Ağırlıklı geometrik merkez metodu ile pratik PI-PD kontrolör tasarımı

Abstract

Bu çalışmada zaman gecikmeli sistemler için ağırlıklı geometrik merkez metodu kullanılarak PI-PD kontrolör tasarımı yapılmıştır. Bunun için öncelikle verilen bir kontrol sistemini kararlı yapan tüm PD kontrolör parametreleri kararlılık sınır eğrisi metodu kullanılarak hesaplanmıştır. ( d f k ,k ) düzleminde çizilmiş olan bu eğriden yararlanılarak belirli bir ( d f k ,k ) parametre çifti elde edilmiştir. Daha sonra yine kararlılık sınır eğrisi metodu kullanılarak sistemi kararlı yapan tüm PI kontrolör parametreleri ( p i k ,k ) düzleminde çizilmiş ve bu kararlılık bölgesi içerisinden ağırlıklı geometrik merkez metodu vasıtasıyla belirli bir ( p i k ,k ) parametre çifti elde edilmiştir. ( d f k ,k ) ve ( p i k ,k ) düzlemlerinde çizilen kararlılık sınır eğrilerden yaralanarak, sistemi kararlı yapan tüm PI-PD kontrolör parametre değerleri hesaplanabilmektedir. Ancak bu bölgeler içerisinden sistem performansını en iyi şekilde sağlayabilecek parametrelerin seçimi önemli bir sorundur. Ağırlıklı geometrik merkez metodu bu soruna oldukça pratik ve kullanışlı bir çözüm sunmaktadır. Metotla ilgili bazı örnekler verilmiş ve birim basamak cevapları incelenerek kullanılan metodun performans analizi yapılmıştır.

Keywords

• PI-PD kontrolör, Kararlılık, Ağırlıklı geometrik merkez, Zaman gecikmesi

Practical tuning algorithm for PI-PD controllers using weighted geometrical center method

Abstract

PID controllers are the most common controller algorithm in industrial applications due to their simple structure and robust performance. It can be said that PID controllers are used more than 90% of practical processes. Since derivative action is not used very often, control loops are mostly PI. Many real systems such as biological, physical, chemical, industrial systems have time delay which leads to oscillations or even instability. Thus, modelling and stability analysis of the systems with time delay are very important. In this paper, a practical tuning algorithm of PI-PD controller for the processes with time delay using the weighted geometrical center (WGC) method has been presented. PID controllers show an acceptable control performance for many open loop stable processes. However, they have some structural limitations and cannot provide good results for controlling of unstable, integrating and resonant processes. A modified form of the PID controller is the PI-PD controller. it has four parameters for tuning and provides an excellent control of unstable, integrating and resonant processes. Many important results for PI-PD controllers have been recently reported. However, some of these studies basically focus on calculating the stability region in the controller parameters plane, or required complex solutions methods. It can be said that many of them are far from the simplicity and could not give a practical solution in terms of selecting controller parameters. In this study, the proposed method provides a simple tuning algorithm to determine the values of controller parameters from the stability region of the system. The important advantages of the proposed method are both calculating of the controller parameters without using complex graphical methods and ensuring stability of the closed loop system. The examples given in the paper show this simple tuning method can perform quite reliable results. In this study, a practical tuning algorithm based on the WGC method for PI-PD controller has been presented for the computation of stabilizing PI-PD controller parameters for the processes with time delay using the stability boundary locus method. The proposed method is based on calculating of all stabilizing PI-PD controller parameters region which is plotted using the stability boundary locus in the ( d f k ,k ) and ( p i k ,k ) plane and computing the weighted geometrical center from this stability region. After selecting PD controller parameters from the stability region plotted in the ( d f k ,k ) plane, the method can be applied to obtain desired PI controller parameters ( p i k ,k ). The proposed tuning method provides quite reliable results for time delay systems as illustrated by the examples presented in the paper. For the future works, the WGC method can be applied to internal feedback loop with PD controller to obtain optimum controller parameter for the system. And, then the proposed method can be used for PI controller. Thus, controller parameter tuning algorithm can be improved. Besides, a gain margin phase margin tester can be implemented in PI control loop to achieve user specified gain and phase margins. The proposed method can be compared with the other tuning methods in the literature to show its effectiveness. This paper is organized as follows: Firstly, stability regions of PI-PD controller using the stability boundary locus are presented. Then, the Weighted geometrical center method is introduced. And, to illustrate the efficiency of the proposed method, some simulation examples are also given. Finally, concluding remarks and discussion for the future projects are given in the last section.

Keywords

• PI-PD controller, Stability, Weighted geometrical center, Time delay