Adaptive stabilizing and tracking control for a nonlinear inverted-pendulum system via sliding-mode technique

Since the system behaviors of a dual-axis inverted-pendulum mechanism including actuator dynamics are highly nonlinear, it is difficult to design a suitable control system that realizes real-time stabilization and accurate tracking control at all times. In this paper, an adaptive sliding-mode control system is implemented to control a dual-axis inverted-pendulum mechanism that is driven by permanent magnet synchronous motors. First, the energy conservation principle is adopted to build a mathematical model of the motor-mechanism-coupled system. Moreover, an adaptive sliding-mode control system is developed for stabilizing and tracking control of the dual-axis inverted-pendulum system, where an adaptive algorithm is investigated to relax the requirement of the bound of lumped uncertainty in the traditional sliding-mode control. In addition, numerical simulation and experimental results show that the proposed control scheme provides high-performance dynamic characteristics and is robust with regard to parametric variations, various reference trajectories, and different initial states.