Stabilizing the angle while controlling the wheel position in single wheel inverted pendulum systems has always been a challenge for control engineers. The current paper presents a novel hierarchically optimized fuzzy controller to overcome this confrontation. At the first step, Lagrange equations are utilized to derive the equations of motion of the system. The overall strategy of choosing between conflicting linguistic rules and determination of the knowledge-based of the system is discussed and explained in detail. Using the well-known combination of the singleton fuzzifier, product inference engine and the center average defuzzifier, a fuzzy controller is designed which is then optimized in two steps: At the first, genetic algorithm is used in the integer programming mode to partially optimize the knowledge-based of the system; In the second stage, the designed controller is tuned and optimized for performance enhancement. Simulation results ensure the stability and performance of the proposed optimal fuzzy controller. The results of this paper can be used in stabilizing real physical systems such as segways and mobile robots that use the wheeled inverted pendulum system as an essential element of the system.

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