On the uncontrollable damped triple inverted pendulum

摘要

In this paper, the controllability of the damped triple inverted pendulum is investigated. The work is concerned with the form of the cancelling pole and zero which appear in the transfer functions of an uncontrollable system, and follows on from earlier work on the damped double inverted pendulum. The investigation considers first the cases where only one of the three arm frictions is non-zero, and then explores the cases when two of the three arm frictions are non-zero. Due to the complexity of this problem, and the difficulties with the symbolic manipulation software, exploratory numerical investigations have been carried out to facilitate the symbolic investigations, all of which are reported here.