Fuzzy Gain Scheduling of Coupled PID Controllers for Stabilization of the Inverted Pendulum

Changes in operating conditions can alter performances of nonlinear processes controlled with a fixed PID algorithm. One way of preventing degradation is to develop a supervised control system. In this paper we present some results about fuzzy gain scheduling of a double PID controller for stabilization of an inverted pendulum on a cart. First, on the basis of the responses obtained with an unsupervised and locally optimized double PID, a simplified fuzzy supervisor is designed, including the cart set-point as the scheduling variable. Subsequently, the rule base is modified with two additional inputs: the pole and cart errors. Finally, a peak observer is introduced to moderate the steady-state error through integral action in the cart PID. The resulting fuzzy supervisor adapts the coupled PIDs to the changing operating conditions. The proposed control strategy is implemented in the MatLab software environment. Results are discussed in comparison with an unsupervised PID algorithm.