LMI-Based Position Control of Underactuated Robotic Systems via an Affine PD Controller: Case Study

In this work, our goal is control the position of underactuated robotic Lagrangian systems through an affine-type PD controller and by adopting the inertia wheel inverted pendulum as an application example. In order to model the condition on feedback gains of the controller for stability, we take the dynamical model that describes the gap between the linearized model and the nonlinear dynamics. Moreover, we assume that this difference satisfies some condition. Furthermore, by virtue of the LMI techniques, we develop the stability conditions. Finally, we provide some results to reveal the efficiency of the proposed controller design.