Examination of Sturm-Liouville problem with proportional derivative in control theory

Yıl 2023, Cilt: 3 Sayı: 4, 335 - 350, 30.12.2023

Bahar Acay Öztürk

https://doi.org/10.53391/mmnsa.1392796

Öz

The current study is intended to provide a comprehensive application of Sturm-Liouville (S-L) problem by benefiting from the proportional derivative which is a crucial mathematical tool in control theory. This advantageous derivative, which has been presented to the literature with an interesting approach and a strong theoretical background, is defined by two tuning parameters in control theory and a proportional-derivative controller. Accordingly, this research is presented mainly to introduce the beneficial properties of the proportional derivative for analyzing the S-L initial value problem. In addition, we reach a novel representation of solutions for the S-L problem having an importing place in physics, supported by various graphs including different values of arbitrary order and eigenvalues under a specific potential function.

Anahtar Kelimeler

Proportional-derivative controller, Sturm-Liouville problem, proportional integral, local derivative, control theory

Kaynakça

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