Design of Cascade Adaptive Fuzzy Sliding-Mode Control for Nonlinear Two-Axis Inverted-Pendulum Servomechanism

Because the dynamic characteristic of a two-axis inverted-pendulum servomechanism is a nonlinear underactuated system, it is difficult to design a suitable control scheme that realizes real-time stabilization and accurate tracking control simultaneously. In general, the techniques developed for fully actuated systems cannot be used directly in underactuated systems. In this study, a cascade adaptive fuzzy sliding-mode control (AFSMC) scheme including inner and outer control loops is investigated for the stabilizing and tracking control of a nonlinear two-axis inverted-pendulum servomechanism. The aim of the inner control loop is to design an AFSMC law with fuzzy estimators so that the stick-angle vector can fit the stick-angle command vector derived from the stick-angle reference model. In the outer loop, the reference signal vector is designed via a fuzzy path-planning scheme so that the cart position vector tracks the cart-position command vector and the stick-angle tracking-error vector converges to zero simultaneously. All adaptive algorithms in the cascade AFSMC system are derived in the sense of Lyapunov stability analysis, so that system stability can be guaranteed in the entire closed-loop system. The effectiveness of the proposed control strategy is verified by numerical simulations and experimental results, and the superiority of the cascade AFSMC system is indicated in comparison with a cascade sliding-mode control system.