Continuous Order Identification of PHWR Models Under Step-back for the Design of Hyper-damped Power Tracking Controller with Enhanced Reactor Safety

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In this paper, discrete time higher integer order linear transfer function models have been identified first for a 500 MWe Pressurized Heavy Water Reactor (PHWR) which has highly nonlinear dynamical nature. Linear discrete time models of the nonlinear nuclear reactor have been identified around eight different operating points (power reduction or step-back conditions) with least square estimator (LSE) and its four variants. From the synthetic frequency domain data of these identified discrete time models, fractional order (FO) models with sampled continuous order distribution are identified for the nuclear reactor. This enables design of continuous order Proportional-Integral-Derivative (PID) like compensators in the complex w-plane for global power tracking at a wide range of operating conditions. Modeling of the PHWR is attempted with various levels of discrete commensurate-orders and the achievable accuracies are also elucidated along with the hidden issues, regarding modeling and controller design. Credible simulation studies are presented to show the effectiveness of the proposed reactor modeling and power level controller design. The controller pushes the reactor poles in higher Riemann sheets and thus makes the closed loop system hyper-damped which ensures safer reactor operation at varying dc-gain while making the power tracking temporal response slightly sluggish; but ensuring greater safety margin.This work has been supported by Department of Science and Technology (DST), Govt. of India, under the PURSE programme

Design Templates for Some Fractional Order Control Systems

Time domain characteristics of first and second order systems are well known. But the same simplicity and explicitness do not exist for low order fractional order systems (FOSs). Considering the step response, the templates are developed for designing the behavior of simple FOSs with a 2-term denominator polynomial (one is unity and the other involves fractional power). Although the explicit relations between design parameters and the performance parameters such as time constant, rise time, overshoot, settling time for fractional order control systems (FOCSs) do not exist and can't be obtainable as in the ordinary integer order control systems, the obtained templates in this paper can be used for designing low order FOCSs. Hence, the drawback of non-existence of similar explicit formulas for FOCSs is eliminated by using these templates

Zaman gecikmesi içeren üçüncü derece sistemler için kesir dereceli PD denetleyici tasarımı

Due to the lack of integral operator, proportional derivative controllers have difficulties in providing stability and robustness. This difficulty is especially felt in higher order systems. In this publication, analytical design method of fractional proportional derivative controllers is presented to ensure the stability of third order systems with time delay. In this method, it is aimed to achieve the frequency characteristics of a standard control system to ensure stability. It is aimed to provide the desired gain crossover frequency, phase crossover frequency and phase margin properties of the system. In this way, the stability and robustness of the system can be obtained by choosing the appropriate values. The reason for choosing a fractional order controller is that the controller parameters to provide these features can be tuned more accurately. In order for the obtained stability to be robust to unexpected external effects, it is aimed to flatten the system phase. In the literature, phase flattening is performed by setting the phase derivative to zero at a specified frequency value. This can lead to mathematical complexity. In this publication, the phase flattening process is provided graphically by correctly selecting the frequency characteristics given above. Thus, an accurate and reliable controller design method is presented, avoiding mathematical complexity. The effectiveness of the proposed method has been demonstrated on three different models selected from the literature. The positive contribution of the method to the system robustness has been proven by changing the system gain at certain rates.İntegral operatörünün eksikliğinden dolayı, oransal türev denetleyiciler kararlılık ve dayanıklılığı sağlama konularında zorlanabilmektedir. Bu zorluk, özellikle yüksek dereceli sistemlerde kendini daha çok hissettirmektedir. Bu yayında, zaman gecikmesi içeren üçüncü derece sistemlerin kararlılığının sağlanması için kesir dereceli oransal türev denetleyicilerin analitik tasarım yöntemi sunulmuştur. Bu yöntemde kararlılığın sağlanması için standart bir kontrol sisteminin sahip olduğu frekans özelliklerine ulaşılması hedeflenmiştir. Sistemin istenen kazanç kesim frekansı, faz kesim frekansı ve faz payı özelliklerini sağlaması hedeflenmiştir. Bu şekilde uygun değerler seçilerek sistemin kararlılığı ve dayanıklılığı elde edilebilecektir. Kesir dereceli bir denetleyicinin seçilme sebebi de bu özelikleri sağlayacak denetleyici parametrelerinin daha doğru şekilde ayarlanabilmesidir. Elde edilen kararlılığın beklenmeyen dış etkilere karşı dayanıklı olması için de sistem fazının düzleştirilmesi hedeflenmiştir. Literatürde faz düzleştirme işlemi, faz türevinin belirlenen bir frekans değerinde sıfırlanması ile gerçekleştirilmektedir. Bu da matematiksel karmaşıklığa yol açabilmektedir. Bu yayında ise faz düzleştirme işlemi yukarıda verilen frekans özelliklerinin doğru şekilde seçilmesi ile grafiksel olarak sağlanmaktadır. Böylece matematiksel karmaşıklıktan kaçınılarak, doğru ve güvenilir bir denetleyici tasarım yöntemi sunulmuştur. Önerilen yöntemin etkinliği literatürden seçilmiş üç farklı model üzerinde gösterilmiştir. Yöntemin sistem dayanıklılığına pozitif katkısı ise sisteme kazancının belli oranlarda değiştirilmesi ile ispatlanmıştır

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools

Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding

Load frequency control for multi-area interconnected power system using artificial intelligent controllers

Power system control and stability have been an area with different and continuous challenges in order to reach the desired operation that satisfies consumers and suppliers. To accomplish the purpose of stable operation in power systems, different loops have been equipped to control different parameters. For example, Load Frequency Control (LFC) is introduced to maintain the frequency at or near its nominal values, this loop is also responsible for maintaining the interchanged power between control areas interconnected via tie-lines at scheduled values. Other loops are also employed within power systems such as the Automatic Voltage Regulator (AVR). This thesis focuses on the problem of frequency deviation in power systems and proposes different solutions based on different theories. The proposed methods are implemented in two different power systems namely: unequal two-area interconnected thermal power system and the simplified Great Britain (GB) power system. Artificial intelligence-based controllers have recently dominated the field of control engineering as they are practicable with relatively low solution costs, this is in addition to providing a stable, reliable and robust dynamic performance of the controlled plant. They professionally can handle different technical issues resulting from nonlinearities and uncertainties. In order to achieve the best possible control and dynamic system behaviour, a soft computing technique based on the Bees Algorithm (BA) is suggested for tuning the parameters of the proposed controllers for LFC purposes. Fuzzy PID controller with filtered derivative action (Fuzzy PIDF) optimized by the BA is designed and implemented to improve the frequency performance in the two different systems under study during and after load disturbance. Further, three different fuzzy control configurations that offer higher reliability, namely Fuzzy Cascade PI − PD, Fuzzy PI plus Fuzzy PD, and Fuzzy (PI + PD), optimized by the BA have also been implemented in the two-area interconnected power system. The robustness of these fuzzy configurations has been evidenced against parametric uncertainties of the controlled power systems Sliding Mode Control (SMC) design, modelling and implementation have also been conducted for LFC in the investigated systems where the parameters are tuned by the BA. The mathematical model design of the SMC is derived based on the parameters of the testbed systems. The robustness analysis of the proposed SMC against the controlled systems’ parametric uncertainties has been carried out considering different scenarios. Furthermore, to authenticate the excellence of the proposed controllers, a comparative study is carried out based on the obtained results and those from previously introduced works based on classical PID tuned by the Losi Map-Based Chaotic Optimization Algorithm (LCOA), Fuzzy PID Optimized by Teaching Learning-Based Optimization (TLBO

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Applicable Solutions in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare