Tri-Parametric Fractional-Order Controller Design for Integrating Systems With Time Delay

This brief introduces a new fractional-order integral derivative (
${\mathrm {FOI}}^{\lambda }\text{D}^{1-\lambda }$
) controller for a class of integrating systems involving time delays. The stability region is explored through the complex root boundary (CRB) analysis which explicitly provides the search space of
${\mathrm {FOI}}^{\lambda }\text{D}^{1-\lambda }$
parameters for integrating time delay systems of any order. The optimal settings are obtained through a three-step optimization algorithm based on the CRB knowledge and the desired performance measures. Comparisons with other recent sophisticated tuning methods are also provided to demonstrate the effectiveness of the suggested control scheme through numerical study. Finally, a case study on a non-linear continuously stirred reactor under model uncertainties is presented to check the efficacy of the new method.