Análise de Correlação de Spearman para Seleção de Funções Custo na Otimização Multiobjetivo de Controladores PID

Abstract

Multiobjective optimization algorithms are useful tools in obtaining solutions for problems that need to optimize multiple cost functions simultaneously. In the control engineering area, being Proportional-Integral-Derivative (PID) controllers widely used in industrial applications, it is possible to notice several advantages regarding the use of multiobjective optimization, where the purpose is to obtain gains calculated to improve the performance against multiple criteria. In general, in optimization procedures, the performance criteria of controllers are used as cost functions. However, there is a lack of studies that help select these functions. Using Spearman’s rank-order correlation, this study analyzed ten cost functions for four different linear transfer functions, allowing an initial understanding of the statistical dependencies between performance criteria and their use as cost functions in multiobjective optimization procedures.