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"This book describes complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations. Coverage includes simulation, fractional-order modeling and filtering fractional-order systems."

"The book tries to briefly introduce the diverse literatures in the field of fractional order signal processing which is becoming an emerging topic among an interdisciplinary community of researchers. The readers should have preliminary knowledge about basic signal processing techniques. Prerequisite knowledge of fractional calculus is not essential and is exposited at relevant places in connection to the appropriate signal processing topics. Basic signal processing techniques like filtering, estimation, system identification, etc. in the light of fractional order calculus are presented along with relevant application areas. The readers can easily extend these concepts to varied disciplines like image or speech processing, pattern recognition, time series forecasting, financial data analysis and modeling, traffic modeling in communication channels, optics, biomedical signal processing, electrochemical applications and many more. Available MATLAB tools to simulate FOSP theories are also introduced."

"Aktuator hidrolik elektrik banyak digunakan dalam bidang industri dengan menggunakan pengendali yang tepat. Sistem aktuator hidrolik elektrik membutuhkan akurasi dari hasil posisi piston dan overshoots yang relatif rendah. Aliran fluida yang mengalir di daerah piston akan menghasilkan tekanan. Ada kendala yang mengakibat aliran fluida tidak memberikan respon yang baik seperti adanya kebocoran seal pada area piston. Dibutuhkan pengendali posisi perpindahan katup piston yang dapat digunakan untuk mengendalikan berbagai aliran fluida dan permasalahan kebocoran namun pada penelitian ini pengendali lokal kebocoran seal piston masih kurang bagus sehingga dirancang PID Orde Fraksi yang diharapkan dapat memberikan respon yang lebih baik. Proses tuning parameter PID menggunakan metode tuning Zigler Nichols, modifikasi Ziegler Nichols, dan Cohen Coon. Metode-metode tuning di analisis dengan mempertimbangkan kestabilan, respon waktu dan steady state error yang paling sesuai spesifikasi. Pada penelitian ini, metode yang paling sesuai modifikasi Ziegler Nichols untuk parameter Kp, Ki, Kd dan perhitungan 2 persamaan non linear untuk mendapatkan parameter. Pengujian disimulasikan untuk mendapatkan perbandingan hasil PID Klasik dan PID Orde Fraksi. Sistem dengan pengendali PID Klasik dapat mencapai kestabilan pada set point dengan dan maksimum overshoots sebesar 32,542% dan PID Orde Fraksi dapat mencapai maksimum overshoots sebesar 10,556%. Steady state error yang dihasilkan dengan menggunakan pengendali PID Klasik sebesar 0,006% dan pengendali PID Orde Fraksi yaitu sebesar 4,6199x10-4%. Dari hasil ini dapat diketahui bahwa pengendali PID Orde Fraksi lebih baik dari PID klasik.

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Electro hydraulic actuators are often used in industry by using precise controllers. Electro hydraulic actuator systems require relatively low accuracy of piston position results and relatively low overshoots. The fluid flow that flows in the piston area will produce pressure. There are problem that result in fluid flow not giving a good response, such as a seal leak in the piston area. It takes a piston valve displacement position controller that can be used to control various fluid flows and leakage problems, but in this study the local controller for piston seal leakage is still not good enough so that a Fractional Order PID is designed which is expected to provide a better response. The PID parameter tuning process uses the Zigler Nichols tuning method, Ziegler Nichols modification, and Cohen Coon. The tuning methods are analyzed by considering the stability, response time and steady state error that best fit the specifications. In this study, the most suitable method is the Ziegler Nichols modification for the parameters Kp, Ki, Kd and the calculation of 2 non-linear equations to get the parameters. The test is simulated to get a comparison of the results of the Classical PID and the Fractional Order PID. The system with Classical PID controller can achieve stability at the set point with maximum overshoots of 32.542% and PID Fractional Order can achieve maximum overshoots of 10.556%. The steady state error generated by using the Classical PID controller is 0.006% and the Fractional Order PID controller is 4,6199x10-4%.  From these results, it can be seen that the Fractional Order PID controller is better than the classic PID."

"Pengendali PID merupakan salah satu pengendali yang umum digunakan, karena memiliki struktur pengendali yang sederhana, performa yang baik dan mudah untuk diimplementasikan. Namun, performa pengendali PID dapat ditingkatkan lagi dengan menggunakan kalkulus orde fraksi untuk pengendali bagian Integral dan Derivative dalam PID, sehingga dikenal dengan nama fractional order PID (FOPID). Penggunaan kalkulus orde fraksi ini menyebabkan terjadinya suatu permasalahan karena pengendali FOPID memiliki parameter yang lebih banyak dibandingkan pengendali PID. Bertambahnya parameter tersebutlah yang membuat penentuan parameter pengendali FOPID menjadi lebih sulit. Maka dari itu, pada penelitian ini akan dibahas mengenai metode tuning FOPID dengan pendekatan FOPI dan FOPD, hasil pengendalian motor DC dan pendulum terbalik menggunakan pengendali FOPID yang telah di-tuning, dan perbandingan hasil pengendalian menggunakan pengendali FOPID dan PID. Dalam penelitian ini, pengendali FOPID dapat diperoleh menggunakan metode tuning yang diajukan, tetapi metode tersebut memiliki beberapa batasan, yaitu sistem yang akan dikendalikan harus stabil/ distabilkan terlebih dahulu dan spesifikasi gain crossover frequency (ωgc) minimum sebesar 10 rad/s. Hasil pengendalian motor DC dan pendulum terbalik yang didapatkan sudah sesuai dengan spesifikasi pengendali FOPID ketika tuning, serta perbandingan pengendali FOPID dengan PID menunjukkan bahwa pengendali FOPID memiliki performa yang lebih baik

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PID Controller is one of the most used type of controller, because of its simple structure, good performance and easy to implement. However, PID controller performance’s can be improved with the use of fractional order Calculus for the Integral and Derivative’s part of PID, so that the name is known as fractional order PID (FOPID). Using fractional order calculus causes a new problem, because of FOPID controller has more parameters to tune than PID controller, the tuning of FOPID controller becomes harder. Because of that, this study will discuss about a tuning method of FOPID controller with FOPI and FOPD approaches, the simulation results of said tuning methods on DC motor and inverted pendulum system, also comparing the results from FOPID controller with PID controller. In this study, FOPID controller can be obtained using the proposed tuning method, although there are some limitation from this tuning method, namely the system to be controlled must be a stable system or must be stabilized first and the minimum gain crossover frequency (ωgc) specification is 10 rad/s. The results of controlling DC motor and inverted pendulum are in accordance with the FOPID controller specification when tuned and the comparison between FOPID controller and PID controller shows that FOPID controller has a better performance than PID controller."

"Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables. It also includes applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods, and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition."

"This book develops systematically and rigorously, yet in an expository and lively manner, the evolution of general random processes and their large time properties such as transience, recurrence, and convergence to steady states. The emphasis is on the most important classes of these processes from the viewpoint of theory as well as applications, namely, Markov processes."

"Provides a comprehensive theory of the approximations of quantile processes in light of recent advances, as well as some of their statistical applications."