Generalized modeling principles of a nonlinear system with a dynamic fuzzy network

Generalized modeling principles of a nonlinear system with a dynamic fuzzy network (DFN) - a network with unconstrained connectivity and with dynamic fuzzy processing units called 'feurons', have been given. DFN model has been trained both in open loop and closed loop forms to satisfy these principles. Several system trajectories with a PRBS input have been used for open loop training. DFN model obtained from open loop training was used in a closed loop training with an extended Kalman filter (EKF) in an observer design. For gradient computations adjoint sensitivity method has been used

Application of dynamics wavelet networks to Load Frequency Control

Frekans kararlılığı açısından iki veya daha fazla sayıda güç bölgesi içeren enterkonnekte güç sistemlerinde, her bir bölgedeki üretim planlı bir güç alışverişini sürdürebilmek için gereklidir. Bu çalışmada içerisinde geri dinamikleri, ortogonal olmayan ana dalgacık aktivasyon fonksiyonları ve iç bağlantı ağırlıkları bulunan bir “Dinamik Dalgacık Ağı’na (DDA)”  dayalı yeni bir uyarlamalı yük frekans denetleyicisi (YFD) tasarımı amaçlanmıştır. Bunun için bir DDA iki bölgeli bir güç sistemi örneğinde bölgeler arasına bağlanmıştır. Adaptasyon, DDA parametrelerinin ayarlanmasına dayanır. Bu da yük frekans hata masraflarını içeren bir ölçütün en aza indirilmesi ile sağlanır. Gerekli olan ölçütün ağ parametrelerine göre gradyanları, ek duyarlılık analizi ile hesaplanmıştır.Yapılan benzetim çalışmaları, bu denetim yaklaşımının geleneksel integral denetime göre daha başarılı olduğu bir iki bölgeli güç sistemi üzerinde göstermiştir.Anahtar Kelimeler: Yük frekans denetimi, güç sistem denetimi, dalgacık dönüşümü, dinamik dalgacık ağı, zeki denetim.Frequency stability is one of the stability criteria for large-scale stability of power system. In interconnected power systems with two or more areas, the generation within each area has to be controlled so as to maintain scheduled power interchange. Load frequency control scheme has two main control loops such as primary and secondary control. In primary loop, a steady state frequency error can occur forever. Secondary loop controls the active power at the tie line between areas. This paper proposes a new adaptive load frequency controller based on a ?Dynamic Wavelet Network (DWN)? that has lag dynamics, non-orthogonal mother wavelets as activation function and interconnection weights. A DWN is connected between the two area power systems. The input signals of the DWN are the ACEs and their changes. The outputs of the DWN are the control signals for the two-area load frequency control. Adaptation is based on adjusting parameters of DWN for load frequency control. This is done by minimizing the cost functional of load frequency errors. The cost gradients with respect to the network parameters are calculated by adjoint sensitivity method. It is illustrated that this control approach is more successful than conventional integral controller for load frequency control in two area systems.Keywords: Load frequency control, power system control, wavelet transformation, dynamic wavelet networks, intelligent control

Fero modelleme ve optimal bulanık kontrol

Bu tezin, veri tabanı üzerinden yayınlanma izni bulunmamaktadır.ÖZET Anahtar Kelimeler: Kula cürufu, bentonit, uçucu kül, taban külü, çimento karışımları. Çimento veya betonda uygun puzolanların, uygun miktarlarda, bilinçli bir şekilde kullanılması bir çok çevresel, teknik ve ekonomik faydalar sağlamaktadır. Bilindiği gibi ülkemiz zengin doğal puzolan yataklarına sahiptir. Bu çalışmada; doğal puzolan olan Kula cürufu ve Çanakkale- Ayvacık bentonit' i, Soma Termik Santrali atıkları (uçucu kül ve taban külü) ve Kütahya-Emet-Espey yöresindeki kolemanit konsantratör atığı ile birlikte değerlendirilmesi amaçlanmıştır. Çalışmada söz konusu doğal puzolanlar ve atıklar çimento üretiminde katkı maddesi olarak kullanılmıştır. Bu sayede çimento üretiminde enerji tasarrufu sağlanması ve atık maddelerin çevreye verebilecekleri olumsuz etkilerin giderilmesi de amaçlanmıştır. Kula cürufu ve bentonit önce ayrı ayrı belirli oranlarda çimento klinkerine katılmış, daha sonra değişik oranlarda Kula cürufu-uçucu kül, Kula cürufu-taban külü, Kula cürufu-kolemanit konsantratör atığı ve bentonit-uçucu kül, bentonit-taban külü, bentonit- kolemanit konsantratör atığı varyasyonları katkı maddesi olarak denenmiştir. Katkıların, çimento priz süresi, hacim genleşmesi, eğme ve basma dayanımı, öğütme süresi gibi özellikleri üzerine etkileri incelenmiştir. Çimento karışımlarına ait fiziksel ve mekanik özellikler TS 24 'e göre tayin edilmiştir. Kimyasal analizler XRF ve volumetrik metotlara göre yapılmıştır. Sonuçlar SEM ve XRD Analizleriyle de desteklenmiştir. Çimento karışımlarının fiziksel, kimyasal ve mekanik özellikleri Türk Standartlarıyla uyum halindedir. Böylece bu çalışmada kullanılan katkıların çimento üretiminde katkı maddesi olarak kullanılabileceği bulunmuştur. XVKeywords: Kula puzzolan, bentonit, fly ashes, bottom ashes, cement mixes. Cement or concrete provide some technical and economical advantages when approprate and suitable quantity of puzzolan are consciously used. It is well know that, our country has rich puzzolan miners. In this study, Kula puzzolan from Kula and bentonite from Çanakkale-Ayvacık with Soma thermal power wastes and colemanite concentrator wastes from Kütahya-Emet- Espey utilize in cement producing as an additive material. Thus energy saving in cement production and elimination of environmental problems caused by these wastes were also investigated. The effects of the additives on setting time, volume expansion, bending and compressive strength and grinding time of cement were studied. The physical and mechanical properties of the cement mixes were determined according to TS 24, chemical analysis were performed by XRF and volumetric methods. The chemical, physical and mechanical properties of cement mixes are suitable in accordance with related Turkish Standarts. The results were supported with SEM and XRD analyses. It was found that the additives used in this study can be utulized as on additive material in producing cement. XV

Lineer olmayan ekzotermik reaktörün optimal kontrolü

Bu tezin, veri tabanı üzerinden yayınlanma izni bulunmamaktadır.ÖZET Anahtar Kelimeler: CSTR, Optimal operasyonlar, Gradyant yöntemi, Başlama, Kapama, Regulasyon Eldeki kaynakların verimli kullanılması ve iş dünyasındaki rekabet yıllardan beri kimyasal endüstrinin arzuladığı güçtür. Bu amaçla proseslerin matematik modelinin oluşturulması onlar üzerinde tasarım hesaplarının yapılmasına izin vermiştir. Aynı zamanda çok hızlı bilgisayarların gelişimi bu hesapların matematiksel model üzerinde uygulanılmasını sağlamıştır. Pratik işlemlerde bilgi ve tecrübe önemlidir. Fakat bunun yanında teorik sonuçlar dizge üzerinde araştırma geliştirme yapılmasında önemli rol oynar. Bu düşünce ile bu tezde ekzotermik tank reaktörlerin lineer olmayan matematik modeli başlangıç olarak alınmıştır. Daha kolay ve anlaşılır bir gerçekleme olması için denklemler normalize edilmiştir. Kimyasal fabrikalar birbirleriyle bağlanmış birçok proses biriminden oluşur. Her birim arasında madde ve enerji aktarımı mevcuttur. Bu aktarmada amaç ekonomik işletim ve üretimdir. Bu nedenle endüstride kontrol sistem tasarımı artık ekonomik nedenlere dayanmaktadır. Klasik kontroller yerini gelişmiş kontrollere bırakmaktadır. Bu çalışmada ekzotermik reaktörün ekonomik işletimi iki ayrı çalıştırma rejiminde incelenmiştir. Birincisi reaktörün başlangıç durumundan sürekli çalıştırma rejimine getirilmesi, diğeri ise reaktörün bu çalıştırma rejiminde tutulmasıdır. Önce bu tezde, işletimi zor ekzotermik devamlı karıştırmalı tank reaktörünün (Continuously Stirred Tank Reactor - CSTR) klasik PID kontrolü ele alınmıştır. Bu kontrolle, sürekli çalışma rejiminde reaktör sisteminin kararlılığının, konsantrasyon beslemesindeki basamak değişime rağmen bozulmadan korunduğu ve reaktör sıcaklılığının istenen çalışma noktasında tutulabildiği gözlenecektir. Daha sonra lineer sistemler için oluşturulan lineer kuadratik regülatör problemleri (LQR), lineer olmayan sistemler için geliştirilmiştir. Ekzotermik devamlı karıştırmalı tank reaktörler lineer olmayan davranışa sahiptirler ve standart doğrusallaştırılmış sistem analizlerine genelde iyi cevap vermezler. Bu çalışmanın amacı, örnekler vererek CSTR sisteminin besleme sıcaklığı ve konsantrasyonundaki bozuculardan kaynaklanan problemlerini vurgulamaktır. Ve lineer olmayan geribesleme optimal kontrolün bu problemleri nasıl çözdüğünü analizlerle görmektir. Farklı bir başlangıç durumundan, ileribesleme optimal kontrol kullanarak, geribesleme kontrolün reaktör sıcaklığını nasıl arzulanan çalışma sıcaklığına getirdiği gözlenecektir. Bu tezde lineer olmayan dizgenin optimal kontrol tasarımı ve gerçeklenmesi iki basamakta sağlanacaktır: 1. Optimal global yörünge tayini 2. Optimal yerel kontrol Birinci basamakta kontrol yörüngesi tayin edilecektir. Bu bir ileribeslemeli kontrol tasarımıdır. İkinci basamak, bu yörünge etrafında yerel optimal kontrolü hesaplayacaktır. Bu da bir geribeslemeli kontrol tasarımıdır. İkinci basamaktaki ağırlık matrisleri global yörünge tarafından tanımlanacaktır.OPTIMAL CONTROL OF NONLINEAR EXOTHERMIC REACTOR SUMMARY Key Words: CSTR, Optimal Operations, Gradient Method, Startup, Shutdown, Regulation The use of available resources and business competition are the force of chemical industry desires for many years. For this reason obtaining the mathematical models of processes help us to design calculations of increasing range and accuracy. At the same time the development of high speed computers have made possible calculations easy to solve. The skill and experience of practical operation are still of importance, but theoretical analysis play role on researches and developments on processes. From this point of view in this thesis mathematical model of an exothermic continuously stirred tank reactor (CSTR) was obtained. For easiness physical variables were transformed into normalised variables, The chemical factory consists of a large number of interconnected process units, each of which is a stage in the transformation of the raw materials into finished products. It is generally desirable to make the profit resulting from this transformation as large as possible. For observation and making developments on system equipment to increase profit there is a need of performance index as a mathematical description. In industry the aim of the control depends on economical reasons. Classical controls are replaced by advanced control techniques. In this thesis at first for bringing CSTR in desired operating point and maintaining the stability of CSTR under disturbances, PID control was used. And the effects of PID control was observed. After that linear quadratic regulator problem (LQR) was developed for nonlinear systems. Exothermic continuously stirred tank reactors have nonlinear behaviour and often do not respond well to standard linearized system analysis. The purpose of this work is to point out, by examples, some of the difficulties of CSTR which may arise from disturbances in feed temperature and concentration. And to see how feedback nonlinear optimal control can overcome these problems. From a different initial condition, by using feedforward optimal control, how feedback control can bring the reactor temperature to the desired operation temperature will be observed. In this thesis, design of nonlinear optimal control and its application to the process will be in two steps: 1. Obtaining optimal global trajectory 2. Optimal global control In the first step control trajectory will be obtained. This is a feedforward control design. In the second step, around this trajectory, local optimal control will be calculated. This is a feedback control design. And in the second step weighting matrices will be defined by the global trajectory

Trajectory priming with dynamic fuzzy networks in nonlinear optimal control

Fuzzy logic systems have been recognized as a robust and attractive alternative to some classical control methods. The application of classical fuzzy logic (FL) technology to dynamic system control has been constrained by the nondynamic nature of popular FL architectures. Many difficulties include large rule bases (i.e., curse of dimensionality), long training times, etc. These problems can be overcome with a dynamic fuzzy network (DFN), a network with unconstrained connectivity and dynamic fuzzy processing units called "feurons". In this study, DFN as an optimal control trajectory priming system is considered as a nonlinear optimization with dynamic equality constraints. The overall algorithm operates as an autotrainer for DFN (a self-learning structure) and generates optimal feed-forward control trajectories in a significantly smaller number of iterations. For this, DFN encapsulates and generalizes the optimal control trajectories. By the algorithm, the time-varying optimal feedback gains are also generated along the trajectory as byproducts. This structure assists the speeding up of trajectory calculations for intelligent nonlinear optimal control. For this purpose, the direct-descent-curvature algorithm is used with some modifications [called modified-descend-controller (MDC) algorithm] for the nonlinear optimal control computations. The algorithm has numerically generated robust solutions with respect to conjugate points. The minimization of an integral quadratic cost functional subject to dynamic equality constraints (which is DFN) is considered for trajectory obtained by MDC tracking applications. The adjoint theory (whose computational complexity is significantly less than direct method) has been used in the training of DFN, which is as a quasilinear dynamic system. The updating of weights (identification of DFN parameters) are based on Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Simulation results are given for controlling a difficult nonlinear second-o- - rder system using fully connected three-feuron DFN.IEEE Computational Intelligence Societ

Phase portrait modeling of a nonlinear system with a dynamic fuzzy network

Fuzzy logic and neural networks are two important technologies for modeling and control of dynamical systems and have been constrained by the non-dynamical nature of their some popular architectures. There exist problems such as large rule bases (i.e., curse of dimensionality), long training times, the need to determine buffer lengths. This article proposes to overcome these major problems in phase portrait modeling of a nonlinear system with a dynamic fuzzy network (DFN) with unconstrained connectivity and with dynamic fuzzy processing units called "feurons". Nonlinear physical system properties can be encapsulated by DFN. As an example, DFN has been used as the modeler for some nonlinear physical system such as chaotic, limit cycle, oscillator. The minimization of an integral quadratic performance index subject to dynamic equality constraints is considered for a phase portrait modeling application. For gradient computation adjoint sensitivity method has been used. Its computational complexity is significantly less than direct sensitivity method, but it requires a backward integration capability. We used first and approximate second order gradient-based methods including Broyden-Fletcher-Golfarb-Shanno algorithm to update the parameters of the dynamic fuzzy networks yielding faster rate of convergence

On a dynamic wavelet network and its modeling application

This study presents a nonlinear dynamical system modeling with dynamic wavelet networks (DWNs). Wavelet is widely used in processing of signals and data. It has been also shown that wavelet can be effectively used in nonlinear system modeling. For this, dynamic wavelet networks (DWNs) structure based on Hoppfield networks has been developed. DWN has a lag dynamic, non orthogonal mother wavelets as activation function and interconnection weights. Network weights are adjusted based on supervised training. With fast training algorithms (quasi-Newton methods), wavelet networks are trained. In this paper, Mexican Hat wavelet. First, a phase-portraits based example is given. For this, it has been shown that DWN has chaos properties. The last, a dynamical system with discrete-event is modeled using DWN. There is a localization property at discrete-event instant for time-frequency in this example.Bogazici Univ Fdn; USAF, European Off Aerosp Res & Dev; Turkish Sci & Tech Res Counci

Modified descend curvature based fixed form fuzzy optimal control of nonlinear dynamical systems

In this study, a fuzzy rule-based optimal controller is designed for nonlinear dynamical systems. The direct second order method (or direct-descend-curvature algorithm) with a modification called "modified descend controller (MDC)" is used for calculating the parameters of the fuzzy feedback controller. The optimal control problem defined here has dynamic constraints of nonlinear system states and static constraint of a known form of fuzzy controller. The form used here is a standard fuzzy system that uses singleton fuzzifier, product inference engine, center average defuzzifier, and with the Gaussian membership functions of the system states to be controlled. The design is developed by minimizing a quadratic performance index selected for the desired operating conditions. Successful simulation results of controlling the temperature of a continuous stirred tank reactor (CSTR) and a bioreactor are given

Generalized modeling principles of a nonlinear system with a dynamic fuzzy network

Generalized modeling principles of a nonlinear system with a dynamic fuzzy network (DFN)-a network with unconstrained connectivity and with dynamic fuzzy processing units called 'feurons', have been given. DFN model has been trained both in open loop and closed loop forms to satisfy these principles. Several system trajectories with a PRBS input have been used for open loop training. DFN model obtained from open loop training was used in an extended Kalman filter (EKF) in an observer design and with a PID controller design for a nonlinear system. For gradient computation adjoint sensitivity method has been used. (C) 2003 Elsevier Ltd. All rights reserved