Balance Control of the Pendubot via the Polynomial Matrix Approach

We present a procedure for the computation of a stabilizing compensator for a double inverted pendulum known as the Pendubot. The procedure relies on a computational algorithm based on various results of “the polynomial matrix approach” and in particular results for the solution of polynomial matrix Diophantine equations required for the computation and parametrization of proper “denominator assigning” and internally stabilizing compensators for linear time invariant multivariable (LTI) systems. The underlying theory regarding the solution of polynomial matrix Diophantine equations leading to proper denominator (pole) assigning stabilizing compensators is reviewed and the computational algorithm emerging from this theory is presented and applied as a case study for the computation to a stabilizing controller for the Pendubot.