Finite time stability control based on higher-order sliding mode for TORA system

Translational oscillators with rotating actuator (TORA) system is a challenge for controller design because of its underactuated character. A finite time stability control method based on higher-order sliding mode is proposed to achieve finite time stability under uncertainty for the TORA system. The TORA dynamical model function is transformed to cascade normal forms. For the second order subsystem, virtual control is introduced and the finite time stability proof is given with the conception of terminal sliding mode. Actual variable tracking virtual control in finite time is achieved by higher-order sliding mode controller. Adaptive robust method is proposed to solve uncertainty problem with unknown upper bounds, and proof of finite time stability is given. Simulation results verify the robustness of the methods.