Robust Generalized Dynamic Inversion Control for Stabilizing Rotary Double Inverted Pendulum

This paper presents the balance control design using Robust Generalized Dynamic Inversion (RGDI) for Rotary Double Inverted Pendulum (RDIP) system. The RGDI control comprised of the particular part and the robust control element. The particular part is responsible to enforce the constraint dynamics based on the attitude deviation functions, and is inverted using Moore-Penrose Generalized Inverse (MPGI) to obtain the control law. An additional robust term based on the concept of sliding mode is integrated to enhance the robust characteristics against system nonlinearities, uncertainties and disturbances. The singularity problem is addressed by incorporating a dynamic scale factor in the expression of MPGI. The proposed RGDI control will guarantee semi-global practically stable angular position tracking of the horizontal rotary arm and the stabilization of the two pendulums at the upright position. Numerical simulations are carried out on the RDIP simulator to analyze the controller performance.