Durum Uzay Metodu İle Ekzotermik (ısı Yayan) Kimyasal Reaktörü Simüle Eden Isıl Sistemin Parametrelerinin Tespiti Ve Geri Beslemeli Kontrolü

Abstract

Kontrol sistemleri açık çevrim kontrol sistemleri ve kaplı çevrim kontrol sistemleri olmak üzere ikiye ayrılır. Açık çevrim sistemlerde sisteme bir giriş etkisi verilir ve çıkan sonuca göre yorum yapılır. Kapalı çevrim sistemlerde ise giriş etkisinin sonucunda oluşan çıktı değerini referans değerle karşılaştıran bir geri besleme mekanizması bulunur. Sistemdeki kontrol edici, hata değerine göre son kontrol elemanına sinyal göndererek sisteme müdahale eder. Kontrol ediciler kapalı çevrim kontrol sistemlerinde ölçüm elemanı ile son kontrol elemanı arasında bulunan cihazlardır. Kimyasal proseslerde en çok kullanılan kontrol ediciler; oransal (P), oransal-integral (PI) ve oransal-integral-türevsel (PID) kontrol edicilerdir. Bunlardan en gelişmişi ve en iyi sonuç vereni PID kontrol edicidir fakat parametrelerinin hesaplanması diğerlerine göre daha zordur. Kaliteli ve ekonomik bir üretim için kimyasal reaktörlerin doğru bir şekilde tasarlanması ve kontrol edilmesi gerekir. Belirli bir sistem için kontrol edici tasarlanırken çeşitli giriş değişkenlerine göre dinamik cevabın eldesi amacıyla dinamik simülasyon yapmak kaçınılmazdır. Böyle bir dinamik simülasyonun yapılabilmesi için önce sistemin tanınması yani dinamik özelliklerinin bilinmesi ve bu dinamik özellikler kullanılarak sistemin doğru bir şekilde modellenmesi gerekir. Sistemin dinamik özelliklerinin belirlenebilmesi için sistem üzerinde çeşitli testler yapılır. Testleri yapmak için sistemin belirli bir giriş değişkenine basamak (step), darbe (impulse), frekans (frequency) etkileri verilir ve sonuçlar kaydedilir. Yapılan testlerin sonuçları bir araya getirilip yorumlanarak sistem parametrelerinin tahmini yapılır. Bu parametreler kullanılarak çeşitli matematiksel denklemlerle sistem modellenir ve dijital ortamda simüle edilir. Simüle edilen sistem üzerinde birçok test yapılarak hızlı ve ekonomik bir şekilde, sistemin düzgün ve verimli çalışabilmesi için uygun olan kontrol edici tasarlanır. Bu çalışmada ekzotermik kimyasal reaktörü fiziksel olarak simüle eden bir ısıl sistem oluşturulmuştur, bu ısıl sistem üzerinde, proses kontrol biliminin temel yöntemleri olan ve bir kontrol edicinin parametrelerinin tespit edilmesinde uygulanan basamak testleri yapılmıştır. Elde edilen değerler ve matematiksel denklemler kullanılarak sistemin durum uzay modeli oluşturulmuş ve sistemin iç sıcaklığı ile ceket soğutma suyu debisi arasındaki transfer fonksiyonu bulunmuştur. Ayrıca, bu tespitlerden sonra sistemin dijital simülasyonu yapılarak ve frekans cevabı elde edilerek kararlılık şartları belirlenmiştir. Sistemin kontrolü için dijital simülasyonda çeşitli kontrol edici parametreleri denenmiştir. Bu parametreler kullanılarak sisteme basamak ve sinüsoidal darbe girişleri verilerek sistemin tepkisi incelenmiş ve sistem için uygun kontrol edici parametreleri tespit edilmiştir. Isıl sistemin geri beslemeli kontrol çevrimi simulink ortamında oluşturulmuş ve bu çevrime uygulanan bozan etkenler(Q ısıtıcı ve Ftnk) regülasyon kontrol ile belli bir süre sonra sistemin tekrar dengeye gelmesi sağlanmıştır. Son olarak ısıl sisteme belli bir sıcaklık referans değeri verilmiş olup, sistemin bu referans değerine ulaşması servo kontrol ile sağlanmıştır.

Since ancient times people have interested in automatic control and they have developed variety of automatic control systems according to their needs. The first known automatic control system that was developed in ancient times is liquid level control system which keeps the level of liquid in a container constant. In later years various control systems such as incubator and steam engine speed control system was developed and presented to usage of humankind. The control technology that was depend of mechanical engineering before the invention of electronic circuits, have showed a rapid development with the use of computers that capable of processing at high speed and accuracy. There are two types of control systems, one of them is open-loop control system and the other is closed-loop control system. In open-loop systems, an input is given to system and system is assessed according to output. In closed-loop systems, there is a feedback mechanism which comparing output, that result of input, with reference value. The system controller intervenes to system by sending a signal to final control element depending on the value of the error. Controller is a device, which located between the measurement device and final control element in closed-loop systems. The most widely used controllers on chemical processes are proportional (P), proportional-integral (PI) and proportional-integral-derivative (PID) controllers. PID controller is the most advanced among them and it gives the best results, but the parameters of PID controller calculation are more difficult than others. Chemical reactors are the essential equipments of a plant that producing chemicals. there are two types of chemical reactors by heat exchange, one of them is endothermic reactor that absorbs energy and the other is exothermic reactor that disperses energy. Exothermic reactors play a significant role among them. Exothermic chemical reactors are non-self regulating equipments that cannot balance them. Even a small variation in the equilibrium temperature causes instability, since an increase in the temperature proceeds the reaction and the progress of a reaction increases the temperature. To keep the system at steady state it should be controlled against the disturbance. Therefore, when the temperature changes in an exothermic chemical reactor, it is practically important know how it will response. For economical and good production, chemical reactors should be well designed and controlled. It is necessary to perform digital simulations in order to obtain the dynamical response according to input variables to design a controller for a specific system. To perform the digital simulation, firstly the system must be identified, which means dynamic properties of the system must be known and then accurate modeling of the system must be made by using these properties. To determine the dynamic properties of the system, various tests are performed on the system. To make the tests; step, pulse, frequency effects are given to a particular input variable of the system and the results are recorded. The results of the tests are gathered, interpreted and the parameters of system are estimated. By using these parameters, the system is modeled with various mathematical equations and is simulated digitally. To make the system work properly and efficiently, several tests are done on the simulated system and suitable controller is designed with fast and economical way. Today real systems are considered in industrial applications, there are multiple-input and output system in general. For multiple- input and output systems, state space method can be used commonly. A state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. The state-space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. Compared with traditional control theory and state-space control method ; traditional control theory in general providing system design by trial and error method while in modern control theory held by state space method, it can be easily obtained transfer functions and easily created of the closed loop system. In Modern control theory system designed with space method, system’s dynamics is important for mathematical definitions. There are many situations in chemical process. Expressing the conditions in a meaningful way is important for stability of the processes. Many chemical processes are multivariate, nonlinear and continuous. Chemical processes defined by mathematical equations with the first order differential equation and differential equations can be combined in the vector matrix. The vector used is a highly simplified version of the matrix representation of the mathematical definition of equation system. Increasing the number of input or output variable does not make the mathematical equation complicated. Control of the system set out in the light of the mathematical definition, static and dynamic characteristics of the system are identified and provided with the system requirements for creating good models of the systems. Mathematical model of the variables defined by state space method; are expressed state variables, input variables and parameters. State variables of a physical system are created during dynamic material and energy balances of composing. These are measuring variables that can be located in dynamic model of the system as an accumulation term (derivative term). The state variables of the system should be selected observable like the system’s temperature (T) and the concentration (C). In the system, the state variables can be observed with respect to time. Input variables are also called disturbances. These variables are not included derivative form in differential equation. Flow rate (F) entering a system or out of the system may be input variables of the system.The system parameters are more or less independent from the physical system variables. In this project, a thermal system that physically simulating the exothermic chemical reactor had established and the parameters of a controller had determined by applying step forcing functions, which are the basic methods of the process control. The state space model of the system was created with the obtained values and the used mathematical equations, after then transfer function of the system between internal temperature of tank and jacket cooling water flow rate, has been found. In addition, after the findings transfer function of the system, stability conditions were determined with digital simulation and frequency response analysis. To control the system, a variety of controller parameters had tested on the digital simulation. By using these parameters, step and sinusoidal pulse inputs are examined on the system and the most suitable controller parameters were found for the system. Feedback control loop of the thermal system was created in Simulink environment and distorting factors applied to this cycle (Q heating and Ftnk ) after a certain time the stability has been brought back with regulation control system. Finally, a certain temperature value is assigned the thermal system, to reach this reference value is provided by the servo control system.