A Cartesian Regulator for an Ideal Position-Servo Actuated Didactic Mechatronic Device: Asymptotic Stability Analysis

Position-servo actuators are by themselves feedback mechatronics systems modeled by Ordinary Differential Equations (ODE). From a technological point of view, position-servos are based upon an electrical motor, a shaft angular position sensor, and a dominant Proportional controller. These position servo actuators are at the core of several real-life practical and didactic mechatronics and robotics systems. The contribution of this study is the introduction of a novel position regulator in Cartesian space and the stability analysis of a real-world mechatronic system involving the following mechatronics ingredients: A position servo actuated pendulum endowed with position sensing for feedback and a novel nonlinear integral controller for direct position regulation in Cartesian space avoiding the inverse kinematics computational burden. Because of the nonlinear nature of the control system, the standard analysis tools from classic linear control cannot be utilized, thus this study invokes Lyapunov stability arguments to prove asymptotic stability and to provide an estimate of the domain of attraction.