An optimal fractional LQR-based control approach applied to a cart-pendulum system
Résumé
Fractional calculus is a branch of mathematics that studies the use of the fractional operators. The evolution of computing allowed its application in many areas, including control theory. Fractional operators are known to well describe memory phenomena, a favorable characteristic for control. Another benefit is that fractional-order of these operators adds more tunable parameters to the controller, allowing greater flexibility and the possibility of improving its performance. This work aims to verify the performance of an inverted cart-pendulum control system using a fractional-order integrators and discover an ideal method for optimizing systems using fractional controller. The strategy is to employ optimization methods like genetic algorithms and cross-entropy, to obtain optimal controller parameters which result in the best control performance, taking into account performance indexes related to the error, settling time and control effort. A comparison is made with the integer-order controller to verify the improvement in the use of fractional control.
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