Phase Trajectory Analysis of Non-singular Terminal Sliding Mode Controlled Flexible Manipulator

For a non-singular terminal sliding mode (NTSM) controlled two-link flexible manipulator, this paper investigates the phase trajectories starting from different original states and gives the existence of a critical surface determining whether the system convergences to the equilibrium point in a short path. By using the output redefinition method, the system is first decomposed into a zero dynamic subsystem and an input-output subsystem-the stability of the former is guaranteed by pole placement technique, while a NTSM controller is designed for the latter to realize its finite time convergence and better control performance. Then twelve possible original states and their corresponding phase trajectories are discussed, proving the distribution rule of phase trajectory. Simulations validates the proposed analysis.