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The control of an aerial flexible joint robot (FJR) manipulator system with underactuation is a difficult task due to unavoidable factors, including, coupling, underactuation, nonlinearities, unmodeled uncertainties, and unpredictable external disturbances. To mitigate those issues, a new robust fixed-time sliding mode control (FxTSMC) is proposed by using a fixed-time sliding mode observer (FxTSMO) for the trajectory tracking problem of the FJR attached to the drones system. First, the underactuated FJR is comprehensively modeled and converted to a canonical model by employing two state transformations for ease of the control design. Then, based on the availability of the measured states, a cascaded FxTSMO (CFxTSMO) is constructed to estimate the unmeasurable variables and lumped disturbances simultaneously in fixed-time, and to effectively reduce the estimation noise. Finally, the FxTSMC scheme for a high-order underactuated FJR system is designed to guarantee that the system tracking error approaches to zero within a fixed-time that is independent of the initial conditions. The fixed-time stability of the closed-loop system of the FJR dynamics is mathematically proven by the Lyapunov theorem. Simulation investigations and hardware tests are performed to demonstrate the efficiency of the proposed controller scheme. Furthermore, the control technique developed in this research could be implemented to the various underactuated mechanical systems (UMSs), like drones, in a promising way.

This article presents a novel control approach for robust fixed-time trajectory tracking in nonlinear dynamic systems affected by external disturbances and model uncertainties, utilizing a fixed-time disturbance observer. Initially, a new fast disturbance observer was designed to reliably estimate external disturbances and model uncertainties within a fixed timeframe, independent of initial conditions and without requiring strict assumptions about the nature of these disturbances and uncertainties. Based on the disturbance estimates, a new robust fixed-time trajectory tracking sliding mode control strategy was developed, incorporating a fixed-time sliding variable and a reaching law with a state-dependent exponent coefficient. Using Lyapunov-based analysis, it is proven that the tracking errors of the closed-loop system converge to a neighborhood of the origin within a fixed time, independent of the initial conditions. Finally, comprehensive simulations were conducted to validate the effectiveness of the proposed strategy, demonstrating its advantages in achieving fast convergence, avoiding singularities, reducing chattering, and compensating for model uncertainties and external disturbances.

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.

This paper proposes a novel fixed-time prescribed performance sliding mode control method, specifically designed to address trajectory tracking issues in wheeled mobile robots (WMRs) affected by wheel slipping, skidding (WSS), and external disturbances. A new prescribed performance sliding surface is first introduced based on a prescribed performance function (PPF) and a non-singular fast terminal sliding function (NFTSF). This design ensures that tracking errors converge to zero within a fixed time while maintaining stability by keeping error states within predefined limits. A novel fixed-time prescribed performance non-singular fast terminal sliding mode control (FPP-NFTSMC) algorithm is proposed based on the sliding function. The control method integrates a uniform second-order sliding mode (USOSM) algorithm to provide a continuous control signal, effectively reducing the chattering effect. This method combines the benefits of PPF, NFTSMC, and USOSM algorithm to achieve high-precision position tracking, minimize chattering, guarantee fixed-time convergence, ensure tracking errors remain within bounds, and maintain robustness against WSS, and external disturbances. The fixed-time stability of the WMR systems is demonstrated by the Lyapunov stability theory. The effectiveness of the proposed method is validated through simulations of tracking straight-line and U-shaped trajectories.

This paper proposes a new fixed-time sliding mode (FSM) control, where the settling time for reaching the system origin is bounded to a constant independent of the initial condition; this is in contrast to the initial condition-dependent constants used in the traditional linear sliding mode (LSM) and terminal sliding mode (TSM) controls. First, a new sliding mode control with a single power term is discussed, where the power term can have any nonnegative value. Except for the traditional LSM and TSM controls, a new sliding mode control called power sliding mode (PSM) is proposed, whose power term is larger than 1. Then, a new FSM control with two power terms is investigated, whose design is based on the combination of TSM and PSM. In particular, the two power terms on the plane in the first quadrant are carefully discussed, and a detailed classification is provided. Here, the first quadrant can be classified into six categories, including LSM, generalized LSM, TSM, fast TSM (FTSM), PSM, and FSM. Furthermore, the analytical settling time is calculated, and three different estimation bounds of the settling time are given for reaching the origin under any initial condition. It is also interesting to derive the lowest bound for the settling time. Finally, FSM control design for general nonlinear dynamical systems with the relative degree from the control input to the output is also discussed.

The challenging tracking control issue for a space manipulator subject to parametric uncertainty and unknown disturbance is addressed in this paper. An observer-based fixed-time terminal sliding mode control methodology is put forward. Firstly, a nonlinear disturbance observer is introduced for exactly reconstructing the lumped uncertainty without requiring any prior knowledge of the lumped uncertainty. Meanwhile, the estimation time’s upper bound is not only irrelevant to the initial estimation error but can be directly predicted in advance via a specific parameter in the observer. Invoking the estimated information, a fast fixed-time tracking controller with strong robustness is designed, where a novel sliding mode surface incorporated enables faster convergence. The globally fixed-time stability of the closed-loop tracking system is rigorously demonstrated through Lyapunov stability analysis. Finally, numerical simulations and comparisons verify the validity and superiority of the suggested controller.

Aiming at the control problem for the speed regulation system of permanent magnet synchronous motor (PMSM), an integral fixed-time sliding mode control algorithm with the disturbance estimation compensation is designed to improve PMSM system’s disturbance rejection ability in this paper. First of all, the integral fixed-time sliding mode surface is selected according to the error dynamical equation. Then an integral fixed-time sliding mode control algorithm is proposed and rigorous analysis method of the Lyapunov function is provided to demonstrate the speed tracking error will converge to zero in a fixed time. Besides, considering the effect of disturbance load torque, an integral fixed-time sliding mode control algorithm with disturbance estimation compensation is proposed. Through disturbance feedforward compensation, the integral fixed-time sliding mode control law can offer a better dynamical performance with smaller value for the speed chattering. Finally, comparison results of numerical experiments are provided to verify the effectiveness and superiority of the integral fixed-time sliding mode control method.

In this work, the problems of active vibration suppression and high accuracy attitude control for a flexible satellite with piezoelectric actuators are studied. Firstly, the attitude error dynamic equation is developed. By utilizing a novel hyperbolic cosecant function and the error transformation equation, the attitude errors can be transferred into new prescribed performance state variables. In order to further ensure better convergence of the new variables, a fixed-time sliding mode control is proposed. Subsequently, a novel fully adaptive component synthesis vibration suppression method is presented to realize vibration suppression during the attitude maneuver by utilizing piezoelectric actuators. Stability analysis of the proposed prescribed performance control is given. Finally, abundant numerical simulation results demonstrate the excellent performances of the proposed control scheme.

This paper proposes a fixed-time method for the tracking control of a quadcopter subject to external disturbances. Compared with finite-time tracking control, the proposed control strategy ensures that the upper bound of the convergence time is independent of the initial state of the system. To determine the external disturbances, we have designed a fixed-time disturbance observer (FTDO). This allows the external disturbances to be compensated precisely, as a result of which the robustness of the control algorithm is enhanced, and the chattering problem is alleviated. We also propose a novel nonsingular fixed-time sliding mode control (FTSMC) technique to provide fixed-time position and attitude tracking control for the quadcopter, which enables a more accurate determination of the convergence time. We validated the fixed-time convergence of the proposed quadcopter tracking control method using Lyapunov stability theory. Finally, we verified the theoretical results not only by simulations but also by experiments.

Despite that multistable isolators have been demonstrated to achieve the superior isolation performance compared with the linear ones, their performances are still inferior at ultra-low frequencies with the multi-solution phenomenon. Furthermore, their performances are dependent on the variation of initial conditions. Therefore, this paper proposes a fast fixed-time sliding mode controller to solve the ineffectiveness of the bistable dual-stage vibration isolator with external disturbances facing the above issues. Firstly, the bistable dual-stage isolator is modelled in the analytical form, and simulated compared with its linear counterpart to show its problems at some conditions. Secondly, the fast fixed-time sliding mode controller is presented with the modeling of sliding manifold and control inputs. Thirdly, the numerical simulation of the bistable dual-stage isolator with the proposed control is conducted, the results of which are compared with the finite-time sliding mode control. Finally, the outstanding feature of the proposed controller is concluded that the short convergence time becomes bounded with increasing initial conditions at both low and high excitation amplitudes. This work provides a valuable method to improve the isolation performance and robustness of the multistable vibration isolators.