Blending mechanism based set-point regulator

Abstract

Automatic control strategies force physical systems to behave in prescribed ways using the error value that is the difference between the system output and the desired reference input. This idea gives rise to feedback control systems. Since the only signal processor is the feedback controller, this classical control structure is also known as a one degree of freedom (1-DOF) control structure. In recent times, there has been considerable interest in more general control structures. In the two degree of freedom (2-DOF) case, the reference input is processed by the filter F(s), and the classical error is processed by the primary controller C(s). The prefilter F(s) is used as the second DOF to weight the set-point change in a desirable manner. In literature, there are many applications that use 2-DOF control structure which is sometimes called as model following control. Since PID controllers assure satisfactory results for a large range of processes and due to the simplicity of their structures, they still often represent the best solution from a cost/benefit ratio point of view. Therefore, the controller C(s) used in 2-DOF control structure is mostly a PID controller. Therefore, through this study, PI and PID controllers are used to design the proposed new structure. Internal Model Control (IMC) based PID is preferred for the feedback controller which is designed for a fast disturbance rejection performance. The processes are modeled as first order plus dead time (FOPDT) systems. Therefore the static gain (K), the time constant (T), and the time delay (L) of the model are obtained using well-known area method. The parameters of the PID controller depend on the process model parameters and in addition on IMC filter time constant (λ). λ is the only tuning parameter to be selected by the designer to achieve an appropriate compromise between the performance and the robustness issues in control system design. A smaller λ provides a faster closed loop response, but causes the manipulated control variable to become more vigorous, while a larger λ provides a slower but smoother response and a mild control effort. In this paper, a new 2-DOF control structure is proposed in which the advantages of 1-DOF and 2- DOF control structures are both exploited. In this new structure, the filtered output of the reference and the pure reference signals are blended so that the overall performance of the system is ameliorated with respect to load disturbance rejection and setpoint following. This new structure proposed in this study is named as a set-point regulator with blending mechanism (HAM-RA, SPR-BM). When the blending dynamics is set to be equal to zero then the proposed structure turns out to be a 2-DOF control structure; when the same dynamics is taken as unity, the proposed structure becomes 1-DOF control structure. The blending dynamics is determined with the aim of producing a system output that exactly matches to the filtered reference signal. The prefilter of the SPR-BM defines the desired behavior of the system and in order not to have an oscillatory behavior it is designed as FOPDT filter. When the feedback controller type is chosen to be a PI, the resulting blending mechanism becomes a pure gain. This blending constant is a function of system time delay (L), prefilter time constant and IMC filter time constant (λ). On the other hand, when the feedback controller is chosen to be a PID type, the blending mechanism then becomes a first order filter. The time constant of the obtained blending filter is half of the system time delay (L). Moreover, the static gain of the filter is again defined using the system time delay (L), prefilter time constant and IMC filter time constant (λ). In order to show the effectiveness of the proposed set-point regulator over classical 1-DOF and 2- DOF control structures, two simulation examples are given. A first order plus dead time (FOPDT) system is chosen for the first example. As a second example, a high order system with large dead time is used and the system is modeled as FOPDT. The aim of the second example is to show the effectiveness of the proposed structure even when there is a modeling error. In order to have a fair comparison of different control structures five different performance criteria are used for simulation studies. The results obtained from the simulation show that the set-point regulator with blending mechanism (SPR-BM) ameliorate the overall performance of the system with respect to load disturbance rejection and set-point following. Also it shapes the reference signal during the transient response; therefore it exhibits the best system output.

Özet

Bu çalışmada, Harmanlama Mekanizması (HM) içeren iki serbestlik dereceli (2-SD) bir kontrol yapısı sunulmuştur. Bu yeni yapıyla, bir Serbestlik Dereceli (1-SD) ve 2-SD kontrol yapıları kaynaştırılmıştır. Harmanlama Mekanizmalı Referans Ayarlayıcı (HAM-RA) olarak adlandırılan bu yeni yapıda birinci mertebeden ölü zamanlı bir filtre çıkışı ile saf referans işareti uygun bir şekilde harmanlanır ve yeni referans işareti oluşturulur. Böylelikle sistemin geçici hal davranışı şekillendirilirken kontrol yapısından dolayı ise yük bozucularını bastırma ve referans değer takibi hedefleri birbirinden ayrılmış olur. Endüstride karşılaşılan süreçlerin oldukça büyük bir bölümü Birinci Mertebeden Ölü Zamanlı (BMÖZ) sistem olarak modellenebilmektedir. Bu sebeple çalışmada ele alınan sistemler öncelikle BMÖZ olarak modellenmiştir. İçsel Model Kontrole dayalı (İMK) PID kontrolörü yük bozucularını bastırmak amacıyla geribesleme kontrolörü olarak tasarlanmıştır. Böylelikle tasarımcı PID kontrolörünün üç parametresini belirlemek yerine İMK filtre sabitini belirleyerek kontrolör parametrelerini bulabilmektedir. Kontrolör PI tipinde seçildiğinde HM’da yer alan harmanlama dinamiği bir sabite dönüşür. Bu harmanlama sabiti modelde belirlenen ölü zamana, İMK filtre sabitine ve HAM-RA yapısındaki önfiltenin zaman sabitine bağlıdır. Öte yandan kapalı çevrim kontrolörü PID tipinde seçildiğinde harmanlama dinamiği birinci mertebeden bir filtre olarak elde edilir. Bu filtrenin zaman sabiti model ölü zamanının yarısıdır. Önerilen HAM-RA yapısının getirilerini göstermek amacıyla iki adet benzetim örneği ele alınmıştır. Elde edilen sonuçlar, önerilen yeni yapının geçici halde 1-SD ve 2-SD yapılara olan üstünlüğünü ortaya koymaktadır.