Design of Cascade Direct Adaptive Fuzzy Control for Two-axis Inverted-pendulum Servomechanism

This study presents and analyzes a cascade direct adaptive fuzzy control (DAFC) scheme including inner and outer control loops for the stabilizing and tracking control of a nonlinear two-axis inverted-pendulum servomechanism. The goal of the inner control loop is to design a DAFC law 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 an adaptive path planner so that the cart position vector tracks the cart-position command vector. Moreover, all adaptive algorithms in the cascade DAFC system are derived in the sense of Lyapunov stability analysis, so that system stability can be guaranteed in the entire closed-loop system. Relying on this cascade structure, the stick-angle and the cart-position tracking-error vectors will converge to zero simultaneously. Numerical simulations are given to verify that the proposed cascade DAFC system can achieve favorable stabilizing and tracking performance and robust with regard to system uncertainties.