Design of Optimal Cost Fuzzy Controller for Spatial Double Inverted Pendulum System

For a spatial double inverted pendulum system, a design method of optimal cost fuzzy controller is developed via the parallel distributed compensation( PDC) approach. Firstly, by using the Lagrange equation, the mathematical model of the spatial double inverted pendulum is derived. Then, a sufficient condition for the existence of optimal cost fuzzy controller is presented with taking into account the ratio between the lengths of two pendulums, and it is formed in terms of linear matrix inequalities. Under a certain cost function, the best ratio between the lengths of two pendulums is solved by this method.

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