Neural-network-based fuzzy logic control of a 3D rigid pendulum

This paper concerns the attitude control problem of a 3D rigid pendulum based on dynamic T-S fuzzy neural model. A generalized 3D rigid pendulum subjected to a constant gravitational force consists of a rigid body supported by a fixed and frictionless pivot with three degrees of freedom. There exist two equilibriums of the 3D rigid pendulum characterized with unstable manifolds near the inverted equilibrium and stable manifolds near the hanging equilibrium. For the attitude control problem at the equilibrium position, T-S fuzzy neural model is adopted to approximate the nonlinear part of the 3D rigid pendulum. The method of parallel distributed compensation is used to form the angular velocity feedback controller to cope with the nonlinearity. Moreover, an attitude feedback controller is designed for the linear part so as to guarantee the overall system’s stability. Numerical simulations are performed to illustrate the validity of the proposed method.