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Adaptive Type-2 Fuzzy Logic Control Applied to the Inverted Pendulum on a Cart Problem

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This paper introduces the design of an adaptive interval type-2 fuzzy logic controller and its implementation on a pendulum-cart system. It includes the theoretical foundations of: type-2 fuzzy logic system, input-output linearization control, fuzzy systems for functions approximation and adaptive systems. Type-2 fuzzy controllers provide an approach for using wide variety of opinions in control design. The above allows minimizing the effect of uncertainties in the rule base of fuzzy logic systems. These types of controllers provide greater flexibility in the application of human knowledge during the design of control systems in contrast to traditional controllers employing type-1 fuzzy logic. We propose to compare an adaptive interval type-2 fuzzy logic controller with its corresponding adaptive type-1 fuzzy logic controller. These controllers are tested in real-time on an inverted pendulum on a cart experimental prototype under the presence of parametric uncertainties in the mass of the pendulum. Five performance indexes are computed to compare both controllers, showing that type-2 fuzzy systems can help to improve the response of type-1 fuzzy systems.
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Type-2 Fuzzy Logic; Interval Type-2 Fuzzy Controller; Adaptive Fuzzy Control

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