Enhancing stability control of inverted pendulum using Takagi–Sugeno fuzzy model with disturbance rejection and input–output constraints

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Abstract
The Takagi–Sugeno (T–S) fuzzy model is a versatile approach widely used in system control, often in combination with other strategies. This paper addresses key control challenges linked to the T–S system and presents important considerations to ensure its successful application using the Lyapunov theorem. One crucial aspect is determining the optimal number of premise variables and selecting accurate fuzzy rules for the T–S model. Additionally, the theorem based on Linear Matrix Inequality (LMI) is developed to enable effective disturbance rejection. To enhance stability control, constraints are imposed on the output angle and control input of a rotary inverted pendulum (RIP). By integrating T–S fuzzy control, disturbance rejection, and input/output constraints, robust stability in controlling the RIP is achieved. Extensive simulations are performed to showcase the efficiency of the suggested method, and the simulation results are thoroughly discussed and analyzed to verify the efficacy of the control method.

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