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Öğe A comparative study on PI-PD controller design using stability region centroid methods for unstable, integrating and resonant systems with time delay(Sage Publications Ltd, 2024) Irgan, Hilal; Menak, Ramazan; Tan, NusretIn 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.Öğe Computation of All Robustly Stabilizing PID Controllers Based on H-∞ Robust Stability Condition(Ieee-Inst Electrical Electronics Engineers Inc, 2024) Menak, Ramazan; Tan, NusretIn this paper, the computation of all robustly stabilizing Proportional-Integral-Derivative (PID) controllers for Single-Input-Single-Output (SISO) Linear Time Invariant (LTI) systems with/without time delay and unstructured uncertainty is presented. The study proposes a graphical technique to plot the regions of all robustly stabilizing PID controllers that satisfy the H-infinity based robust stability condition. These regions are formed by the Real Root Boundary (RRB), the Complex Root Boundary (CRB), and the Infinite Root Boundary (IRB), which represent the transitions of the roots of the characteristic equation from the left half-plane to the right half-plane (or vice versa), based on Hurwitz stability criteria. The regions are depicted in the (k(i)-k(d)), (k(p)- k(i)), and (k(p)- k(d)) 2-D planes for fixed values of k(p), k(d), and k(i), respectively. The methodology is detailed step by step and demonstrated through various examples. Additionally, stability analyses are visually performed using Nyquist envelopes and uncertainty discs.Öğe H-∞ Norm Based Robustly Stabilizing PI-PD Controller Design for the Unstructured Uncertainty Modelling(Springer Heidelberg, 2025) Menak, Ramazan; Tan, NusretThe design of effective control systems in real-world applications is frequently complicated by system uncertainties and the limitations of conventional controllers. While widely adopted, proportional-integral-derivative controllers often struggle with complex processes such as unstable, integrating, or oscillating systems, particularly in the presence of uncertainties. The proportional integral-proportional derivative (PI-PD) controller structure offers a more robust four-parameter framework that provides superior control capabilities for these challenging systems. However, determining the optimal values or regions for these four tuning parameters remains a significant and complex challenge, especially when systems include various forms of uncertainty. This paper addresses the identification of the region containing all PI-PD controllers that robustly stabilize systems subjected to unstructured uncertainty, using H-infinity norm robust stability conditions. The proposed study is based on the graphical representation of the nominal stability boundary locus and robust stability boundary locus in the (kd-kf)-plane for the inner loop and the (kp-ki)-plane for the outer loop. The methodology is systematically outlined and illustrated with an example. Furthermore, stability analyses are conducted visually using Nyquist envelopes and uncertainty discs.Öğe Kontrol sistemlerinde dayanıklı kararlılık analizi ve kontrolör tasarımı(İnönü Üniversitesi, 2025) Menak, Ramazan; Tan, NusretBu tez çalışmasında zaman gecikmeli ve gecikmeden bağımsız rastgele dereceli tek giriş - tek çıkış (SISO) doğrusal zamanla değişmeyen (LTI) sistemler için kararlılık sınır eğrisi (SBL) yöntemi kullanılarak nominal kararlılığı sağlayan tüm PID ve PI-PD kontrolör bölgeleri sistematik bir şekilde elde edilmiştir. Literatürde mevcut üç farklı kararlılık bölgesi merkezi nokta yöntemine ek olarak bu yöntemlerden türetilen yeni bir merkezi nokta yöntemi sunulmuştur. Bu yöntemler kullanılarak nominal kararlılık bölgelerinden kontrolör parametreleri seçilmiş ve bu parametreler kullanılarak sistemlerin performans karşılaştırmaları yapılmıştır. Aynı sistemler için SBL yöntemi kullanılarak H-? normu tabanlı nominal performans, dayanıklı kararlılık ve dayanıklı performans kriterlerini karşılayan tüm PID kontrolör bölgelerinin (ki-kd), (kp-ki) ve (kp-kd) düzlemlerinde hesaplanmasını sağlayan yöntemler geliştirilmiştir. Ayrıca PI - PD kontrolör yapısı için yine SBL yöntemi kullanılarak H-? normuna dayalı dayanıklı kararlılık kriterlerini sağlayan tüm kontrolör bölgelerinin (kd-kf) ve (kp-ki) düzlemlerinde hesaplanmasını mümkün kılan grafiksel bir yöntem PI-PD kontrolör yapısı için ilk kez sunulmuştur. Dayanıklı kararlılık ve performans analizlerinde kontrol edilen sistem yapısal olmayan belirsizlik içeren model olarak ele alınmıştır. Nominal kararlılık, nominal performans, dayanıklı kararlılık ve dayanıklı performans analizleri Nyquist eğrileri ile birlikte performans ve belirsizlik diskleri kullanılarak grafiksel bir yaklaşımla gerçekleştirilmiştir. Bu yaklaşım sayesinde kararlılık ve performans şartlarının eş zamanlı olarak tek bir grafik üzerinde görselleştirilmesi sağlanmıştır. Tez boyunca elde edilen sonuçlar, kontrol sistemlerinde nominal ve yapısal olmayan belirsizlik içeren sistem modelleri için nominal kararlılık, nominal performans, dayanıklı kararlılık ve dayanıklı performans şartlarını sağlayan PID/PI-PD kontrolör tasarımlarının etkin bir şekilde yapılabildiğini ortaya koymuştur.
