Considering that in the trajectory tracking control of a nonlinear robotic manipulator system, the control effect is easily limited by the initial state of the system, and the system has modeling error, unknown disturbance, and friction in the actual control, to overcome the above problems, a fixed-time sliding mode control (SMC) strategy based on adaptive disturbance observer (ADO) is developed in this paper. Firstly, feedforward compensation of the system is achieved by developing an ADO to accurately estimate the compound disturbances in the system. Second, a new fixed-time sliding mode (SM) surface is presented to overcome the singularity issue and accelerate the error convergence. In addition, to enhance the performance of the reaching phase, a variable exponential power reaching law (VEPRL) is developed, which can effectively adjust the convergence rate. Through rigorous theoretical analysis, it is shown that the system state can be stabilized at a fixed time, and an upper bound on the convergence time is also given. Finally, the effectiveness of the control method is verified by comparing it with different control schemes in simulation. K E Y W O R D Sadaptive disturbance observer (ADO), fixed time, robotic manipulator system, sliding mode (SM) surface, variable exponential power reaching law (VEPRL)
This article focuses on the high-speed train with unknown speed delays; a spatial adaptive iterative learning control (SAILC) algorithm is designed to solve the displacement-speed trajectory tracking problem by using the spatial differential operator to transform the train temporal dynamic model into a spatial model. First, parametric adaptive control is used to reduce the influence of system uncertainties. Second, a Lyapunov-Krasovskii-like spatial composite energy function (SCEF) is established, the stability of the designed controller and the convergence of the tracking error are demonstrated by verifying the differential negative definiteness and boundedness of the function. In addition, the train speed needs to be maintained within a certain range due to the speed loss when it passes through the neutral zone and overspeed protection. Therefore, the state-constrained mechanism is implanted into the train control algorithm to ensure that the train operates within the speed limits. Finally, the proposed SAILC algorithm is compared with proportional-integral-derivative (PID) and iterative learning control (ILC) algorithm; the results of the numerical simulations prove the effectiveness of the proposed method. After 20 iterations, the maximum absolute error of SAILC is 0.05 m/s, which is 4.7% of PID and 10.7% of ILC. It meets the requirements of Automatic Train Operation (ATO) that the tracking error should not be greater than 1% of the train operating speed.
In this paper, an adaptive fixed-time controller is raised for the manipulator system with uncertain disturbances to boost the rate and precision of its trajectory tracking and solve the convergence time dependence on the system's initial conditions. First, a nonsingular fixed-time sliding mode (SM) surface and a reaching law based on an arctangent function are constructed to enhance the control scheme performance. Second, the upper bound is difficult to obtain because of the uncertainty of the disturbance. The disturbance upper bound is estimated by adaptive techniques, which do not require a priori knowledge about the upper bound and effectively inhibit the effect of disturbance on the system. Finally, the fixed-time convergence of the states is analyzed by rigorous theoretical proof, and the validity of the presented control scheme is demonstrated by simulation.
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