Nonlinear Observers-Based State Feedback Control: Application to an Inverted Pendulum

In This paper, we present a robust high gain output feedback control for a class of uniformly observable and controllable nonlinear systems. Our main goal here is to apply an output feedback controller which regulates the output of the plant to a constant reference. While the smooth state feedback control law is constructed based on the use of a high gain sliding mode controller, the estimation of the non measured states is carried out by a sliding mode observer which is compared to a high gain observer. It’s shown that the resulting closed loop is asymptotically stable, and the performance recovery includes asymptotic stability of the origin, the region of attraction and trajectories. Furthermore, the system equation is augmented through a filtered integral action which is incorporated into the control law to ensure asymptotic rejection of step like states and/or output disturbances, and measurement noise. As a particular application, we consider the open loop unstable inverted pendulum on a cart. Finally, computer simulations are developed for showing the robustness of the controller including sliding mode observer against step like disturbance, noisy measurements and parametric uncertainties.