroughly examines and analyzes the proposed SMHOESO’s convergence using the Lyapunov technique. According to this analysis, the SMHOESO is asymptotically stable, and the estimation error can be significantly reduced under real-world conditions. In addition to the SMHOESO, a modified Active Disturbance Rejection Control (ADRC) scheme is built, which includes a nonlinear state error feedback (NLSEF) controller and a nonlinear tracking differentiator (TD). Several nonlinear models, including the Differential Drive Mobile Robot (DDMR), are numerically simulated, and the proposed SMHOESO is compared to several alternative types, demonstrating a significant reduction in controller energy, increased control signal smoothness, and accurate tracking of the reference signal.

Improved Position Sensorless Control for PMLSM via an Active Disturbance Rejection Controller and an Adaptive Full-Order Observer

Position and speed information are very important to realize the efficient control for permanent magnet linear synchronous motor (PMLSM). In order to obtain more accurate position estimation signals, this article investigates an improved position sensorless control method for PMLSM by combining an active disturbance rejection control (ADRC)-based speed controller and an adaptive full-order observer (AFO)-based position estimator. The AFO is constructed based on model reference adaptive system (MRAS), which can obtain more accurate position estimation signal by introducing a current error feedback gain matrix. However, there are lots of thrust fluctuations existing in PMLSM caused by end effect, which will affect the estimation accuracy. Since it is difficult to reduce the influence of thrust fluctuation by only improving the observer itself, an ADRC-based speed controller is designed to improve the anti-interference ability of control system, thereby improving the position estimation accuracy. For the ADRC controller, an second-order linear extended state observer (LESO) is designed to observe the thrust fluctuation and an nonlinear state error feedback (NLSEF) control law is introduced to compensate the observed disturbance. The effectiveness and superiority of the proposed method have been verified by simulation and experimental results.

Unbalanced vibration control of active magnetic bearing using an active disturbance rejection notch decoupling technique

Aiming at the position coupling, gyroscopic effect, and synchronized vibration caused by the unbalance mass in the magnetic bearing rotor, a linear active disturbance rejection notch decoupling control method is proposed. Firstly, a model with coupling and unbalanced vibration of the system was established. The terms of position coupling, gyroscopic effect, and unbalanced vibration in the system are estimated by Extended State Observer and the estimator is treated as the system disturbance to be compensated, then the radially existing coupled and unbalanced vibration systems are decoupled into four independent second-order series-integrated subsystems. The nonlinear state error feedback control law is designed to implement the decoupling control of each subsystem. For the problem of unbalanced vibration of the rotor after decoupling, the suppression method of the dynamic unbalanced force of the same frequency notch filter is designed, and then the closed-loop feedback structure of the new method is deduced, and its frequency characteristics are analyzed. Then the rules and principles of controller parameter selection are summarized using Bode diagram. The simulation results show that the designed linear active disturbance rejection notch decoupling controller not only achieves the decoupling control of the respective degrees of the magnetic bearing rotor but also suppresses the unbalanced vibration of the rotor. At the same time, it solves the influence of the gyroscopic effect on the control under the high-speed running of the magnetic bearing rotor.

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.

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.

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.

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.

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.

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.

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.

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.

Nonlinear Control of Marine Surface Vessels

In the present study, a robust yaw control law design derived from nonlinear extended state observer (NESO) based nonlinear state error feedback controller (NSEFC) in conjunction with nonlinear tracking differentiator (NTD) for marine surface vessels is presented. As marine vessel operates in an environment where significant uncertainties and disturbances are present, an NESO is used to estimate the effect of the uncertainties and disturbances along with the plant states leading to a robust design through disturbance estimation and compensation. Convergence of NESO and NTD is demonstrated. The notable feature of the formulation is that to achieve robustness, accurate plant model or any characterization of the uncertainties and disturbances is not needed. Efficacy of the design is illustrated by simulation. Further, performance of the proposed design is compared with some existing controllers to showcase the effectiveness of the proposed design.