Adaptive Neural Sliding Mode Control of an Inverted Pendulum Mounted on a Ball System

Abstract

Underactuated systems are mechanical systems with fewer actuators than the system degrees of freedom, i.e., some degrees of freedom are not directly driven by actuators. Many benchmark underactuated systems have been developed to study the nature of underactuated dynamics and their possible controller designs. These systems include, but are not limited to, the acrobot, pendubot, cart pole system, overhead crane, translational oscillator/rotational actuator (TORA) system, and rotary inverted pendulum. Unlike fully actuated systems where many control strategies are available for an entire class of systems, there are few results applicable to even a small class of underactuated mechanical systems. In this paper, an adaptive neural sliding mode controller (ANSMC) is proposed in order to stabilize an inverted pendulum mounted on a ball system; this latter an interesting underactuated mechanical system for which the controller designs are a pending task, i.e. the performance for different control strategies could be explored. The performance of our proposal is verified via numerical simulation using the mathematical model for a benchmark prototype based on the LEGO Mindstorms NXT kit, showing the robustness against time-varying uncertainties and disturbances.