Stabilization of Second Order Underactuated System Using Fast Terminal Synergetic Control

Abstract

The control of underactuated mechanical systems (UMS) has been the subject of active scientific research, provided by the wide applications of such systems in different disciplines. The main purpose of studying these systems is to control certain variables in parallel, knowing that underactuated systems admit more degrees of freedom than the actuators. The lack of actuator complicates the task of controlling such systems. In this chapter, our objective is to find a control law which guarantees the finite time convergence and the stability of a class of second order underactuated system, for this reason, we have chosen to use the fast terminal synergetic control (FTSC), this latter is considered among robust controls, and has already proven its effectiveness in several applications of nonlinear systems. The UMS is divided into two sub-systems, and each one has its macro variable, which is constructed in hierarchical manner. To prove the efficiency of the proposed strategy of control, we show simulation results of a second order underactuated system example.