Kapalı çevrimli örneklenmiş-verili kontrol sistemlerinde optimum kontrol parametrelerinin tayini
Optimum controller settings of closed - loop sampled - data process control systems
- Tez No: 66630
- Danışmanlar: PROF. DR. A. TALHA DİNİBÜTÜN
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1997
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Makine Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Makine Teorisi ve Kontrol Bilim Dalı
- Sayfa Sayısı: 148
Özet
ÖZET Geri beslemeli kontrol sistemleri tasarımında II. Dünya Savaşı' ndan beri bir çok gelişme olmuştur. İlk zamanlarda sanayide fazla yaygın olarak kullanılmayan kontrol çevrimleri şu an vazgeçilmez hale gelmiştir. Özellikle seri üretim yapılan sektörlerde otomatik kontrol son derece önemlidir. İyi yönde yapılacak her değişiklik seri ve kitle üretiminde çok büyük ekonomik kazançlar sağlayacaktır. Bu nedenle, son yıllarda endüstrinin çeşitli kollarında yaygın olarak kullanılan proses kontrol sistemlerinde, optimum kontrolün sağlanması problemi çok önem verilen bir konu haline gelmiştir. Bu çalışma esas olarak, yukarıda sözü edilen problemin dijital simülasyon metodu ile çözümünü amaçlamaktadır. Örneklenmiş - verili kapalı çevrimli bir otomatik kontrol sisteminde, kontrol organı olarak PI ve PID' ye çeşitli performans kriterlerinin uygulanması ile optimum kontrol parametreleri bulunarak karşılaştırılmaları elde edilmiştir. Üzerinde çalışılan proses kontrol sisteminin şekli ve parametreleri uygulamadan (İngiltere' de ICI Billingham Endüstriyel Kuruluşu' nun kendi testleri ile bulduktan parametre gruplarından) alınmıştır. Çalışılan sistemin proses transfer fonksiyonu, iki zaman sabiti ve bir zaman gecikmesinden oluşmaktadır. Ayrıca geri besleme kolu üzerinde süreksiz ölçmeler bulunmaktadır. Ölçme için kullanılan kromatograf cihazı bir örnekleme zamanına ve bir tutucuya sahiptir. Cihazda cevap gecikmesi (analiz zaman) ve sistemde iletim gecikmesi bulunmaktadır. Kontrol organı olarak PI ve PID seçilmiştir. Sisteme referanstan birim basamak girişi uygulanarak çıkış alınmıştır. Bu çalışmada öncelikle kontrol organı ve optimum kontrol organı için kullanılan performans kriterleri tanıtılmıştır. Sistemin simülasyonu ve optimizasyonu Turbo C (Version 2.01) kullanılarak yapılmıştır. Sistem üzerinde yapılan çalışmada, başlangıç kontrol parametreleri (K, Ti ve Td) kullanılarak sisteme performans kriterleri uygulanmış ve sistem cevabı alınmıştır. Daha sonra bunların karşılaştırılması yapılmıştır. Ayrıca bozucuya birim basamak girişi uygulanarak sistem üzerindeki etkileri incelenmiştir. Son olarak farklı örnekleme zamanlan için optimum ayar değerleri bulunarak incelenen sistemin senkronize çalışıp, çalışmadığı tespit edilmiştir. XVU
Özet (Çeviri)
SUMMARY When a performance criterion or a set of performance specifications is stipulated for a system and these conditions are not met, a control problem exists. Generally, in order to obtain the desired system performance additional equipment must be used in conjunction with the basic system. Either modern control or conventional design techniques are utilized to determine the configuration and parameters of the required additional equipment. By the nature of the modern control technique a specified performance criterion ( PI = J e2dt to be minimum) is met exactly, and a unique design is obtained. The performance of the system is therefore said to be optimal in terms of the defined performance criterion. In contrast, the conventional technique satisfies a required set of performance specifications. These requirements may be met by a number of different designs. In general, these designs do not simultaneously meet a defined optimal performance criterion. Therefore, these designs may be called suboptimal. The characteristics used to judge performance are as follows: 1. Maximum overshoot Mp 2. Time to reach the maximum overshoot (peak time) tp 3. Settling time (also called solution time), which is the time for the response to settle within a given percentage of the final value, t, 4. Frequency of oscillation of the transient Wd 5. Steady-state error for a given input ess The ready availabilility of the digital computer has led to the development and exploitation of modern control theory. This permits the achievement of an optimal system performance which meets some specified performance criterion. It involves minimizing (or maximizing) a performance index. This method, in contrast to the conventional design technique, relies on the extensive use of mathematical analysis. The selection of a performance index is often based on mathematical convenience, i.e., the selected performance index permits the mathematical design of the system. While the method yields a unique mathematical solution, the actual system performance may not have all the desired performance characteristics. xviuIn other words, the resulting optimal control satisfies the mathematical performance index but may not yield desired values of Mp, tp, ts, etc. A compromise must be made between specifying a performance index which includes all the desired system characteristics and a performance index which can be achieved with a reasonable amount of computation. It should further be noted that it is most difficult to analyze multiple-input multiple- output systems by conventional control theory, whereas modern control theory is quite adaptable to the analysis and design, with the use of the digital computer, of such systems. One of the major problems in the process control systems is the determination of the controller settings to obtain satisfactory transient performance. A number of useful methods for determining optimum settings of industrial controllers have been developed. The research presented here considers a closed-loop sampled-data system which consisted of a distillation column, a chromatograph as a measuring instrument, a chromatograph sampler and a controller. The mathematical model of the process consisted of two time- constant and pure time delay. In the practical application of process control systems, some methods for tuning and process identification are needed. The selection of controller modes depends on the process to be controlled. Proportional control is simple, but the response exhibits offset. The derivative action in PD control makes it possible to increase the controller gain with the result that the response has less offset and responds more quickly compared to proportional control. To eliminate offset, integral action must be present in the controller in the form of PI and PID control. PI control often causes the response to have large overshoot and a slow return to the set point especially for high- order processes. The presence of derivative action in a PID controller gives less overshoot and a faster return to the set point, compared to the response for PI control. Proportional (P) control action. For a controller with proportional control action, the relationship between the output of the controller m(t) and the actuating error signal e(t) is m(t) = K.e(t) or, in Laplace-transformed quantities, M(s)/E(s)=K where K is termed the proportional sensitivity or the gain. XIXIntegral (T) control action. In a controller with integral control action, the value of the controller output m(t) is changed at a rate proportional to the actuating error signal e(t). The transfer function of the integral controller is M(s)/E(s)=l/TiS where Ti represents the integral time. Tjis an adjustable constant. If the value of e(t) is doubled, then the value of m(t) varies twice as fast. For zero actuating error, the value of m(t) remains stationary. The integral control action is sometimes called reset control. Proportional-plus-integral (PI) control action. The transfer function of the controller is M(s)/E(s) = K.(l + l/Tis) where K represents the proportional sensitivity or gain, and Tj represents the integral time. Both K and Tj are adjustable. The integral time adjusts the integral control action, while a change in the value of K affects both the proportional and integral parts of the control action. The integral time Tj is called reset control. Proportional-plus-derivative (PD) control action. The transfer function of the controller is M(s)/E(s) = K.(l+Tds) where K represents the proportional sensitivity and Ta represents the derivative time. Both K and Ta are adjustable. The derivative control action, sometimes called rate control, is where the magnitude of the controller output is proportional to the rate of change of the actuating error signal. The derivative time Ta is the time interval by which the rate action advances the effect of the proportional control action. Note that derivative control action can never be used alone because this control action is effective only during transient periods. Proportional-plus-integral-plus-derivative (PH>) control action.The combination of proportional control action, integral control action, and derivative control action is termed proportional-plus-integral-derivative control action. This combined action has the advantages of each of the three individual control actions. The transfer function of the controller is M(s) / E(s) = K.(l + 1 / TiS + T“s) where K represents the proportional sensitivity, Ta represents the derivative time, and Ti represents the integral time. Errors analysis. Errors in a control system can be attributed to many factors. Changes in the reference input will cause unavoidable errors during transient periods and may also cause steady-state errors. Imperfections in the system components, such XXas static friction, backlash, and amplifier drift, as well as a ging or deterioration, will cause errors at steady 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 steady-state error in response to certain types of inputs. A system may have no steady-state error to a step input, but the same system may exhibit nonzero steady-state error to a ramp input. (The only way we may be able to eliminate this error is to modify the system structure.) Whether or not a given system will 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. Error criteria. In the design of a control system, it is important that the system meet given performance specifications. Since control systems are dynamic, the performance specifications may be given in terms of the transient-response behavior to specific inputs, such as step inputs, ramp inputs or the specifications may be given in terms of a performance index. Performance indexes. A performance index is a number which indicates the ”goodness " of system performance. A control system is considered optimal if the values of the parameters are choosen so that the selected performance index is minimum or maximum. The optimal values of the parameters depend directly upon the performance index selected. Requirements of performance indexes. A performance index must offer selectively; that is, an optimal adjustment of the parameters must clearly distinguish nonoptimal adjustments of the parameters. In addition, a performance index must yield a single positive number or zero, the latter being obtained if and only if the measure of the deviation is identically zero. To be useful, a performance index must be a 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. Error performance indexes. 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 system parameters, once a performance index is specified, the optimal system can be designed by adjusting the parameters to yield, say, the smallest value of the integral. To compare the quality of control on a numerical basis, several criteria that integrate some function of the error with respect to time have been proposed. Various error performance indexes have been proposed in the literature. We shall discuss the following six in this work. These performance indexes are as follows: 1. ISE (Integral of squared error) criterion 2. IAE (Integral of absolute value of error) criterion 3. ITSE (Integral of time weighted by squared error) criterion XXI4. ITAE (Integral of time weighted by absolute value of error) criterion 5. ISTSE (Integral of squared time weighted by squared error) criterion 6. ISTAE (Integral of squared time weighted by absolute value of error) criterion Integral of squared error (ISE) criterion. According to the integral of squared error (ISE) criterion, the quality of system performance is evaluated by the J e2(t)dt integral. Where the upper limit oo may be replaced by T which is chosen sufficiently large so that e(t) for T
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