Reaching phase elimination in terminal sliding mode control of second order systems

In this paper reaching phase elimination in the sliding mode control of the second order system is considered. Therefore, the robustness is guaranteed from the very beginning of a control process. A time-varying sliding curve is introduced and designed so that the regulation error converges to zero in finite time. The proposed control signal guarantees the stable sliding motion for the whole regulation process. Furthermore, the regulation time is minimized subject to input signal constraint. Theoretical considerations presented in the paper are verified by means of a simulation example.