Modified Fractional-Order PID Controller Design for the Mixing Tank Process

Abstract

Controlling multiple input–multiple output (MIMO) processes is challenging due to loop interactions. This study explores a modified fractional-order PID (MFOPID) controller for a two-input, two-output mixing tank system. MFOPID design involves individual loop controllers based on the Nelder–Mead algorithm. Relative gain array analysis optimizes loop interactions, complemented by a simplified decoupler. Comparative evaluation against Ziegler–Nichols, internal model control, and standard FOPID controllers demonstrates a superior performance of MFOPID controller offering smoother signals and demonstrating significant improvement in various performance indices. These findings underscore the efficacy of the MFOPID controller in enhancing control performance in MIMO systems. © 2025 Wiley-VCH GmbH.