A computational investigation of pole-zero cancellation for a double inverted pendulum

Modern symbolic computational systems which perform automated manipulation of algebraic variables offer insights into a variety of mathematical problems. This work uses the symbolic manipulation toolbox available in MATLAB to investigate pole-zero cancellation of the uncontrollable double inverted pendulum algebraically, following exploratory numerical computation. The ability of the software to factorise complicated multi-variable polynomials is exploited to identify, in algebraic form, the anticipated pole-zero term cancelling throughout the transfer functions of the uncontrollable pendulum system. The controllability of pendulum systems may be investigated for any of the control inputs. In this paper, the system has been considered with respect to the force on the trolley, for which it is a conditionally uncontrollable problem, and with respect to each of the torques on the arms, which are unconditionally uncontrollable problems.