Cascade direct adaptive fuzzy control design for a nonlinear two-axis inverted-pendulum servomechanism

This paper presents and analyzes a cascade direct adaptive fuzzy control (DAFC) scheme for a two-axis inverted-pendulum servomechanism. Because the dynamic characteristic of the two-axis inverted-pendulum servomechanism is a nonlinear unstable nonminimum-phase underactuated system, it is difficult to design a suitable control scheme that simultaneously realizes real-time stabilization and accurate tracking control, and it is not easy to directly apply conventional computed torque strategies to this underactuated system. Therefore, the cascade DAFC scheme including inner and outer control loops is investigated 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 using the 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 cart position tracking-error vectors will simultaneously converge to zero. Numerical simulations and experimental results are given to verify that the proposed cascade DAFC system can achieve favorable stabilizing and tracking performance and is robust with regard to system uncertainties.