Design of Fuzzy Control System with Optimal Guaranteed Cost for Planar Inverted Pendulum.

For the problem of control a planar inverted pendulum system (PIP) with non-uniform density pendulum, a design method of optimal guaranteed cost fuzzy control is developed via the parallel distributed compensation(PDC) approach. Firstly, by using the Lagrange equation, the mathematical model of the planar inverted pendulum is derived. Then, a sufficient condition for the existence of guaranteed cost fuzzy controller is presented with taking into account a given quadratic performance index, and a deviation amplitude of the center-of-mass of the rod. Finally, simulation results show the effectiveness of the proposed design method.