In this paper, controller tuning methods based on stability region centroid methods reported in the literature are used to design PI-PD controllers for unstable, integrating and resonant systems with time delay. By analyzing the stability boundary locus (SBL) for the PD controller, which is utilized in the inner loop of this structure, the controller parameters are obtained using three methods which are the Weighted Geometric Center (WGC), Centroid of Convex Stability Region (CCSR), and Stability Triangle Approach (STA). These techniques were applied analytically, step by step. For the closed loop transfer function obtained in the inner loop of the controlled system, these three methods were utilized to design the PI controller in the outer loop, individually. Unit step responses of the controlled system, using PI-PD gains determined by each method, have been obtained. Furthermore, a disturbance of a certain time and amplitude was added to the systems to test the disturbance rejection behavior and the robustness performance of the methods. Perturbed responses were obtained through changing the model parameters at a certain rate. Time domain performance metrics were analyzed to compare the responses. The simulations were evaluated using settling time, rise time, and percentage overshoot as the assessment criteria. As a result of this study, the effectiveness of three methods, namely WGC, CCSR, and STA, in controller design for unstable, integrating, and resonant time-delay systems has been demonstrated. In addition, a comparison of time domain performance metrics is presented for the nominal and perturbed systems. Based on these comparisons, it is concluded that the methods outperform each other only in some time response performance measures. The presented results showed the advantages of these methods over each other in terms of some performance criteria. The contribution of this study to the literature is the comparative analysis of these three analytical methods.

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.

This study focuses on designing PI controllers for time-delay systems using various model order reduction techniques to reduce complexity. The stability boundary locus method was used to determine PI parameters that stabilizing reduced order models. After the PI parameters have been determined using the weighted geometric center method, the calculated controller parameters have been implemented in the original system. In this way, the efficiency of the controller design is effectively demonstrated through the reduction techniques. In addition, the study investigated the effectiveness of reduction methods with increasing time delay and adding an integrator to the system. The importance of these results is that they demonstrate the use of model order reduction techniques in the design of controllers for time-delay systems and reveal the advantages of these methods.