Akademik Veri Yönetim Sistemi
Processes, cilt.13, sa.5, 2025 (SCI-Expanded)
Recently, studies on delay-based controllers that consider the positive effects of time delay have been increasing in the literature. In this context, a proportional integral retarded (PIR) controller structure has been proposed. There are two important factors in the design of a delay-based controller: closed-loop stability and controller tuning. The motivation for this study is that there is no previous literature on stability region analysis on PIR controllers. To address this gap in the literature, this paper presents, for the first time, a comprehensive stability region analysis for PIR controllers. The study derives the stability boundary locus (SBL) equations for time-delay processes with PIR controllers, allowing stable regions to be defined analytically and graphically in the two-dimensional controller parameter space. In order to obtain the SBL, the stability boundary line equations are derived, and the variations in the case of different types of time-delay processes are presented with mathematical equations and proved with examples. Another novelty of this work is its systematic investigation of how the controller time delay affects the stability region when it is smaller, equal or larger than the process delay. The proposed method fills a critical gap in the design and tuning of PIR controllers by providing a reliable tool by which to visualize and understand stability properties.