High-Low Gain Redesign for a 4 DOF Spherical Inverted Pendulum

We revisit a previous high-low gain control idea for a 4 DOF spherical inverted pendulum using a different approach that provides explicit tuning rules to deal with certain bounded external disturbance. To this end, we propose a design method, inspired by a nested saturation design procedure proposed by Marconi and Isidori, to design some low and high gain controllers to two decoupled subystems of the original system, where explicit tuning rules are given to make two feedback interconnected subsystems satisfying ISS from external disturbances. The update controller is a robust, decentralized and ``global" controller.