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Modeling and Stabilization Fuzzy Control Strategies of a Nonlinear Cart-Pendulum System: a Comparative Study

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In this paper, we propose and validate an unsimplified nonlinear state-space model of the cart-pendulum system. Then, we present several fuzzy control strategies in order to stabilize and control both the pendulum angle in upright position and the cart position into a desired position. These strategies are built upon two separate fuzzy logic controllers (FLC), having the same characteristics. To achieve this goal, we used various structures of two-input fuzzy controllers such as fuzzy proportional-derivative (FPD), fuzzy proportional-integral (FPI), FPI plus FPD and FPI derivative (FPID), designed by two basic fuzzy inference systems, i.e., Mamdani or zero-order Takagi-Sugeno. Then, the effectiveness of different strategies was tested and compared using several performance integration indices. Many tests were carried out and the obtained simulation results proved that the strategy, based on the zero-order Takagi-Sugeno FPID structures, could be applied to control the coupled variables of a nonlinear system. Furthermore, the proposed unsimplified nonlinear state-space model of the cart-pendulum system, might be used for validating new nonlinear control strategies.
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Nonlinear Cart-Pendulum System; Nonlinear State-Space Model; Stabilization; Two-Input Fuzzy Controllers; Performance Integration Indices

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