Controladores fracionários sintonizados por metaheurísticas em dinâmica não linear

Abstract

Fractional calculus is a branch of mathematics that studies the use of fractional operators. The evolution of computing has allowed its application in many areas, including control theory. Fractional operators are known to describe memory phenomena well, a favorable characteristic for control. Another benefit is that the fractional order of these operators adds more adjustable parameters to the controller, allowing greater flexibility and the possibility of improving its performance, especially in complex and nonlinear problems. However, classical controller tuning methods, such as linearization, are not effective in fractional control applied to nonlinear systems. For these cases, it is preferable to consider tuning techniques that directly address nonlinear dynamics, such as optimization methods. In this context, this work addressed the performance of fractional controller tuning using the Cross Entropy (CE) method. The performance of CE optimization is evaluated on the fractional controllers FOSMC and FOPID applied to four different systems: the inverted pendulum car, the bistable energy harvester, the active vehicle suspension and the SIRDQ epidemiological model. The research explored the effectiveness of the CE method in comparison with the Genetic Algorithm (GA), traditionally used for this type of problem. In all cases, the CE method not only improved the performance of the controllers, but also better computational time and greater clarity in the process than the GA. In addition, the GA method presented difficulties when subjected to constraints, requiring adjustments in its control parameters. While the CE demonstrated to be promising for applications in nonlinear control systems with constraints, in addition to having a transparent and easy-to-implement optimization process. The fractional control framework adjusted via CE proposed in this work is novel, especially in nonlinear and constrained approaches.