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.
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.
Details
| Other ID | JA69EV73YS |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | December 1, 2016 |
| Submission Date | December 1, 2016 |
| Published in Issue | Year 2016 Volume: 7 Issue: 3 |