Development of adaptive sliding-mode control for nonlinear dual-axis inverted-pendulum system

Since the dynamic characteristics of a nonlinear inverted-pendulum mechanism are highly nonlinear and time varying, it is difficult to design a suitable control system that realizes real time stabilization and accurate tracking control at all time. In this study, an adaptive sliding-mode control system is implemented to control a dual-axis inverted-pendulum mechanism that is driven by permanent magnet (PM) synchronous motors. 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 simulations show that the proposed control scheme provides high-performance dynamic characteristics and are robust with regard to parametric variations, various reference trajectories and different initial states.