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To enhance the position and attitude-control of quadrotor for trajectory tracking, we propose a fast decay function utilizing exponential property to improve the performance of global sliding-mode control, allowing the initial value to quickly reach equilibrium. The main research is focused on deriving the finite settling time using the proposed decay function and presenting a detailed calculation process, instead of making a simple modification to a monotonic exponential-decay function. Moreover, we adopt an adaptive control law to ensure the robustness of the quadrotor, even without knowing the upper bound for disturbances. In addition, we perform time-varying mass simulations because the quadrotor’s load mass may change during maneuvering. Furthermore, using the Lyapunov function, the stability of the entire closed-loop system is ensured by the step-by-step stabilization of each subsystem. The simulation results show that the rapid global sliding-mode control (RGSMC) we designed is more effective than the conventional global sliding-mode control and adaptive sliding mode control with respect to stabilization and tracking against external disturbances. Hence, the fast decay property of the proposed global function is verified.

An improved non-singular fast terminal sliding mode control (INFTSMC) is proposed in this study, to improve the dynamic speed regulation and tracking accuracy of a surface-mounted permanent magnet synchronous motor (SPMSM) system. A sliding surface that completely removes singularities from the controller input is proposed. The key characteristics of the INFTSMC are fast convergence of errors, high tracking accuracy, and robustness against disturbances. The controller designed in this study is proven to be stable, with convergence in finite time and stability based on the Lyapunov theory. The proposed INFTSMC has a fast response and better performance than conventional sliding mode control and terminal sliding mode control, as demonstrated by simulation and hardware experiments in both virtual and real-time scenarios.

This study investigates the speed control of permanent magnet synchronous motors in the presence of external load disturbances via fast terminal sliding-mode control (FTSMC). First, to enhance the speed tracking performance, a logarithmic FTSMC method based on a novel sliding surface is proposed to improve the previously introduced FTSMC. Second, we have derived an enhanced settling time, demonstrating its superiority over that of recently introduced exponential FTSMC through the utilization of a logarithmic sliding surface. Third, the proposed logarithmic FTSMC and exponential FTSMC are compared to demonstrate that the convergence time of the logarithmic FTSMC is less than that of the exponential FTSMC. Forth, super-twisting reaching law is adopted in logarithmic FTSMC to counteract perturbations since it has an ability against various unknown disturbances, such as parameter mismatch, load torque variation, and friction force. Finally, the simulation results show that the proposed strategy can effectively improve the dynamic performance and robustness of permanent magnet synchronous motor systems.