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This article deals with a novel adaptive robust controller for uncertain nonlinear systems relying on a proportional–integral–derivative-type nonsingular fast terminal sliding mode control. In this nonsingular proportional–integral–derivative-type terminal sliding mode controller nonsingular fast terminal sliding mode control, the nonsingular fast terminal sliding mode control sliding surface is modified with integral to match with the proportional–integral–derivative-type structure to obtain the essential attributes, namely, quick transient response, finite-time convergence, negligible steady-state error, and chattering cancellation. Furthermore, a novel rapid reaching law is also suggested with dynamic proof for providing the robustness during transient phase. The controller stability and convergence is mathematically analyzed using the Lyapunov theory. The overall control structure is simulated on MATLAB® software and tested for trajectory tracking of a two-degree-of-freedom revolute–prismatic joint industrial robotic manipulator. The rigorous test results show the performance efficacy of the innovative controller.

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In this research work, an output tracking problem of a kind of nonlinear motion control systems influenced by exogenous uncertainties using second-order super-twisting sliding mode control is studied. It is shown that when second-order super-twisting sliding mode control is implemented with finite-time convergent homogeneous extended state observer, the second-order sliding mode is achieved on the selected sliding manifold with efficient disturbance attenuation from the output. The presented control structure is tested on the air-gap control of an electromagnetic levitation suspension system using MATLAB platform. The observations prove the efficacy of the proposed algorithm providing excellent robust control efficiency along with precise attenuation of various disturbances.

This paper presents a novel adaptive fuzzy high-order super-twisting sliding mode controller, based on the modified super-twisting control (STC), to achieve accurate trajectory tracking for a robotic manipulator with unknown structured uncertainties, parametric uncertainties, and time-varying external disturbances. Initially, a non-linear homogeneous sliding manifold is designed to achieve finite-time convergence, better robustness, and good transient characteristics. Afterwards, conventional STC is modified with the new sliding surface that eliminates the limitation of STC application only on relative degree 1 systems. Moreover, two adaptive fuzzy systems are designed to replace the STC signals for handling the chattering problem and overestimating the controller gains. These fuzzy systems are continuously adjusted by two adaptation laws that are deduced from the Lyapunov stability theory. These adaptive laws need only a sliding surface variable as an input and generate the optimal controller gains as an output. The finite-time convergence and stability of the proposed controller is analyzed by the homogeneous Lyapunov stability theory. Finally, to show the efficacy of the proposed method, the controller is simulated on a 2-degree-of-freedom planar robotic manipulator to obtain the accurate trajectory tracking. Simulation results demonstrate the superiority of the proposed control scheme in the presence of structured and unstructured uncertainties.