Tuning optimal and robust decentralized PID controllers for two-input two-output time delay systems with a decoupler based on frequency domain robustness specifications

Abstract

Interactive two-input two-output processes with time delays (TITOTD) generally have strong loop interactions and exhibit complex response characteristics. This study develops an alternative method to rapidly and graphically tune optimal and robust decentralized PID (ORDPID) controllers to stabilize TITOTD systems using the designer-defined frequency domain robustness specifications. To eliminate loop interactions, a decoupler is initially used to decompose the TITOTD system, so two independent time-delayed single-input single-output subsystems (SISOTD) are derived. To guarantee the frequency domain specifications for a controlled system in terms of gain margin (GM) and phase margin (PM), each SISOTD subsystem is incorporated with a gain-phase margin tester (GPMT). Without approximating the delay terms and reducing the orders of the SISOTD processes, the stability equation method determines the GM and PM-associated boundaries in the parameter plane. For each decoupled SISOTD process, a GM and PM specification-oriented region (GPMSOR) that encloses all admissible robust decentralized PID (RDPID) controllers is graphically characterized in the parameter plane. Two independent ORDPID controllers are searched within the determined GPMSORs by minimizing the IAE or the ISE performance index. For verification, the determined ORDPID controllers are evaluated using the original TITOTD processes with four simulation examples from the literature.