Optimal Controller Settings For Feedback Control Of A Process With Dead Time And Sampled Measurement

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1996Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 1996Günümüz endüstrisi, mümkün olan en kısa sürede en fazla üretimi yaparak pazar koşullarına uyum sağlayabilir. Bu nedenle, endüstriyel sistemlerin, verimliliği temel alınarak tasarlanması gereklidir. Üretimde, yaygın olarak kullanılan otomatik kontrol sistemlerinin, optimum kontrolünün sağlanması problemi üzerinde durulması gereken bir konudur. Endüstriyel sistemlerde kullanılan kontrol sistemlerinin, ayarında genellikle deneysel yöntemler tercih edilmektedir. Bu deneysel yöntemlerden Ziegler-Nichols' ün önerdiği sürekli titreşim metodu ve proses reaksiyon eğrisi metodu sürekli sistemler için kullanılabilir ayar değerleri vermektedir. Fakat endüstrideki sistemlerin çoğu sürekli sistemlerden oluşmamaktadır. Bu deneysel yöntemelerhı bu sistemler içinde kabul edilebilir değerler verip vermediğinin incelenmesi pratik uygulama açısından önem taşımaktadır. Bu çalışmada geri besleme kolu üzerinde süreksiz ölçmeler bulunan bir sistemle, sürekli bir sistem bu deneysel yöntemler ve performans indeksleriyle deneye tabi tutulmuş ve sonuçlan karşılaştınlmıştır. Proses kontrol sisteminin şekli ve parametreleri uygulamadan alınmıştır.One of the major problems in the process control is the determination of the controller settings to obtain satisfactory transient performance. A number of useful methods for determining optimum settings of industrial conrollers have been developed- The research presented here considers a closed-loop sampled-data system which consisted of a distillation column, a chromatograph as ameasuring instrument, a chromatograph sampler and a controller. The mathematical model of the process consisted of two time-constant and pure time delay. A pneumatic industrial controller provided P, PI, PD and PK) controls; and simulating the close-loop operation numerically. Errors in a control system can be attributed to many factors. Changes in the reference input will cause inavoidable errors during transient periods and may also cause steady-state errors. Imperfectionsin the system compnents such as static friction, backlash and amplifiier drift as well as a ging or deterioration, will cause errors at state. The steady state performance of a stable control system is generally judged by the steady state error due to step, ramp, or acceleration inputs. Any physical control system inherently suffers stady state error in responce to certain types of inputs. A system may have no staedy state error to a step input, but the samesytem may exhibit nonzero steady state error to a ramp input. Whether or not a given systemwill exhibit steady state error for a given type of input depends upon the type of open loop transfer function of the system to be discussed in what follows. In the desing of a control system, it is important that the system mmet given performance specifications. Since control systems are dynamic, the performance specifications may be given in yterms of the transient response behavior to specific inputs such IX as step inputs ramp inputs etc., or the specifications may be given in terms of a performance index. A performance index is a number which indicates the goodness of syste performance. A control system is considered optimal if the values of the parameters are chosen so that the selected performance index is minimum or maximum. The optimal values of the parameters depend directly upon the performance index selected. A performance index must offer selectively ; that is an optimal adjustment of the parameters must clearly distinguish nonoptimal adjustment of the parameters. In addition a performance index must yield a single positive number or zero the latter being obtaine if and only if the measure of the devation is identically zero. To be useful a performance index must be function of the parameters of the system and it must exhibit a maximum or minimum. Finally to be practical a performance index must be easily computed analytically or experimentally. In what follows we shall discuss several error criteria in which the corresponding performance indexes are integrals of some function or weighted function of the deviation of the actual system output from the desired output Since the values of the integrals can be obtained as functions of the parameters once a performance index is specified the optimal system can be designed by adjusting the paremeters yield, say, the smallest value of the integral. Various error performance indexes have been proposed in the literature. We shall discuss the following four in this section. These indexes are ISE, ITSE, IAE and ITAE. According to the integral square-error ( ISE ) criterion, the quality of the system performance is evaluated by theje2 ( t )dt integral. Where the upper limit maybe replaced by T which is chosen sufficiently large so that e (t ) for is negligible. The optimal system is the one which minimizes this integral. This performance index has been used extensively for both deterministic inputs ( such as step inputs ) and statiscial inputs because of the ease of computing the integral both analytically and experimentally. A characteristic of this performance index is that it weighs large errors heavily and small errors lightly. A system dessigned by this criterion tends the show a rapid decrease in a large initial errors. Hence the responce is fast and oscillatory. Thus the system has poor relative stability. Note, however, that the integral square error criterion is often of practical significance because the minimization of the performance index results in the minization of power consumption for the system such as spacecraft systems. The performance index based on the integral-of-time-multiple square error ( ITSE ) criterion is te2 (t ) dt The optimal system is the one which minimizes this integral. This criterion has a characteristic that in the unit step responce of the system a large initial error is weighed lightly while errors occoring late in the transient response are penalized heavily. This criterion has a better selectivity than the integral square error criterion. The performance index defined by the integral absolute error ( IAE ) criterion is Jj e( t ) | dt. This is one of the most easily applied performance indexes. If this criterion is used both highly underdamp and highly overdamp systems cannot be made optimum. An optimum system based on this criterion is a system which has reasonable damping and satisfactory transient-response characteristic however the selectivity of this performance index not too good. Although this performance index cannot easily be evaluated. According to integral of time multiplied absolute error criterion ( ITAE ) the optimum systems is the one which minimizes the following performance index. As in the preceding criteria a large initial error in a unit step response is weighed lightly and errors occurring late in the transient response are penalized heavily. A system designed by use of this criterion has a characteristic that the over shoot in the transient responcse is small and oscillations are well damped. This criterion possesses good selectivity and is an improvement over the integral absolute error criterion. It is however very diffucult to evaluate analytically although it can be easily measured experimentally. XI Control systems are designed to perform specific tasks. The requirements imposed upon the control system are usually spelled out as performance specifications. They generally relata to accuary relative stability and speed responce. For routine desing problems, the performance specifications may be given in terms of precise numerical values. In other cases they may be given partially in terms of precise numerical values and partially in terms of qualitive statements. In the latter case the specifications may be have to modified during the course of design since the given specifications may never be satisfied or may lead to a very expensive system. Generally speaking, the performance specifications should not be more stringent than necessary to perform the given task. If the accuary at steady state operationis of prime importance in a given control system then we should not require unnecessarily rigid performance specifications on the transient response since such specifications will require expense componenets. Remembers that the most important pert of control system design is to state the performance specifications precisely so that they will yield an optimal control system for the given purpose. In most practical cases the design method to be used may be determined by the performance specifications applicable to the particular case. In designing conrol systems if the performance specifications are given in terms of time domain performance measures such as phase margin gain margin resnoat peak value or bandwith then we have no choice but to use a trial and error approach based on the root locus method and or frequency responce methods. In this work, the Z-N methods are applied to a sampled data process control system which consisted of a binary distillation column, a chromatografas a measuring instrumant and an industrial controller. The Mathematicals maodels of the distillation column and the chromatograf, representing a real plant. The close loop sampled data system was digitally simulated Kmax and Pu values for this system were determined by applying the simulated Z- N procedure, and then the controller settings were computed according ti relationships listed above. These settings and the corresponding time histories of the output of the distillation process obtained from the simulation study are compared with ISE,ITSE,IAE and ITAE criterion. XII The general block diagram represention of the process control system is shown in Figl. r(t) _ e(t) -?$> Controller Disturbance *® -. Proses c(t) ?*» i transportation delay I retention hold «*- _\. sampler Figure 1. Block diagram of the sampled-data process control system.Yüksek LisansM.Sc