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This study focuses on the design of a fixed-time disturbance observer-based robust fault-tolerant tracking control scheme for an uncertain quadrotor unmanned aerial vehicle (UAV), which allows the quadrotor UAV to track a presupposed trajectory despite the simultaneous existence of model uncertainties, external disturbances, actuator faults, and input delay. First of all, the combination of Pade approximation and an intermediate variable is employed to reduce the complexity of studying the quadrotor system with input delay. Secondly, the fixed-time disturbance observer is proposed to eliminate the effects of the composite disturbances without requiring some serious assumptions. Subsequently, the new nonsingular fixed-time sliding mode manifold and the auxiliary system are developed to overcome the singular problem without any piecewise continuous functions. In the sense of the Lyapunov theorem, it is proved that the tracking errors of the closed-loop system converge to the origin within a fixed time regardless of the initial conditions. Eventually, extensive comparative simulations are performed to manifest the feasibility and validity of the proposed control strategy in terms of disturbance rejection, fault-tolerance, chattering elimination, and singularity-free.

The fixed-time stabilization of high-order integrator systems with both matched and mismatched disturbances is investigated. A continuous non-switching control law is designed based on the bi-limit homogeneous technique for arbitrary-order integrator systems. Combining with fixed-time disturbance observer, the proposed continuous control law for the system with matched and mismatched disturbances guarantees that the convergence time is uniformly bounded with respect to any initial states. Finally, the numerical results are provided to verify the efficiency of the developed method.

An accurate dynamic model of a robot is fundamentally important for a control system, while uncertainties residing in the model are inevitable in a physical robot system. The uncertainties can be categorized as internal disturbances and external disturbances in general. The former may include dynamic model errors and joint frictions, while the latter may include external payloads or human-exerted force to the robot. Disturbance observer is an important technique to estimate and compensate for the uncertainties of the dynamic model. Different types of disturbance observers have been developed to estimate the lumped uncertainties so far. In this paper, we conducted a brief survey on five typical types of observers from a perspective of practical implementation in a robot control system, including generalized momentum observer (GMO), joint velocity observer (JVOB), nonlinear disturbance observer (NDOB), disturbance Kalman filter (DKF), and extended state observer (ESO). First, we introduced the basics of each observer including equations and derivations. Two common types of disturbances are considered as two scenarios, that is, constant external disturbance and time-varying external disturbance. Then, the observers are separately implemented in each of the two simulated scenarios, and the disturbance tracking performance of each observer is presented while their performance in the same scenario has also been compared in the same figure. Finally, the main features and possible behaviors of each type of observer are summarized and discussed. This survey is devoted to helping readers learn the basic expressions of five typical observers and implement them in a robot control system.

This study proposes a novel nonlinear resilient trajectory control for a quadrotor unmanned aerial vehicle (UAV) using backstepping control and nonlinear disturbance observer. First, a nonlinear dynamic model for the quadrotor UAV that considers external disturbances from wind model uncertainties is developed. A nonlinear disturbance observer is then constructed separately from the controller to estimate the external disturbances and compensate for the negative effects of the disturbances. Based on the estimates from the given observer, a nominal nonlinear backstepping trajectory-tracking position controller is designed to stabilize the subsystems step by step until the ultimate control law is obtained. An extra term is added to the nominal controller to address the problem of actuator effectiveness loss and to ensure system resilience. The stability of the resilient controller is analyzed using Lyapunov stability theory. Simulation results are presented to demonstrate the effectiveness and robustness of the proposed nonlinear resilient controller.

In recent years, the agricultural applications of unmanned vehicles have garnered significant attention thanks to the rapid development of global positioning systems, inertial navigation technology, and control theory. In this study, a novel sliding mode controller for farm vehicles lateral path tracking control in the presence of unknown disturbances is created. Based on the standard kinematic model and the study of agricultural circumstances, the kinematic error model with unknown external disturbances and severe nonlinearity is initially constructed. To deal with the disturbances that exist in the lateral path tracking system, this work offers a finite-time disturbance observer-based composite terminal sliding mode control (FDOB-CTSMC). Meanwhile, the finite-time disturbance observer-based composite adaptive terminal sliding mode control (FDOB-CATSMC) is developed on the basis of the sliding mode filter and the adaptive control technology, which will significantly reduce the controller chattering issue. Using the Lyapunov theory, the finite-time convergence of the lateral deviation and the sliding variable can be verified. The numerical simulations demonstrate that the proposed controller is far better than the traditional path tracking controllers.

This paper studies the fractional-order disturbance observer (FODO)-based adaptive sliding mode synchronization control for a class of fractional-order chaotic systems with unknown bounded disturbances. To handle unknown disturbances, the nonlinear FODO is explored for the fractional-order chaotic system. By choosing the appropriate control gain parameter, the disturbance observer can approximate the disturbance well. On the basis of the sliding mode control technique, a simple sliding mode surface is defined. A synchronization control scheme incorporating the introduced sliding mode surface and the designed disturbance observer is then developed. Under the control of the synchronization scheme, a good synchronization performance is realized between two identical fractional-order chaotic systems with different initial conditions. Finally, the numerical simulation results illustrate the effectiveness of the developed synchronization control scheme for fractional-order chaotic systems in the presence of external disturbances.

This paper investigates the problem of fixed-time tracking control for a class of high-order nonlinear systems with matched disturbances. A novel continuous fixed-time sliding mode disturbance observer is first proposed to accurately estimate the external disturbances. Then, a new integral high-order sliding mode (IHOSM) surface is proposed in the sense of fixed-time stability by the bi-limit homogeneous method. Subsequently, utilizing the disturbance estimation information, an IHOSM-based fixed-time control scheme is proposed which can enforce the closed-loop control system reach the real sliding mode surface. Meanwhile, it is applied to an error dynamic system of a wheeled mobile robot to achieve fast accurate trajectory tracking. Finally, the comparative experiment results demonstrate the effectiveness and superiority of the proposed control approach.

In this paper, a nonlinear disturbance observer-based backstepping finite-time sliding mode control scheme for trajectory tracking of underwater vehicles subject to unknown system uncertainties and time-varying external disturbances is proposed. To reduce the influence of the uncertainties and external disturbances, a nonlinear disturbance observer is developed without any acceleration measurements to identify the lumped disturbance term. Additionally, the finite-time trajectory tracking controller is designed by combining second-order sliding mode control and backstepping design technique with the nonlinear disturbance observer. The finite-time convergence of motion tracking errors and the stability of the overall closed-loop control system are guaranteed by the Lyapunov approach. Besides, comprehensive simulation studies on trajectory tracking control of underwater vehicles are provided to demonstrate the effectiveness and performance of the proposed control scheme.

This paper investigates the leader–follower formation problem of multiple underactuated autonomous surface vessels in the presence of model uncertainties and environmental disturbances. Specially, the formation is defined in the body-fixed coordinates of the leader vessel and velocities of the leader are unavailable to followers. A novel robust adaptive formation control scheme based on the minimal learning parameter (MLP) algorithm and the disturbance observer (DOB) is presented. To address related formation configurations and unknown velocities of the leader, adaptive programming of the virtual vessel is introduced. By the neural networks (NNs) technique, the DOB is constructed and the formation controller is developed with different MLP-based adaptive laws. Under the proposed controller, it is shown that the desired formation can be achieved only with the position and yaw angle of the leader. And formation errors are guaranteed to be semiglobal uniformly ultimately bounded. Compared with existing results, the NNs-based DOB can compensate disturbances effectively with less model information. Meanwhile, the formation controller and the DOB can share the same set of NNs with smaller computational effort, where only two parameters need to be learned online for each of them. Simulations and comparison results are provided to illustrate the effectiveness of theoretical results.

This paper concerns the speed regulation problem for permanent magnet synchronous motor (PMSM) drive system with matched and mismatched disturbance. A novel single-loop speed and current control strategy with continuous integral-type terminal sliding mode control (ITSMC) and disturbance observer (DOB) is proposed. Firstly, the nonlinear motor model including the lumped disturbance is constructed. Then, by introducing a virtual control, a continuous integral-type sliding mode controller, which has the non-cascade structure, is developed based on terminal sliding mode surface, and it has the globally asymptotic stability based on Lyapunov criterion. However, when the drive system has large disturbance, especially for unmatched external disturbance, the performance of the whole system will be influenced. To further improve the anti-disturbance performance, a disturbance observer is introduced to estimate both the matched and mismatched disturbance in the system, and it is used for the feed-forward compensation, and the stability of the system is proved. Finally, the novel scheme is tested on a surface-mounted PMSM by experiment, and the comparative results in different operation conditions verify that the proposed method has the fast transient response and the strong robustness for the disturbance.