Finite-time Extended State Observer Research Articles

Fast Finite-Time Composite Controller for Vehicle Steer-by-Wire Systems with Communication Delays

The modern steer-by-wire (SBW) systems represent a revolutionary departure from traditional automotive designs, replacing mechanical linkages with electronic control mechanisms. However, the integration of such cutting-edge technologies is not without its challenges, and one critical aspect that demands thorough consideration is the presence of nonlinear dynamics and communication network time delays. Therefore, to handle the tracking error caused by the challenge of time delays and to overcome the parameter uncertainties and external perturbations, a robust fast finite-time composite controller (FFTCC) is proposed for improving the performance and safety of the SBW systems in the present article. By lumping the uncertainties, parameter variations, and exterior disturbance with input and output time delays as the generalized state, a scaling finite-time extended state observer (SFTESO) is constructed with a scaling gain for quickly estimating the unmeasured velocity and the generalized disturbances within a finite time. With the aid of the SFTESO, the robust FFTCC with the scaling gain is designed not only for ensuring finite-time convergence and strong robustness against time delays and disturbances but also for improving the speed of the convergence as a main novelty. Based on the Lyapunov theorem, the closed-loop stability of the overall SBW system is proven as a global uniform finite-time. Through examination across three specific scenarios, a comprehensive evaluation is aimed to assess the efficiency of the suggested controller strategy, compared with active disturbance rejection control (ADRC) and scaling ADRC (SADRC) methods across these three distinct driving scenarios. The simulated results have confirmed the merits of the proposed control in terms of a fast-tracking rate, small tracking error, and strong system robustness.

Finite-time extended state observer enhanced nonsingular terminal sliding mode control for buck converters in the presence of disturbances: design, analysis and experiments

Finite-time extended state observer enhanced nonsingular terminal sliding mode control for buck converters in the presence of disturbances: design, analysis and experiments

Distributed Lyapunov-Based Model Predictive Control for AUV Formation Systems with Multiple Constraints

This paper focuses on the formation tracking issue of autonomous underwater vehicles (AUVs) subject to multiple constraints in three-dimensional space. We developed a novel distributed Lyapunov-based model predictive controller (DLMPC) with a fast finite-time extended state observer (FFTESO). Initially, the external disturbances and internal uncertainties of each AUV were precisely compensated using the designed FFTESO. Subsequently, we proposed DLMPC-based position tracking and velocity tracking controllers, which solved an online optimization problem to determine optimal velocities and control forces. This hierarchical framework effectively managed system constraints, such as state constraints and actuator saturation. Additionally, the Lyapunov-based backstepping control law was applied to construct stability constraints in the distributed optimization problem, ensuring the recursive feasibility and closed-loop system stability of the proposed scheme. Sufficient conditions and attraction regions to ensure stability were explicitly provided. Finally, the simulation results demonstrated that the proposed method improved both the convergence speed and tracking accuracy by at least 30% compared to other methods.

FTESO-adaptive neural network based safety control for a quadrotor UAV under multiple disturbances: algorithm and experiments

PurposeQuadrotors have been applied in various fields. However, because the quadrotor is subject to multiple disturbances, consisting of external disturbances, actuator faults and parameter uncertainties, it is difficult to control the unmanned aerial vehicle (UAV) to achieve high-precision tracking performance. This paper aims to design a safety controller that uses observer and neural network method to improve the tracking performance of UAV under multiple disturbances. The experiments prove that this method is effective.Design/methodology/approachFirst, to actively estimate and compensate the synthetic uncertainties of the system, a finite-time extended state observer is investigated, and the disturbances are transformed into the extended state of the system for estimation. Second, an adaptive neural network controller that does not accurately require the dynamic model knowledge is designed based on the estimated value, where the weights of the neural network can be dynamically adjusted by the adaptive law. Furthermore, the finite-time bounded convergence of the proposed observer and the stability of the system are proved through homogeneous theory and Lyapunov method.FindingsThe figure-“8” climbing flight simulation and real flight experiments illustrate that the proposed safety control strategy has good tracking performance.Originality/valueThis paper proposes the safety control structure of the UAV, which combines the extended state observer with the neural network method. Numerical simulation results and actual flight experiments demonstrate the effectiveness of the proposed control strategy.

An Improved Super-Twisting Sliding Mode Composite Control for Quadcopter UAV Formation

Aiming at the nonlinear and multiple disturbances in the multi-quadcopter UAV system, this paper proposes a leader–follower composite formation control strategy based on an improved super-twisted sliding mode controller (ISTSMC) and a finite-time extended state observer (FTESO). For the designed sliding mode control algorithm, the integral term’s switching function is replaced with a non-smooth term to reduce the vibration in the control, further improving the overall performance of the system. For external disturbances, the finite-time extended state observer achieves rapid and accurate observation of external disturbances. Finally, through formation control experiments, the reliability and superiority of the proposed composite formation controller (CFC) is validated.

Smooth Sliding Mode Control for Path Following of Underactuated Surface Vehicles Based on LOS Guidance

In this paper, a solution to the problem of following a curved path for underactuated unmanned surface vehicles (USVs) with unknown sideslip angle and model uncertainties is studied. A novel smooth sliding mode control (SSMC) based on a finite-time extended state observer (FTESO) for heading control is proposed. Firstly, the model of a USV with rudderless double thrusters is established. Secondly, the path-following error dynamics of a USV is established in a path-tangential reference frame. Thirdly, a finite-time observer is introduced to estimate the unidentified sideslip angle, and the line-of-sight (LOS) guidance law is applied to produce the desired heading angle. Finally, an SSMC controller is proposed to force USV tracking at the desired heading angle and surge speed, in which FTESO is used to estimate and compensate the unknown disturbance in sliding mode dynamics. The theoretical analysis for FTESO-SSMC verifies that the controller can provide finite-time convergence to and stability on the sliding surface. Simulation studies and contrast test are conducted to demonstrate the robustness and rapidity of the proposed FTESO-SSMC controller.

Distributed Dual Closed-Loop Model Predictive Formation Control for Collision-Free Multi-AUV System Subject to Compound Disturbances

This paper focuses on the collision-free formation tracking of autonomous underwater vehicles (AUVs) with compound disturbances in complex ocean environments. We propose a novel finite-time extended state observer (FTESO)-based distributed dual closed-loop model predictive control scheme. Initially, a fast FTESO is designed to accurately estimate both model uncertainties and external disturbances for each subsystem. Subsequently, the outer-loop and inner-loop formation controllers are developed by integrating disturbance compensation with distributed model predictive control (DMPC) theory. With full consideration of the input and state constraints, we resolve the local information-based DMPC optimization problem to obtain the control inputs for each AUV, thereby preventing actuator saturation and collisions among AUVs. Moreover, to mitigate the increased computation caused by the control structure, the Laguerre orthogonal function is applied to alleviate the computational burden in time intervals. We also demonstrate the stability of the closed-loop system by applying the terminal state constraint. Finally, based on a connected directed topology, comparative simulations are performed under various control schemes to verify the robustness and superior performance of the proposed scheme.

Robust MPC-based trajectory tracking of autonomous underwater vehicles with model uncertainty

A robust model predictive control (MPC) method with dual closed-loops is presented to handle trajectory tracking of autonomous underwater vehicle (AUV) with uncertain model parameters and random external perturbations. First, constraint conditions are set for the motion state and control input of the underwater vehicle based on its motion characteristics. The position controller takes the velocity increment as input, thus providing a smoothly varying desired velocity for the velocity controller. The velocity controller comprises nominal MPC and a nonlinear auxiliary control law to overcome the effect of random perturbations on AUV tracking control. Then, a finite-time extended state observer (FTESO) is designed to compensate for dynamic model uncertainty. Furthermore, Lyapunov stability theory is employed to analyse the stability of the controller and FTESO. Ultimately, through comparative simulation experiments, the proposed control framework's effectiveness and robustness are verified, proving it to be a feasible AUV trajectory tracking control method.

Output Constrained Control of Lower Limb Exoskeleton Based on Knee Motion Probabilistic Model With Finite-Time Extended State Observer

Due to randomness and uncertainty of individual walking gait, this study uses the sparse Gaussian process (SGP) to construct a knee motion probabilistic model related to its corresponding hip motion. Since the SGP can quantify output uncertainty, a time-varying constrained boundary of knee position is presented to guarantee the operator's safety and comfort in human-exoskeleton cooperative motion. First, a low-cost gait acquisition system (called CJD-1) composed of inertial measurement unit is constructed to collect the operator's gait information. Then, a virtual interaction torque field and an output-dependent universal barrier function are designed to realize the coordinated transformation of the time-varying constrained boundary generated by the SGP. Hence, the exoskeleton joint position is constrained by the desired output constrained boundary, which is complied with the operator's gait law. Then, a backstepping controller with a finite-time extended state observer is proposed to estimate and compensate unmeasured joint velocity and lumped uncertainty. The effectiveness of the proposed control scheme is verified by both simulations and experimental results of human-exoskeleton cooperative motion.

Safety-Guaranteed, Robust, Nonlinear, Path-Following Control of the Underactuated Hovercraft Based on FTESO

On account of the external disturbances and difficult maneuverability of a hovercraft, this paper devises a safety-guaranteed, robust, nonlinear, path-following control strategy of a hovercraft targeted for unknown dynamics, unavailable velocity, and unknown external ocean disturbances. Firstly, for the sake of accurately observing unavailable lumped disturbances and unavailable velocity measurements, a finite-time extended state observer (FTESO) is proposed. Secondly, a line-of-sight (LOS) guidance law constructed with a bounded-gain-forgetting (BGF) adaptive estimator is devised to follow the desired path while considering external environmental disturbances accurately, in which the tracking errors and the parameter estimation are both proven to be bounded. In addition, for the sake of safety, a safety-guaranteed auxiliary system that can constrain the drift angle during the hovercraft’s navigation is proposed. Thirdly, the robust, nonlinear, path-following controllers achieved high tracking performance with the constructed safety-guaranteed compensation backstepping method. Finally, according to the Lyapunov and homogeneous theories, the observation error can be guaranteed to zero and the tracking error can converge to an arbitrarily small region near zero in finite time. Numerical simulations illustrate the effectiveness for the proposed robust, nonlinear, path-following scheme.

Finite-Time Fault-Tolerant Control for Swashplate of Integrated Hydraulic Transformer With Uncertain Mismatched Interference

The precision position control for the swashplate servomechanism of the integrated hydraulic transformer (IHT) with mismatched interference is considered in this paper. Compared with the type of port-plate-rotating IHT, the swashplate-rotating IHT has smaller leakage and higher efficiency, but suffers from parameters uncertainty, and time-varying uncertain torque from the plungers. To enhance the robustness of the proposed system, a novel robust control scheme based on a finite-time extended state observer (FTESO) is developed. In the proposed control scheme, the system nonlinearities, parameter uncertainty, actuator failure are both taken into account. And a novel FTESO is established to obtain the state variables, load torque, and failure signals. By introducing the nonsingular terminal sliding mode surface and finite-time technique in each step of the backstepping design, the novel control scheme is able to enhance the robustness of servomechanism and realize finite-time stability of the tracking errors. Finally, the comparative experiment is performed to verify the effectiveness of the controller design.

Piecewise Compensation Model Predictive Governor Combined With Conditional Disturbance Negation for Underactuated AUV Tracking Control

With respect to the accurate tracking control for autonomous underwater vehicles (AUVs), this paper proposes a novel control architecture consisting of piecewise compensation model predictive governor and conditional disturbance negation-based active disturbance rejection controller. The designed piecewise compensation mechanism is implemented to eliminate the steady tracking errors resulting from the underactuation problem of AUVs, and the model predictive governor aims to generate reference tracking velocities satisfying the constraints. Concurrently, a finite-time extended state observer is designed to improve the convergence performance of the estimation errors. In addition, the concept of conditional disturbance negation is employed to endow AUVs with the capability of taking advantage of disturbances rather than only rejecting disturbances. Finally, comprehensive analyses of the simulations and the experiments demonstrate the impressive control performance, verifying the feasibility of potential applications on real AUVs.

Finite-Time Refined Antidisturbance Velocity Tracking Control for Gimbal System of Control Moment Gyros With Harmonic Drive

This paper is concerned with high-precision and fast velocity-tracking control for the harmonic drive-based gimbal system of control moment gyro (CMG). As a major challenge in the controller design, the simultaneous presence of multiple matched and mismatched disturbances should be carefully addressed. Specifically, the rotor imbalance inherent in the CMG will cause vibration of the output torque that significantly degrades the tracking performance. On the other hand, the integration of harmonic drives will lead to nonlinear torsional stiffness and introduce additional frictions into the control system. Furthermore, practical tasks such as fast attitude maneuver have posed higher requirement on the rapidity of the anti-disturbance control schemes. To overcome the aforementioned difficulties, we propose a finite-time refined anti-disturbance velocity tracking controller, which consists of a finite-time harmonic disturbance observer (FTHDO) to compensate for the imbalance vibration, an adaptive finite-time extended state observer (AFTESO) to handle the remaining disturbances with unknown rate of change, and a finite-time controller to ensure fast convergence of the tracking error. Both numerical simulation and hardware-in-the-loop (HIL) experimental results show that the proposed scheme outperforms the existing methods in terms of accuracy and rapidity.

High-Precision Finite-Time Positioning Control for an Inertial Reference Unit With Asymmetric Loads and Mover Sideslip

In this article, a finite-time controller is designed on high-precision positioning for an inertial reference unit (IRU) with asymmetric loads and mover sideslip based on a finite-time extended state observer (ESO). The asymmetric loads caused by centroid deviation from central axis are a negative factor, which results in a negative load torque for IRUs. The mover sideslip is another negative factor that brings about output forces errors between actual output forces and theoretical output forces for voice coil motors. The finite-time ESO is designed to estimate and compensate the asymmetric loads and mover sideslip. The finite-time controller is proposed with high convergence rate for the IRU. Experimental results are presented to show effectiveness of the proposed finite-time control method in high-precision positioning under asymmetric loads and mover sideslip.

Output-Feedback Flexible Performance-Based Safe Formation for Underactuated Unmanned Surface Vehicles

This article studies a cooperative time-varying formation of underactuated unmanned surface vehicles (USVs) with position-heading measurements, following the philosophies of (i) balance operation between performance constraints and safety requirements including collision avoidance and connectivity maintenance, and (ii) concise finite-time control design based on the integrated finite-time extended state observer (IFTESO) to facilitate the practical implementation. At first, to accomplish the guidance design of networked vehicles in the complex ocean environment and guarantee the performance of cooperative tracking errors, a flexible performance-based control scheme is investigated by feeding the potential effects of safety requirements into the modification signals of the user-specified performance functions. Then, without the application of cumbersome nonlinear tracking differentiators and backstepping techniques, a output-feedback IFTESO-based method provides a concise solution with a convenient design by taking advantage of homogeneous system theories, which further reduces the traditional computation consumption. Finally, the performance of the proposed scheme is validated by numerical simulations.

Finite-time ESO-based cascade-free FCS-MPC for NNPC converter

This article addresses a novel finite control-set model predictive control solution for nested neutral point-clamped converter. More specifically, it is formed by incorporating a finite-time extended state observer design into a cascade-free finite control-set model predictive control architecture. In this architecture, a finite-time extended state observer is developed to estimate the total disturbances, and an integral error term and a dynamic reference design point of view are embedded into the proposed design so as to improve the performance. The main features of this proposal are: first of all, the detailed knowledge of the physical structure of the controlled plant is not required; second, a cascade-free structure is achieved in finite control-set model predictive control solution without weighting factors and steady-state error; and third, the proposed methodology can operate with different systems not just power converters, while keeping the fast transient response. In contrast to existing finite control-set model predictive control approaches, it can be found that our modification not only can track fast to their references but also can have superior robustness performance. Finally, the proposed solution is verified by comprehensive results that prove the theoretical researches for nested neutral point-clamped converter, while meeting the harmonic standards.

Finite-time extended state observer based collision-free leaderless formation control of multiple AUVs via event-triggered control

Finite-time extended state observer based collision-free leaderless formation control of multiple AUVs via event-triggered control

Finite time extended state observer based nonsingular fast terminal sliding mode control of flexible-joint manipulators with unknown disturbance

To solve the problems concerning with finite time trajectory tracking of the flexible-joint manipulator subject to unknown disturbance, a singular perturbation theory (SPT) based decoupling controller is proposed in this paper. SPT is employed to decouple the basic dynamic model of the flexible-joint manipulator into a fast subsystem and a slow subsystem. For the slow subsystem, a finite time extended state observer (FTESO) is proposed to estimate the unknown disturbance. In order to avoid the singularity and accelerate the convergence speed of terminal sliding mode controller (TSMC), a novel nonsingular fast terminal sliding mode controller (NFTSMC) is designed to achieve finite time trajectory tracking. Besides, to attenuate the chattering effect, a nonsingular terminal sliding mode controller (NTSMC) is introduced for the fast subsystem. Finally, the finite time stability of the closed-loop system is proven by means of the Lyapunov theory and some comparative simulations are performed to verify the effectiveness of the proposed controller.

Trajectory Tracking of UAVs Using Sigmoid Tracking Differentiator and Variable Gain Finite-Time Extended State Observer

The problem of quadrotor attitude and position control is considered in the presence of generally lumped disturbances: external disturbances and model uncertainty. The improved active disturbance rejection controller (ADRC) for quadrotor trajectory tracking is proposed for compensating the lumped disturbances. Firstly, the improved sigmoid tracking differentiator (ISTD), combining improved Sigmoid function and sliding mode terminal attractor is proposed, which can accelerate the global convergence rate and effectively reduce the chattering. Secondly, a novel variable gain finite-time extended state observer (VGFESO) approach is proposed to effectively estimate the lumped disturbances, while the observation errors are convergent to zero in finite time. Then, a super-twisting sliding model controller (STWSMC) is utilized for tracking control of the desired position and attitude. Finally, the convergence of VGFESO and the closed-loop stability of the control system are proved. The results show that the convergence time of the proposed control scheme is the shortest, and the integral absolute error of improved ADRC is reduced from 2.64 to 0.91. The anti-disturbance capability of the proposed controller is fully illustrated when compared with ADRC and robust adaptive nonsingular fast terminal sliding-mode controller (RANFTSMC).

Finite-Time Extended State Observe Based Fault Tolerant Control for Autonomous Underwater Vehicle with Unknown Thruster Fault

This paper investigates the problem of fault tolerant control (FTC) for autonomous underwater vehicles (AUVs) with multiple thrusters in the presence of current disturbances, thruster faults, and modelling uncertainty. This paper focuses on the problems of reducing the energy consumption caused by the chattering of control signals and improving the tracking accuracy of an AUV operating in deep-sea environments. In view of the problem of large energy consumption in some other methods, a fault tolerant control method for multiple-thruster AUVs based on a finite-time extended state observer (FTESO) is proposed. More specifically, a FTESO based on an integral sliding mode surface is designed to estimate the generalized uncertainty compounded using current disturbances, thruster faults, and modelling uncertainty. The fast finite-time uniformly ultimately bounded stability of the proposed FTESO is analyzed. Then, based on the estimated value of FTESO, an FTC method based on non-singular fast terminal sliding mode surfaces is developed for AUVs. The finite-time convergence of the closed-loop control system is proved theoretically. In this design, two different sliding mode surfaces are used to design FTESO and FTC, in order to avoid the appearance of singularities. Moreover, a parameter adjustment method is designed to improve tracking accuracy. Finally, comparative numerical simulations show that the proposed control scheme is effective at reducing energy consumption and improving tracking accuracy.