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Mean-variance mapping optimization for tuning scaling gains of a fuzzy control applied to a cart-inverted pendulum

Abstract:

This paper presents the design of a Proportional Derivative (PD) fuzzy controller applied to an inverted pendulum mounted on a cart. The proposed methodology consists in the definition of rules for the controller based on the knowledge of the behavior of the plant. The proposed controller consists of two scaling gains in the input and one in the output, to adjust the response of the system in closed loop (feedback) to stabilize the pendulum in a desired position. The scaling gains are tuned using the Mean-Variance Mapping Optimization (MVMO) algorithm, minimizing a fitness function, in this case, the Integral Square Error (ISE). This performance metric allows knowing how fast the controller takes the system output to the desired reference with the restriction of not saturating the output signal of the controller applied to the cart actuator. The non-optimized and optimized fuzzy controllers are tested through simulations in the complete model of the plant in order to compare the response of both systems.