Error Feedback Control Research Articles

Adaptive RISE-based tracking control of uncertain nonlinear systems: A FAS approach

A fully actuated system (FAS) approach integrated with adaptive robust integral of the sign of the error (ARISE) feedback control strategy is proposed for multi-input multi-output nonlinear systems in the presence of both external disturbances and parametric uncertainties. Owing to an inability to eliminate unmeasured disturbances and model inaccuracies simultaneously, the existing results based on the FAS approaches are typically limited to the uniformly ultimate boundedness of the tracking errors. To achieve the asymptotic tracking performance confronted with parametric uncertainties and time-varying disturbances, an ARISE feedback controller with desired compensation is synthesized to suppress the adverse effects arising from nonlinearity and uncertainty of the system. The improvements compared to the traditional RISE feedback control are attributed to two aspects: (i) the feedback gains in the RISE term are adjustable-online without having to know the prior bounds of disturbances and their time derivatives; (ii) a desired compensation-based adaptive feedforward term, primarily employing the desired trajectories in place of the measured states, could weaken the underlying interaction between the adaptive compensation and robustness part. A rigorous stability analysis is provided to demonstrate that the system state can asymptotically track a bounded desired trajectory in spite of bounded disturbances and parametric uncertainties. Comparative simulations on an under-actuated planar manipulator, possessing an equivalent multi-order FAS model, have been conducted to verify the effectiveness and merits of the developed controller. Experimental validation on a two-wheeled self-balancing robot is also provided to show the feasibility of the proposed approach.

Resonance Suppression Method Based on Hybrid Damping Linear Active Disturbance Rejection Control for Multi-Parallel Converters

The parallel operation of multiple LCL-type converters will result in a deviation of the resonant frequency and resonance phenomena. The occurrence of harmonic resonance can cause problems such as an increase in harmonic voltage and current. This can lead to the malfunction of relay protection and automatic devices, causing damage to system equipment. In severe cases, it can cause accidents and threaten the safe operation of the power system. A hybrid damping active disturbance rejection control (HD-ADRC) method is proposed in this paper to suppress the harmonic resonance of parallel LCL-type converters. First, a third-order linear disturbance rejection controller (LADRC) including the linear extended-state observer and the error-feedback control rate is designed based on LCL-type converter model analysis. The proposed method considers the resonance couplings caused by both internal and external disturbances as the total disturbance, thus improving the anti-disturbance capabilities as well as the operational stability of converters in parallel. Then, a hybrid damping control is proposed to reconstruct the damping characteristics of converters to suppress the parallel resonance spike and reduce the resonance frequency offset. And the parameter selection of the control system is optimized through a stability analysis of the tracking performance and anti-disturbance performance of the HD-ADRC controller. Finally, all the theoretical considerations are verified by simulation and experimental results based on the Matlab/Simulink 2018B and dSpace platform. The simulation and experimental results show that the PI controller gives a THD of 5.33%, which is reduced to 4.66% by employing the HD-LADRC, indicating an improved decoupling between the converters working in parallel with the proposed control scheme.

Active Disturbance Rejection Control of Hydraulic Quadruped Robots Rotary Joints for Improved Impact Resistance

Hydraulic actuated quadruped robots have bright application prospects and significant research values in unmanned area investigation, disaster rescue and other scenarios, due to the advantages of high payload and high power to weight ratio. Among these fields, inevitable collision of robots may occur when contact with unknown objects, step on empty objects, or collapse, all of which have an impact on the working hydraulic system. To overcome the unknown external disturbances, this paper proposes an active disturbance rejection control (ADRC) strategy of double vane hydraulic rotary actuators for the hip joints of the quadruped robots. Considering the order of the valve-controlled actuator model, a three-stage tracking differentiator, a four-stage extended state observer, and a state error feedback controller are designed relatively, and the extended state observer is adopted to observe and compensate the uncertainty of external load torque of the system. The effectiveness of the ADRC method is verified in simulation environment and a single joint experimental platform. Moreover, the impact experiments of the limb leg unit are carried out after introducing the proposed ADRC strategy into hip joint, the limb leg unit of quadruped robots presents better impact resistance ability.

A semi-active adaptive pneumatic vibration isolator based on frequency response analysis and nonlinear control

In this work, an adaptive nonlinear error feedback controller based on fuzzy state observer is proposed to a novel rubber pneumatic vibration isolator (PVI) system. First, a novel rubber PVI system is designed and developed. Harmonic balance method is applied to establish the dynamic model of the PVI system, so as to analyze the frequency response characteristics of the system. Second, to improve the PVI performance in low-frequency vibration, a nonlinear state error feedback control system based on fuzzy state observer is designed for the active PVI system. Furthermore, the experiment system is established. Finally, through the experimental comparison under 5 Hz, 7 Hz, 20 Hz, and 40 Hz, an adaptive PVI strategy is proposed. The experimental results demonstrate that the adaptive PVI shows better performance in vibration isolation.

A Practical Approach to Alignment and Error Feedback Control for Long-Span Arch Bridges

The accurate installation of long-span arch bridges’ arch ribs remains a challenge due to the complex calculations required for cable forces and arch rib displacements, as well as the significant influence of environmental and construction loads. In this study, we propose a practical approach to alignment and error feedback control for long-span arch bridges. Cable forces were optimized using multiple control objectives based on influence matrix principles. The impact of temperature on the next segment to be installed was analyzed using the metastatic GM(1, 1) model and fitting results. Several tunable parameters were employed to account for parameter errors and environmental interference. These parameters were adjusted based on the deviations between practical and theoretical alignments for different arch rib segments, achieving a model output of an offset-free-tracking arch rib structure. This technology was applied to monitor the construction of the Tian’e Longtan Grand Bridge. Compared to conventional alignment control approaches, the proposed method achieved excellent arch ring alignment after the closure of the high-accuracy arch rib and cable release, as well as effective control of cable force uniformity and tower deviation. Field measurement data indicate that the closing deviation of the arch ring is only 3 mm. This study provides a valuable reference for the construction control of long-span arch bridges.

Space and time joint optimization for vertical takeoff and landing aircraft in dense obstacles and interference environments

ABSTRACT The Vertical Takeoff and Landing Aircraft (VTOL) is capable of both low-speed hovering and high-speed flight. This paper proposes an autonomous motion planning and anti-wind disturbance control algorithm for the VTOL, implemented spatial and temporal joint motion planning for VTOL, under the limitation of maximum flight speed of the aircraft, VTOL can achieve fully autonomous flight in complex environments, which can realize the autonomous flight of a single aircraft in a complex and dense environment, achieve real-time perception and avoidance of static and dynamic obstacles. The information generated by motion planning includes the position, velocity, and acceleration information of the aircraft, and proposes a wind disturbance estimation and active control strategy in a wind disturbance environment, accurate estimation of wind disturbance is achieved through a state observer, and the wind disturbance was suppressed through nonlinear error feedback control law, implemented wind disturbance estimation and suppression for aircraft in wind disturbance environments, and achieved complete autonomous motion planning and trajectory tracking of VTOL in a complex and wind disturbance environment. Our work can provide a basis for the collaborative control of multiple UAVs.

Fault-tolerant control of automatic carrier landing using direct lift control based on nonsingular terminal sliding mode and active disturbance rejection control

This paper presents a fault-tolerant control scheme, combining nonsingular terminal sliding mode and active disturbance rejection control (NTSM-ADRC) to address actuator failure and external disturbances during the automatic carrier landing process of a carrier-based aircraft using direct lift control (DLC). First, the carrier-based aircraft model, the carrier air-wake model, and the actuator fault model were established. Second, the NTSM-ADRC controller is designed, The unmodeled dynamics of the system, the air-wake disturbance, and the fault term are treated as total disturbances and estimated accurately by extended state observer (ESO). To improve the response characteristics of the controller, the nonlinear error feedback control law is designed by combining the NTSMC. The Lyapunov function is constructed to prove the stability of the closed-loop system. The controller is applied to the aircraft DLC channel, attitude auxiliary channel, and approach power compensation system. The DLC improves the performance of fixed-wing aircraft by directly generating high lift through the flaps to change the aircraft trajectory. Finally, the method is tested by introducing various types of actuator failures. Simulation results demonstrate that the designed longitudinal fault-tolerant carrier landing system exhibits strong robustness and fault tolerance, thereby improving the accuracy of aircraft landing trajectory tracking.

A novel intelligent RISE feedback control of autonomous tethered underwater vehicles: Design & real-time experiments

This paper deals with the tracking control problem of small autonomous tethered underwater vehicles. It proposes a new extended robust integral of the sign of the error (RISE) feedback control. The proposed RISE-based extension benefits from a fuzzy inference system to automatically and online tune the parameters of the RISE controller. The resulting intelligent control scheme is named Fuzzy RISE (FRISE) feedback control. Several real-time experimental scenarios, in different operating conditions, were conducted on Leonard underwater vehicle to demonstrate the efficiency and robustness of the proposed control scheme. It was also compared with some existing controllers from the literature to show its performances.

Adaptive Active Disturbance Rejection Control for Vehicle Steer-by-Wire under Communication Time Delays

In this paper, an adaptive active disturbance rejection control is newly designed for precise angular steering position tracking of the uncertain and nonlinear SBW system with time delay communications. The proposed adaptive active disturbance rejection control comprises the following two elements: (1) An adaptive extended state observer and (2) an adaptive state error feedback controller. The adaptive extended state observer with adaptive gains is employed for estimating the unmeasured velocity, acceleration, and compound disturbance which consists of system parameter uncertainties, nonlinearities, exterior disturbances, and time delay in which the observer gains are dynamically adjusted based on the estimation error to enhance estimation performances. Based on the accurate estimations of the adaptive extended state observer, the proposed adaptive full state error feedback controller is equipped with variable gains driven by the tracking error to develop control precision. The integration of the advantages of the adaptive extended state observer and the adaptive full state error feedback controller can improve the dynamic transient and static steady-state effectiveness, respectively. To assess the superior performance of the proposed adaptive active disturbance rejection control, a comparative analysis is conducted between the proposed control scheme and the classical active disturbance rejection control in two different cases. It is worth noting that the active disturbance rejection control serves as a benchmark for evaluating the performance of the proposed control approach. The results from the comparison studies executing two simulated cases validate the superiority of the suggested control, in which estimation, tracking response rate, and steering angle precision are greatly improved by the scheme proposed in this article.

Sensorless control of permanent magnet synchronous motor based on adaptive enhanced extended state observer

SummaryThis article proposes an enhanced adaptive disturbance rejection control strategy for sensorless control of permanent magnet synchronous motor. The traditional fixed bandwidth quadrature phase‐locked loop (Q‐PLL) is insufficient to meet system dynamics in the event of sudden speed changes or motor disturbances, resulting in a significant decrease in control performance. Meanwhile, conventional extended state observers usually rely on a fixed high gain for fast convergence, which raises concerns about their sensitivity to noise. To overcome these challenges, the proposed method introduces a third‐order adaptive cascaded linear extended state observer (ACLESO) in place of the conventional PLL to accurately estimate the speed, phase, and overall disturbances, ensuring timely and accurate estimation of the total disturbance. Then, a speed controller based on linear state error feedback control law (LSEFCL) was designed to enhance the dynamic performance of the system. Based on the stability analysis using the Lyapunov function, finally, extensive experimental tests were carried out to verify the validity of the proposed method.

Trajectory tracking control of autonomous vehicles based on Lagrangian neural network dynamics model

The autonomous vehicles make decisions and plans based on the environmental perception and generate the target command of the control layer. The vehicle dynamics model is an important factor that affects the vehicle control. The dynamic mechanism model has strong interpretability and good stability. However, in extreme conditions, the model accuracy is reduced due to the tire entering the nonlinear region. The data-driven dynamic model achieves high modeling accuracy. However, due to the lack of physical constraints and rationality in the data-driven models, the interpretability and stability of the control is reduced, which in turn increases the unpredictable risk in the driving process. This paper innovatively proposes a deep Lagrangian neural network dynamics model (DeLaN) for autonomous vehicles based on the Lagrangian mechanics and uses a neural network to encode the differential equations. This not only retains the interpretability of the physical model but also makes full use of the learning ability and fitting ability of the neural network to effectively capture the complex dynamic characteristics of the vehicle. To improve the robustness of the control system, this work uses DeLaN as feed-forward control and preview error feedback control to form a closed loop of trajectory tracking control for autonomous vehicles. The experimental results show that the trajectory tracking error of the proposed DeLaN is significantly reduced, the yaw stability and comfort are significantly improved, good longitudinal and lateral cooperative control performance is achieved, and the physical rationality of the neural network is also improved. Therefore, the proposed DeLaN has important engineering application value.

Robust Adaptive Leader-Following Formation Control of Nonlinear Multiagents Using Three-Layer Neural Networks.

This article studies a formation control problem for a group of heterogeneous, nonlinear, uncertain, input-affine, second-order agents modeled by a directed graph. A tunable neural network (NN) is presented, with three layers (input, two hidden, and output) that can approximate an unknown nonlinearity. Unlike one- or two-layer NNs, this design has the advantage of being able to set the number of neurons in each layer ahead of time rather than relying on trial and error. The NN weights tuning law is rigorously derived using the Lyapunov theory. The formation control problem is tackled using a robust integral of the sign of the error feedback and NNs-based control. The robust integral of the sign of the error feedback compensates for the unknown dynamics of the leader and disturbances in the agent errors, while the NN-based controller accounts for the unknown nonlinearity in the multiagent system. The stability and semi-global asymptotic tracking of the results are proven using the Lyapunov stability theory. The study compares its results with two others to assess the effectiveness and efficiency of the proposed method.

Unified synchronization and fault‐tolerant anti‐disturbance control for synchronization of multiple memristor‐based neural networks

SummaryThis work primarily concentrates on the design of fault‐tolerant anti‐disturbance control for synchronization of multiple memristor‐based neural networks subject to time delay, matched and mismatched disturbances. Moreover, in the addressed network model, we consider parameter uncertainties and actuator faults. Firstly in order to estimate the matched disturbances generated by the exogenous system, a disturbance observer is devised. Whereas, the mismatched part is tackled by employing the mixed and passivity performance indexes. Subsequently, a unified controller is designed by incorporating error feedback control and the disturbance estimate. Further, with the assistance of Lyapunov stability theory and linear matrix inequality technique, an adequate criteria is procured to ascertain the required synchronization criteria for the assayed network model with the mixed and passivity performance indexes. Following this, by basing on the established conditions, the explicit form of the controller and observer gain matrices is obtained. In the end, a numerical example with simulation results is shown to confirm the potential and usefulness of the conclusions acquired from the theoretical analysis.

Adaptive error feedback regulator problem for a 1-D wave equation with velocity recirculation

In this paper, we consider the error feedback regulator problem for a 1-D wave equation with velocity recirculation. There are harmonic disturbances in all channels of the system and the reference signal is also a harmonic type. We first introduce an invertible transformation such that the disturbances are only on the left boundary, which is non-collocated with the control. Then we propose an adaptive error-based observer by utilizing the measurable non-collocated tracking error and its derivative. Next, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and make all internal signals bounded. Finally, the results are illustrated with simulations.

Trajectory Tracking Control of Pneumatic Servo System: A Variable Gain ADRC Approach.

In this article, a novel error-driven variable gain active disturbance rejection control (ADRC) approach is developed for pneumatic servo system, and the desired performance of trajectory tracking and the disturbance rejection can be guaranteed. The proposed variable gain ADRC includes three parts: 1) variable gain tracking differentiator (TD); 2) variable gain extended state observer (ESO); and 3) variable gain error feedback controller (EFC). The proposed variable gain TD is noise tolerant and possesses a variable gain, which can be dynamically adjusted according to the tracking error, and the performance for tracking the reference signal and extracting its derivative is improved. The variable gain ESO is also equipped with a variable gain driven by estimation errors to improve the estimation performance. Then, the variable gain EFC is further designed to improve control accuracy. Finally, simulations and experimental results are presented to verify the efficiency of the proposed methods.

Super-Twisting Sliding Mode Active Disturbance Rejection Control of Permanent Magnet Synchronous Motor Based on Vector Control

The vector control speed regulation system of the permanent magnet synchronous motor founded on traditional control has some weaknesses of poor rapidity and robustness, and it is hard to satisfy the current control requirements. A new control method combining active disturbance rejection control technology with improved super-twisting sliding mode control technology (STSM-ADRC) comes up. In active disturbance rejection control, the tracking differentiator is simplified; the extended state observer is designed to observe all internal and exterior disturbances of the system; the improved super-twisting sliding mode control law is going to take the place of the error feedback control law; and the simulation is carried out. Compared with the existing control algorithms, this new control method can overcome the influence of load disturbances and track the given speed effectively. And the responsiveness and robustness of the system are strengthened.

Active Disturbance rejection Hopf bifurcation suppression strategy based on DC microgrid DC-DC converter

To solve the problem that the output voltage of the Buck converter is easily affected by the change of system parameters, which reduces the energy transmission quality, a linear active disturbance rejection control strategy is proposed in this paper. Firstly, a discrete mathematical model is established to analyze that Hopf bifurcation disturbance is the cause of low-frequency oscillation of output voltage, and the existence of Hopf bifurcation disturbance is verified by simulation. Secondly, based on the theoretical analysis, the suppression effect of improving the error feedback control rate on Hopf bifurcation disturbance is designed. Moreover, the stability of the control strategy under Hopf bifurcation disturbance is analyzed by using frequency-domain theory. Finally, the suppression of Hopf bifurcation disturbance by the proposed control strategy and the traditional PI control strategy under different working conditions is compared by simulation analysis. The results show that the proposed linear active disturbance rejection control strategy can effectively suppress Hopf bifurcation disturbance and guarantee the performance of the Buck converter.

Disturbance Rejection Speed Control Based on Linear Extended State Observer for Isokinetic Muscle Strength Training System

Isokinetic muscle strength training is a type of rehabilitation therapy that can effectively improve the motor dysfunction of limbs and enhance joint muscle strength. In active isokinetic training, how to plan the speed reasonably and improve the performance of speed control to fit individualized needs is the core problem of isokinetic muscle strength training equipment control. In this study, a control strategy for isokinetic muscle strength training equipment is proposed, which identifies the user&#x2019;s motion intention and performs speed planning according to the user&#x2019;s motion participation so that the equipment produces a dynamic damping effect. This ensures active interaction between the user and the equipment and meets the force-speed requirements of elbow joint muscle training. To handle the uncertain disturbance in the training process, a linear extended state observer is used to estimate the disturbance term, and a tracking differentiator and nonlinear error feedback control are used to improve the speed tracking performance. The experimental results show that the proposed control scheme realizes effective speed control in isokinetic muscle strength training. <i>Note to Practitioners</i>&#x2014;The bottleneck of isokinetic muscle strength training equipment control system lies in how to plan the speed according to the patient&#x2019;s movement intention reasonably, and how to improve the performance of speed control in the process of rehabilitation training. This paper designs a speed auto disturbance rejection control strategy for isokinetic muscle strength training system with external interference and model uncertainty in practical application. The experimental results show that the performance of the controller is better than the traditional PI controller, and it can realize isokinetic muscle training. This study provides a method for practitioners interested in developing control systems for isokinetic rehabilitation training equipment.

Observer‐based robust control for N‐coupled wave equations

AbstractIn this article, we consider robust output regulation for an MIMO wave system with disturbance and reference produced from an exosystem. The approach we adopt is the observer‐ based approach from partial differential equation (PDE) perspective. The main differences from our previous works are two points: (a) the eigenvalues of the exosystem are not necessarily required to be algebraically simple; (b) tracking error feedback dynamic controls are designed directly from the uncertain PDE itself, not a nominal system where disturbance and reference are specially chosen so that the nominal waves and exosystem are detectable. To this purpose, we introduce transformations to transfer the original system into a disturbance free system, and at the same time, each reference is transformed into a linear combination of the exosystem. An observer is designed to estimate the states of the transformed disturbance free system and the unknown linear combinations of the exosystem. The feedforward controls are designed where the input disturbances are then written based on the linear combinations of the exosystem. A set of observer‐based feedback controls is then designed by replacing the state and disturbance with their estimates from the observer. The robustness of the closed‐loop system is discussed by analyzing the stability of the transformed tracking error system and the observer error system. The numerical simulations are presented to validate visually the effectiveness of the proposed tracking error feedback control.

Robust error feedback output regulation of a 2 × 2 hyperbolic system

Abstract In this paper, we consider the robust error feedback output regulation problem for a linear $ 2 \times 2 $ hyperbolic system with system uncertainties and disturbance signals. Using the backstepping method, the state feedback controller for the system without the system uncertainties and the external disturbance signals (nominal system) is designed. In terms of the measurable regulation error, an observer system is designed to recover the state of the nominal system, and an observer-based error feedback controller is obtained to solve the robust output regulation problem. Moreover, we prove that the controller is robust to the system uncertainties and the disturbance signals, and show that the state of the closed-loop system is bounded. The numerical simulations are presented to illustrate the effectiveness of the theoretical results.