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This study investigates a new chattering-free robust predefined-time sliding mode control (CFRPSMC) scheme for the trajectory tracking control problem of a three-degree-of-freedom (3-DOF) remotely operated vehicle (ROV) in the presence of matched uncertainties. The advanced notion of predefined-time stability is used to provide a maximum convergence time as desired that can be set during the control design and independently of the initial conditions. Based on defining a new form of sliding surfaces, a new control law is designed to ease the undesirable chattering phenomenon without damaging the robustness properties and tracking precision. The proposed control scheme can not only solve the predefined-time tracking controller design problem, but also provide the robustness to various uncertainties. The Lyapunov stability theory is used to establish the stability analysis of the closed-loop system in both the reaching phase and the sliding phase. The performance of the proposed CFRPSMC scheme is evaluated for the 3-DOF ROV through two comparative simulation cases using Simulink/MATLAB. The comparative simulation results and analytical comparisons demonstrate the efficacy and superiority of the proposed method compared with other relevant conventional methods.

This paper proposes a new chattering-free Fixed-time Observer-Based Sliding Mode Control (FOBSMC) scheme for synchronization of two bilateral teleoperations under unknown time-varying delay. The system is subjected to unknown disturbances which are estimated in a fixed time by utilizing the Disturbance Observer-based SMC scheme. The fixed-time State Observer-based SMC is designed to estimate the unmeasured velocity state, while the position state is assumed to be available. Fixed-time stability method is used to provide the system convergence time independently of initial states. A FOB-SMC scheme is first designed for master system of bilateral teleoperation under unknown time-varying delay to track the environmental torque by the human operating torque in the presence of time delay in the communication channel, as well as estimating the unknown disturbances and unmeasured states. A FOBSMC scheme is designed to synchronize slave system to master system in the presence of time delay in the communication channel, as well as estimating disturbances and states. The stability analysis is performed for closed-loop system of combined controller-observer by using Lyapunov theory. The efficacy of the proposed method to fulfill a good transparency and stability under time-varying communication delays is tested by performing numerical simulation in Simulink/MATLAB.

The presence of uncertainties and external disturbances is one of the unavoidable problems with various practical systems which might be unavailable in real-time. Sliding Mode Control (SMC) is one of the effective robust control methods to deal with these uncertainties and external disturbances. In this paper, two novel controllers are designed by using Nonsingular Terminal SMC (NTSMC) and Adaptive Nonsingular Terminal SMC (ANTSMC) methods for synchronization of dual smart grid chaotic systems with various uncertainties and external disturbances. Indeed, both adaptive and non-adaptive controllers based on NTSMC are proposed to provide two alternatives which can adjust by changing operating conditions and dynamics. The concept of SMC method guarantees controller robustness against various uncertainties and external disturbances. Elimination of the undesirable chattering phenomenon is addressed in this study which is one of the common deficiencies with conventional SMC method. Additionally, finite time concept is used to speed up the convergence rate. Finite time stability proof is performed by using Lyapunov stability theory. The numerical simulation is carried out in Simulink/MATLAB to reveal the validity of the proposed controllers for the smart grid chaotic system. A comprehensive comparison is made by performing simulation for the Fractional Order Adaptive Sliding Mode Control (FOASMC) controller and defining three performance criteria, among the proposed controllers in this study and FOASMC controller.

It is essential to consider chattering alleviation of Sliding Mode Control (SMC) design along with providing the system convergence regardless of initial states utilizing the fixed‐time stability notion. Unknown states and disturbance are two major issues in practical applications, which can be effectively solved by using sliding mode observers. This paper deals with state and disturbance Observers‐based Chattering‐Free Fixed‐time SMC (OCFFSMC) design for a class of high‐order nonlinear systems with unknown disturbance, while only the first state is measured physically. A new form of the combined observer‐controller is designed to provide estimated data of unknown disturbance and unmeasured states in the control law. The designed disturbance observer‐based sliding mode controller is not only capable of estimating unknown disturbance but also capable of alleviating the chattering problem in the control signal. Based on defining a new form of the sliding surface, a new control law is designed to alleviate chattering problem and achieve trajectory tracking in a fixed time independently of initial conditions. The fixed‐time stability proof of the closed‐loop system is obtained using Lyapunov stability theory. The validity of the proposed control scheme, OCFFSMC, is verified by applying two examples and simulating in Simulink/MATLAB.