PI‐PD controller design for time delay systems via the weighted geometrical center method

Abstract

In this study, a PI‐PD controller tuning method is presented using the weighted geometrical center method, which is based on the calculation of the weighted geometric center of the stability region obtained by the stability boundary locus method. The proposed method for tuning of PI‐PD controller parameters (kd,kf,kp and ki) is performed in three steps. In the first step, the (kd,kf) parameter region for the inner loop with PD controller is obtained, and then the weighted geometric center of this region is calculated. In the second step, the inner PD loop is reduced to a single block using the numerical values of (kd,kf) that are obtained in the first step. Then, the (kp,ki) values of the external loop with PI controller are determined by the same procedure. This tuning method has some advantages over other tuning methods in terms of simplicity and robustness. The simulation examples show that a PI‐PD controller designed using the proposed method provides good performance results when compared to other tuning methods presented in the literature.

PI-PD Controller Design for Magnetic Levitation Systems Via Weighted Geometrical Center Method

“…Daha küçük adım boyutlu ω seçmenin (örneğin, 0.01, aynı zamanda daha büyük m değerlerine neden olur), büyük adım boyutundan daha doğru sonuçlar almamızı sağlayacağı bir gerçektir. Sonuçlar adım boyutu değişikliklerinden etkilenebilir ancak kararlılık açısından önemli bir etkisi yoktur [25]. Böylece, PD kontrolcüsünün AGM noktası (k d , k f ) = (-0.06177, -2.361) olarak elde edilir.…”

“…PI denetleyicisinin hedefi, kapalı döngü sisteminin referans izleme, bozulma reddi ve gürbüzlük performanslarını yerine getirmektir. Bu çalışmada, manyetik top levitasyon sistemi için ilk olarak Onat [24,25] tarafından önerilen AGM konseptine dayalı bir PI-PD tasarım prosedürü önerilmiştir. Prosedürün ilk adımında, PD kontrolcülü ve ağırlıklı geometrik merkezi ile iç döngü için kararlı kılan kontrolcü parametreleri bölgesi (oransal kazanç: kf ve türevsel kazanç: kd) hesaplanmıştır.…”

Proportional-integral-derivative controller design for time-delay systems via stability region centroid

“…Though the method produced good results, it is computationally intensive. PI-PD controller for time-delay systems was tuned by [20] using WGC method which yields satisfactory performance compared to some other methods in the literature. In [14] CCSR method for PI-PD controller design was proposed for unstable systems with time-delay.…”

A graphical approach for controller design with desired stability margins for a DC–DC boost converter

“…A robust and non‐fragile PI controller was designed by calculating the centroid stable point of the all stability region in [25]. PI/PD controller parameters were obtained by computing weighted geometrical centre (WGC) from the all stability region in [26]. A method for obtaining the PI/PD controller parameters by calculating the centroid from the all stability region has been reported in [27].…”