Error Feedback Control Research Articles

Contour error dynamic analysis and predictive control for multi-axis motion system

Contour tracking accuracy is the key performance index of a multi-axis motion control system. In the previous design of the contour error feedback controller, the independent design idea of the tracking controller and contour controller of each logic axis is often adopted, which is not easy to realize the optimal control of tracking accuracy and contour accuracy. The coupling increment of each controller is inevitable in motion control compensation, which impacts the control system’s stability. Here, we propose a predictive control method for contour error. At first, through the state space model of the feed system, the system dynamics are judged to predict the contour accuracy in the future finite time domain. Besides, the linear quadratic performance index function of contour error is established, and the performance of the control objective is continuously optimized during the limited time domain with the form of rolling optimization. A closed-loop solution is obtained, which is most suitable for the current motion situation and could add to the system to realize the optimal control considering the trajectory contour and the tracking stability of each servo axis in the subsequent few sampling cycles. Finally, utilizing comparative experiments on the three-axis motion control platform, it is verified that the proposed contour predictive control strategy not only effectively reduces the tracking error but also significantly improves the contour accuracy, which is suitable for application in a complex industrial environment.

Three-Dimensional Trajectory Tracking of AUV Based on Nonsingular Terminal Sliding Mode and Active Disturbance Rejection Decoupling Control

This paper presents a nonsingular terminal sliding mode and active disturbance rejection decoupling control (NTSM-ADRDC) scheme for the three-dimensional (3D) trajectory tracking of autonomous underwater vehicles (AUV). Firstly, the AUV model is decoupled into five independent single input–single output (SISO) channels using ADRDC technology. Secondly, the NTSM-ADRDC controller is designed. The linear extended state observer (LESO) is used to observe the AUV state variables, and estimate the total disturbance of the system. In addition, to improve the system error convergence rate, the combination of exponential reaching rate and NTSM constitutes a nonlinear states error feedback control law for the controller. Finally, the stability of the proposed control law is proved using the Lyapunov theory. The simulation results demonstrate the effectiveness and robustness of the designed NTSM-ADRDC trajectory tracking approach.

Feedback control of the mechanical spindle thermal error based on thermal simulation with bearing heat sources analysis

The thermal error stability (STE) of the spindle seriously affects the machining accuracy of a machine tool, however existing empirical heating model-based active cooling strategies mainly focus on suppressing the spindle’s overall thermal deformation and cannot effectively stabilize the thermal error. This study regards the “active cooling-spindle” system as a feedback control system and employs a data-driven thermal error model to provide feedback. Thus, the spindle thermal error can be stabilized for a long time owing to the homeostasis of the feedback control system under disturbance. A mechanical spindle with an external cooling scheme is taken as the study object. Bearings are the primary heat sources of the mechanical spindle; thus, the angular contact ball-bearing heat generation is precisely modeled based on local heat sources analysis of bearing components, elastohydrodynamic lubrication, and micro-contact theory. Thermal simulation of the spindle under varying-coolant temperature cooling is conducted to pre-validate the thermal error suppression and variation trend influencing effect, and obtain the Reference Input of Thermal Error (RITE) for the feedback control under different work conditions. Subsequently, a spindle thermal error feedback control system is developed, including computation, cooling, and real-time monitoring modules with inter-communication. Finally, the thermal error feedback control strategy is applied on the mechanical spindle, and experimental comparisons with constant coolant temperature cooling show that the thermal equilibrium time is advanced by 61.46%, 59.16%, 40.51%, and 58.08%. The thermal error variation range (TEVR) after the preheating stage is reduced to1.92, 1.52, 1.91, and 1.69 μm, respectively. The significant reduction in TEVR validated the effectiveness of the proposed strategy for spindle thermal error stabilization.

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.

Transient Response Characteristics Improvement of Permanent Magnet Synchronous Motor Based on Enhanced Linear Active Disturbance Rejection Sensorless Control

The compactness, cost decrease, and reliability of the auxiliary drive permanent magnet synchronous motors (PMSMs) for battery electric commercial vehicles can be further improved by adopting the position sensorless control technique. The conventional extended back electromotive force (EEMF) based sensorless control algorithm usually requires a phase-locked loop (PLL) and low pass filter to postprocess the estimated rotor position, which deteriorates the transient response of the PMSM significantly. To solve this problem, this article proposes an active disturbance rejection control based EEMF sensorless control method. By designing an extended state observer (ESO) considering the differential term of the position estimation error, timely and accurate estimation of the load disturbance and rotor position can be achieved simultaneously. The adaptive mechanism of the ESO exhibits sound system antidisturbance performance. Moreover, a linear state error feedback controller and feedforward compensation of load disturbance can replace the speed loop PI controller accordingly. Through stability and tracking performance analysis, the proposed method is superior in both steady-state performance and transient-state performance. The proposed scheme is experimentally validated by a 3 kW automotive power steering oil pump motor drive system. The results show that the transient response characteristics are obviously enhanced compared with the conventional methods. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>

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.

Fuzzy Linear Active Disturbance Rejection Control Method for Permanent Magnet Electromagnetic Hybrid Suspension Platform

The permanent magnetic suspension (PMS) train has distinct advantages in reducing energy consumption and increasing the suspension air gap. Aiming at the problems of uncontrollable magnetic field and underdamping of the PMS system, the electromagnetic damping structure is introduced, and a fuzzy linear active disturbance rejection control (Fuzzy-LADRC) method with an air gap deviation integrator is proposed. Firstly, the permanent magnet electromagnetic hybrid suspension (PEMS) system is constructed, and the model analysis is carried out to prove that the system is controllable and observable, and the hardware experimental platform is built. Secondly, a LADRC method is designed based on the model of the platform suspension control unit, and fuzzy control is introduced into the LADRC state error feedback control theory for parameter self-tuning to improve the adaptability and robustness of the platform. At the same time, an air gap deviation integrator is introduced to further improve the control accuracy. Finally, the comparison experiments with LADRC and PID control methods are carried out in terms of stability, anti-interference, robustness and adaptability. The experimental results show that the proposed Fuzzy-LADRC method has the best control effect. It provides practical reference for improving the stability of the PMS train.

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.

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.

Robust Output Regulation for Multi-Dimensional Heat Equation

In the past few years, we have developed internal model principle for some 1-d partial differential equations (PDEs) from PDE perspective, by which one can find the analytic form of the tracking error feedback control. However, the conditional robustness is only limited to some special cases because it is difficult to formulate the conditional robustness in the framework of PDEs. In this paper, we investigate output regulation for a boundary controlled multidimensional heat equation. We obtain not only an analytic tracking error feedback control but also prove the conditional robustness. This is a first time to combine the abstract result and PDE design, which takes advantages of both frameworks.

Linear-Nonlinear Switching Active Disturbance Rejection Speed Controller for Permanent Magnet Synchronous Motors.

To combine the advantages of linear active disturbance rejection control (LADRC) and nonlinear active disturbance rejection control (NLADRC) and improve the contradiction between the response speed and control precision caused by the limitation of parameter α in NLADRC, a linear-nonlinear switching active disturbance rejection control (SADRC) strategy based on linear-nonlinear switching extended state observer (SESO) and linear-nonlinear switching state error feedback control law (SSEF) is proposed in this paper. First, the reasons for the performance differences between LADRC and NLADRC are analysed from a theoretical point of view, then a linear-nonlinear switching function (SF) that can change the switching point by adjusting its parameters is constructed and then propose SESO and SSEF based on this function. Subsequently, the convergence range of the observation error of the SESO is derived, and the stability of the closed-loop system with the application of SSEF is also demonstrated. Finally, the proposed SADRC control strategy is applied to a 707 W permanent magnet synchronous motor (PMSM) experimental platform, and both the dynamic and static characteristics of SADRC are verified. The experimental results show that the proposed SADRC control strategy can well combine the performance advantages of LADRC and NLADRC and can better balance the response speed and control precision and has a better capacity for disturbance rejection, which has potential application in engineering practise.

Simulation of a Quadrotor under Linear Active Disturbance Rejection

The quadrotor aircraft has the characteristics of simple structure, high attitude maintenance performance and strong maneuverability, and is widely used in air surveillance, post−disaster search and rescue, target tracking and military industry. In this paper, a robust control scheme based on linear active disturbance rejection is proposed to solve the problem that the quadrotor is susceptible to various disturbances during the take−off process of non−horizontal planes and strong disturbances. Linear Active Disturbance Rejection Control (LADRC) is a product of a tracking differentiator (TD), a linear extended state observer (LESO) and an error feedback control law (PD) and is a control technique for estimating compensation for uncertainty. Radial Basis Function Neural Networks (RBFNN) is a well−performing forward network with best approximation, simple training, fast learning convergence and the ability to overcome local minima problems. Combined with the advantages and disadvantages of LADRC, Adaptive Control and Neural Network, the coupling force between each channel, gust crosswind disturbance and additional resistance of offshore platform jitter in the flight state of the quadrotor are optimized. In the control, the RBF neural network is designed, the nonlinear control signal is wirelessly approximated and the uncertain disturbance to the quadrotor is identified online. Finally, the real−time estimation and compensation are performed by LESO to realize the full−attitude take−off of the quadrotor. In addition, this paper uses adaptive control to optimize the parameters of LADRC to reduce the problem of many LADRC parameters and difficulty to integrate. Finally, the robust control system mentioned in this paper is simulated and verified, and the simulation results show that the control scheme has the advantages of simple parameter adjustment and stronger robustness.

Asymptotic tracking with novel integral robust schemes for mismatched uncertain nonlinear systems

AbstractMotivated by the desire to extend the well‐known robust integral of the sign of the error (RISE) feedback control to handle both matched and mismatched disturbances simultaneously, two novel continuous integral robust control algorithms with asymptotic tracking performance will be constructed for a class of high‐order uncertain nonlinear systems. By skillfully introducing a set of filtered error variables and asymptotic filters as well as an auxiliary system, they will be integrated via an improved backstepping framework. Significantly, the virtual control law integrated at each procedure will pass through a novel asymptotic filter and then the filtered signal will be adopted in the subsequent backstepping iteration. Notably, one of the control algorithms is constructed via the integral of the sign of the filtered error variable introduced at each step, which makes it incalculable due to the unmeasurable states. In order to implement this controller, two measures for calculating the sign function in terms of the filtered error variable will be expounded. More importantly, the stability of the closed‐loop system under each controller will be strictly proved and meanwhile application examples will be performed to demonstrate the theoretical results.

Active Disturbance Rejection Control for Static Power Converters in Flexible AC Traction Power Supply Systems

Flexible traction power supply systems (FTPSSs) can solve problems in traditional systems and envision a promising future for rail transit power supply. The traction network voltage is determined by static power converters (SPCs), so the voltage control of SPCs is very important for the safe and stable operation of the system. The uncertainty of the train load, the power redistribution in the case of SPC disconnections from the network because of SPC internal faults, and the real-time cooperative control of multiple SPCs bring challenges to the voltage control of SPCs. Compared to classical error feedback control, active disturbance rejection control (ADRC) has better transient performance and immunity. An ADRC-based voltage-current dual-loop control strategy for SPCs is proposed in this paper. The equivalent block diagram and transfer function are deduced. The stability and immunity of the system are analyzed. Finally, the effectiveness and superiority of the proposed control strategy under different operating conditions are verified by simulation and experiment.

Rotating mirror servo system control based on modified sliding mode-active disturbance rejection controller

In order to improve the tracking accuracy and robustness of the rotating mirror servo system, a modified sliding mode-active disturbance rejection control (MSM-ADRC) strategy is proposed. Firstly, the structure and working principle of the rotating mirror servo system are analysed, and its mathematical model is established to prepare for the design of the controller. Then, a MSM-ADRC is proposed to reduce the influence of unknown disturbance and improve the tracking accuracy. Among them, the modified sliding mode extended state observation (MSM-ESO) is designed by replacing the traditional nonlinear function with the designed optimal control function, which enhances the observation accuracy of the system state quantity and total disturbance. Meanwhile, an improved approach law is proposed, and an improved sliding mode nonlinear error feedback control law (MSM-NLSEF) is designed based on this approach law, which improves the convergence speed and accuracy of the control law. In addition, the stability of the designed MSM-ESO and MSM-NLSEF is proved. Finally, the proposed control method is validated by simulation and experimental comparison with other state-of-the-art controllers. Results reveal that the proposed control method has satisfying tracking performance and strong disturbance rejection ability.

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.

Prescribed Performance Fault-Tolerant Control for Uncertain Nonlinear MIMO System Using Actor-Critic Learning Structure.

This article studies the prescribed performance fault-tolerant control problem for a class of uncertain nonlinear multi-input and multioutput systems. A learning-based fault-tolerant controller is proposed to achieve the asymptotic stability, without requiring a priori knowledge of the system dynamics. To deal with the prescribed performance, a new error transformation function is introduced to convert the constrained error dynamics into an equivalent unconstrained one. Under the actor-critic learning structure, a continuous-time long-term performance index is presented to evaluate the current control behavior. Then, a critic network is used to approximate the designed performance index and provide a reinforcement signal to the action network. Based on the robust integral of the sign of error feedback control method, an action network-based controller is developed. It is shown by the Lyapunov approach that the tracking error can converge to zero asymptotically with the prescribed performance guaranteed. Simulation results are provided to validate the feasibility and effectiveness of the proposed control scheme.

Robust output regulation of a thermoelastic system

In this paper, we consider the robust output regulation problem for the thermoelastic system where the boundary control input and the output are located at the left end of the wave equation and the disturbance input is located at the right end of the heat equation. We formulate the system as a boundary control system and prove that it is impedance passive and well-posed. We design a finite-dimensional controller based on the internal model principle and show that the controller can achieve robust output tracking and disturbance rejection. The numerical simulations demonstrate that the finite-dimensional dynamic error feedback controller can make the output track the reference signal asymptotically and the state of the closed-loop system is bounded.

An Adaptive Active Disturbance Rejection Control Strategy for Speed-Sensorless Induction Motor Drives

Speed-sensorless control of induction motor drives based on the extended state observer (ESO) attracts much popularity due to its key characteristics, e.g., satisfactory estimation performance, and high robustness against disturbances. However, the conventional ESO generally uses fixed high gains to achieve fast convergence. This may bring about the concern of noise sensitivity. Moreover, a proportional-integral (PI)-type speed controller is mostly adopted in speed-sensorless control of induction motor drives, which may cause unsatisfactory system dynamics. To address these, an adaptive active disturbance rejection control (ADRC) strategy is proposed for speed-sensorless induction motor drives in this article. In this scheme, a third-order adaptive ESO (AESO) is first used to estimate the speed, the phase, and the overall disturbance. Then, a speed controller based on the state error feedback control rate (SEFCR) is designed to improve system dynamics. In practice, disturbances like dc offsets may further challenge estimation performance, and hence, a closed-loop flux observer (CLFO) is employed to deal with this issue. Additionally, a parameter sensitivity analysis of the CLFO is also provided to evaluate the performance of the proposed scheme. Finally, extensive experimental tests have been carried out to validate the effectiveness of the proposed.

Error-feedback temperature regulation for a reverse flow reactor driven by a distributed parameter exosystem

This work is devoted to solve the state and error-feedback control problems for a catalytic reverse flow reactor (CFRR), which is modeled by nonlinear partial differential equations (PDEs). These two regulation problems will be solved based on the linearized infinite-dimensional representation. The objective is to track a desired output reference under the presence of disturbances. Both the reference trajectory and the disturbance profiles are generated by a distributed parameter exosystem. First, a state feedback stabilizing regulator is designed which drives the process output to a reference trajectory. The second main aim is to develop a dynamical controller that uses the tracking error as an input. Furthermore, it has been demonstrated that the closed-loop plant is exponentially stable and the tracking error asymptotically goes to zero. The developed regulators are evaluated through numerical simulations for the case study of methane combustion.