An Inverted Pendulum System Control with Fuzzy Linear Quadratic Regulator Method: Experimental Validation

In this study, a dynamic model for an inverted pendulum system (IPS) attached to a car is created, and two different control methods are applied to control the system. The designed control algorithms aim to stabilize the pendulum arms in the upright position and the car to reach the equilibrium position. Grey Wolf Optimization-based Linear Quadratic Regulator (GWO-LQR) and GWO-based Fuzzy LQR (FLQR) control algorithms are used in the control process. To improve the performance of the LQR and FLQR methods, the optimum values of the coefficients corresponding to the foot points of the membership functions are determined by the GWO algorithm. Both a graphic and a numerical analysis of the outcomes are provided. In the comparative analysis, it is observed that the GWO-based FLQR method reduces the settling time by 22.58% and the maximum peak value by 18.2% when evaluated in terms of the angular response of the pendulum arm. Furthermore, this approach outperformed comparable research in the literature with a settling time of 2.4 s. These findings demonstrate that the suggested GWO-based FLQR control method outperforms existing literature in terms of the time required for the pendulum arm to reach equilibrium.