Design of robustly stabilizing low order, stable controllers for two-link underactuated planar robots

This study is aimed to find low order, stable and proper controllers for the linearized models of two well known underactuated robots i.e. Acrobot and Pendubot around their upright equilibrium points in order to maximize the robustness of the feedback loop to uncertainties. The proposed method makes use of the robust stabilization of finite dimensional plants by Nevanlinna-Pick interpolation problem. This method does not necessarily yield a stable controller and also the resulting controller is not proper if boundary interpolation conditions are not taken into account. In this paper, additional simple constraints are defined to handle these problems to find a stable and proper controller for Acrobot and Pendubot. Third order stable controllers for these robots are designed with improvements in the robustness margin when compared to other relevant controllers from the literature. Also the integral action controller design is revisited and fourth order, stable, proper controllers are designed in this manner.