Fast Terminal Synergetic Control of Underactuated System

In the last few years, control of underactuated systems has become an active field of research. The underactuated property means that the system has less number of actuators than their degrees of freedom. Underactuated systems are constructed by the reason of reducing cost weight and consumed energy. In this paper we consider the application of the fast terminal synergetic to the control problem of a class of second order underactuated mechanical systems in order to guarantee the fast finite-time stability. This strategy of control is considered as a solution of the chattering phenomenon, which is a big problem in sliding mode control. The macro-variables are constructed for the whole system in hierarchical structure. We give some simulation results in the end of this work, to prove the effectiveness of the studied control.