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Öğe Computation of Limit Cycles in Nonlinear Feedback Loops with Fractional Order Plants(Ieee, 2014) Atherton, Derek P.; Tan, Nusret; Yeroglu, Celaleddin; Kavuran, Gurkan; Yuce, AliThe paper deals with an aspect of the analysis of nonlinear feedback control systems with a fractional order transfer function. A review of the classical describing function (DF) method is given and its application to a control system with a fractional order plant is demonstrated. Unlike the DF method the frequency domain approach of Tsypkin is known to give exact results for limit cycles in relay systems and it is shown that this approach extends to systems with fractional order transfer functions. The formulation is done in terms of A loci which are related to and more general than the Tsypkin loci. Programs have been developed in MATLAB to compute the limit cycle frequency and also to show the results graphically. Examples are provided to illustrate the approach for a relay with no dead zone.Öğe Electronic realisation technique for fractional order integrators(Wiley, 2020) Yuce, Ali; Tan, NusretIn this study, a new method is presented for the realisation of the fractional order integrator. First, integer order approximate methods are analysed, then based on this analysis and using existing successfully applied approximate methods given in the literature, the design of fractional order integrators with active circuit elements is studied. In other words, fractance elements are developed. Operational amplifier is preferred in the design of fractional order integrator. Time responses of fractional order integrator circuits are computed by using Multisim software of National Instruments. Then the results are compared and verified with the results obtained from Matlab.Öğe Estimating the Time Response of Control Systems with Fractional Order PI from Frequency Response(Ieee, 2015) Tan, Nusret; Yuce, Ali; Atherton, Derek P.; Deniz, Furkan NurThis paper deals with the time response computation of closed loop control systems with fractional order PI controllers using the frequency response data of the closed loop system. The time response of fractional order transfer functions from frequency response data was first obtained by the authors using Fourier Series Method(FSM) and Inverse Fourier Transform Method(IFTM). In this paper, these methods are further extended for estimating unit step and unit impulse responses of control systems with fractional order PI controllers from the frequency response information of the closed loop system.Öğe An experimental analog circuit realization of Matsuda's approximate fractional-order integral operators for industrial electronics(Iop Publishing Ltd, 2021) Koseoglu, Murat; Deniz, Furkan Nur; Alagoz, Baris Baykant; Yuce, Ali; Tan, NusretAnalog circuit realization of fractional order (FO) elements is a significant step for the industrialization of FO control systems because of enabling a low-cost, electric circuit realization by means of standard industrial electronics components. This study demonstrates an effective operational amplifier-based analog circuit realization of approximate FO integral elements for industrial electronics. To this end, approximate transfer function models of FO integral elements, which are calculated by using Matsuda's approximation method, are decomposed into the sum of low-pass filter forms according to the partial fraction expansion. Each partial fraction term is implemented by using low-pass filters and amplifier circuits, and these circuits are combined with a summing amplifier to compose the approximate FO integral circuits. Widely used low-cost industrial electronics components, which are LF347N opamps, resistor and capacitor components, are used to achieve a discrete, easy-to-build analog realization of the approximate FO integral elements. The performance of designed circuit is compared with performance of Krishna's FO circuit design and performance improvements are shown. The study presents design, performance validation and experimental verification of this straightforward approximate FO integral realization method.Öğe First-time anterior shoulder dislocation after snowboard accidents in amateur athletes(2021) Yuce, Ali; Dedeoglu, Semih; Imren, Yunus; Yerli, Mustafa; Gurbuz, HakanAim: The glenoid rim fractures, bony bankart lesions and/or tuberculum majus fractures that occurred due to snowboarding-related first-time shoulder dislocations may have differences specific to these athletes. Thus, we aimed to examine the characteristics of bone lesions in cases with snowboarding-related first-time shoulder dislocation. Materials and Methods: The cases diagnosed with first-time shoulder dislocation and received a closed reduction in the emergency department between 2018 and 2020 were examined retrospectively. 18 patients with snowboarding-related dislocation, and 24 patients with first-time shoulder dislocation by a different injury mechanism other than winter sports injury mechanism were included in the study. Those with snowboarding-related injuries were classified as Group A and other cases were classified as Group B. Comparison was made between the two groups. Results: The average age was 27.11 ± 6.14 years in Group A, and 26.17 ± 5.44 years in Group B (p:0.656). There were 12 men (M) and 6 women (W) in Group A, and 16 M and 8 W in the Group B (p:0.999). The two groups were similar in terms of Hill-Sachs lesion, tuberculum majus fracture, bony bankart lesion, and additional injury (p>0.05). In the snowboarders, a relationship was found between the injured side and the lead foot (p: 0.013). There was a significant difference between the injury mechanism and the presence of Hill-Sachs lesion in the snowboarders (p:0.033). Conclusion: The characteristics of bone lesions in snowboarding-related first-time shoulder dislocations may be similar to that of shoulder dislocations occurred by different mechanisms. In snowboarding, the direction of sliding may put the shoulder at a higher risk of dislocation for a particular side. For these athletes, the injury mechanism may be a factor affecting the formation of Hill-Sachs lesion.Öğe Fractional Order PI Controller Design for Time Delay Systems(Elsevier Science Bv, 2016) Yuce, Ali; Tan, Nusret; Atherton, Derek P.This paper aims to look into the fractional PI controller design for a closed loop system having a plant with time-delay. The ultimate frequency of the system is found using a relay auto tuning test and then the parameters of a PI controller are estimated using this frequency in the Ziegler-Nichols (Z-N) tuning formula. These parameters are then used for a fractional order PI controller and the effect of varying the fractional integrator order (2) of the PI controller on the closed loop step response is examined. Finally, for a given example, the table that includes specifications of the control system for different A. values has been obtained and according to the desired specifications, optimum fractional order PI controller is designed. The presented results are illustrated with some examples. (C) 2016. IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Öğe IIR Filter Design based on LabVIEW(Ieee, 2015) Yuce, Ali; Tan, NusretIn this paper, IIR filter has been designed using LabVIEW graphical based computer program belonging to National Instruments company. The LabVIEW program that consists of front panel and function diagram is used to develop virtual instrument. The program can be used to design filters by two different methods such as classical and order estimated methods. Also the designed filter has been tested for a noisy ECG signal. The aim of this study is to assist the applications in signal processing courses given in educational institutions and thus purposed to give lectures more efficiently.Öğe An interactive design strategy for fractional order PI controllers in LabVIEW(Inderscience Enterprises Ltd, 2018) Yuce, Ali; Deniz, Furkan Nur; Tan, Nusret; Atherton, Derek P.This paper presents an interactive design for fractional order PI (FOPI) controller based on inverse Fourier transform method (IFTM) in accordance with stability region of a closed-loop control system in LabVIEW, which is a powerful graphical program. Stability boundary locus (SBL) method is used to obtain the stability region including all stabilising FOPI controller parameters in (K-p, K-i) plane. The time response of the closed-loop control system with FOPI controller is then obtained by IFTM using the stabilising controller parameters selected from stability region. Changing the selected fractional order controller parameters in stability region, users can observe the step response of the system interactively.Öğe Inverse Laplace Transforms of the Fractional Order Transfer Functions(Ieee, 2019) Yuce, Ali; Tan, NusretThe history of the fractional calculus goes back to approximately 300 years. In the recent years, it is common to come across fractional calculus in many publications of control systems. The systems with non-integer order of derivative in their differential equations are called fractional order systems. The Laplace transformation of such systems results fractional order transfer functions. However, the inverse Laplace transformation of a fractional order transfer function and its time responses can present a challenge to express analytically. In this work, the first order transfer functions and their fractional cases are considered. Furthermore, approximate inverse Laplace transformation, i.e., time response of the system, is obtained analytically by using MATLAB curve fitting method. These analytical equations are presented in a table for the interval of the fractional orders 0.1 <= alpha <= 0.9. Then the calculations of approximate inverse Laplace transform of a particular transfer function are presented numerically.Öğe Limit Cycles in Nonlinear Systems with Fractional Order Plants(Mdpi, 2014) Atherton, Derek P.; Tan, Nusret; Yeroglu, Celaleddin; Kavuran, Gurkan; Yuce, AliIn recent years, there has been considerable interest in the study of feedback systems containing processes whose dynamics are best described by fractional order derivatives. Various situations have been cited for describing heat flow and aspects of bioengineering, where such models are believed to be superior. In many situations these feedback systems are not linear and information on their stability and the possibility of the existence of limit cycles is required. This paper presents new results for determining limit cycles using the approximate describing function method and an exact method when the nonlinearity is a relay characteristic.Öğe Limit cycles in relay systems with fractional order plants(Sage Publications Ltd, 2019) Yuce, Ali; Tan, Nusret; Atherton, Derek P.In this paper, limit cycle frequency, pulse width and stability analysis are examined using different methods for relay feedback nonlinear control systems with integer or fractional order plant transfer functions. The describing function (DF), A loci, a time domain method formulated in state space notation and Matlab/Simulink simulations are used for the analysis. Comparisons of the results of using these methods are given in several examples. In addition, the work has been extended to fractional order systems with time delay. Programs have been developed in the Matlab environment for all the theoretical methods. In particular, Matlab programs have been written to obtain a graphical solution for the A loci method, which can precisely calculate the limit cycle frequency. The developed solution methods are shown in various examples. The major contribution is to look at finding limit cycles for relay feedback systems having plants with a fractional order transfer function (FOTF). However, en route to this goal new assessments of limit cycle stability have been done for a rational plant transfer function plus a time delay.Öğe Methods for computing the time response of fractional-order systems(Inst Engineering Technology-Iet, 2015) Atherton, Derek P.; Tan, Nusret; Yuce, AliThere is considerable interest in the study of fractional-order systems but obtaining accurate time domain responses is a difficult problem. This is because all methods reported on to date use approximations for the fractional derivative both for analytical-based computations and more relevantly in simulation studies. This means unlike in integer systems exact simulations are not available and thus for considering non-linear problems and comparisons with measured data no exact solution reference exists. In this study, the authors provide a major breakthrough for this situation by developing methods which allow the exact computation of the time responses of fractional-order systems.Öğe A New Integer Order Approximation Table for Fractional Order Derivative Operators(Elsevier, 2017) Yuce, Ali; Deniz, Furkan N.; Tan, NusretThere is considerable interest in the study of fractional order calculus in recent years because real world can be modelled better by fractional order differential equation. However, computing analytical time responses such as unit impulse and step responses is still a difficult problem in fractional order systems. Therefore, advanced integer order approximation table which gives satisfying results is very important for simulation and realization. In this paper, an integer order approximation table is presented for fractional order derivative operators (s(alpha)) where alpha is an element of R and 0 < alpha <1 using exact time response functions computed with inverse Laplace transform solution technique. Thus, the time responses computed using the given table are almost the same with exact solution. The results are also compared with some well-known integer order approximation methods such as Oustaloup and Matsuda. It has been shown in numerical examples that the proposed method is very successful in comparison to Oustaloup's and Matsuda's methods. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Öğe Obtaining the Time Response of Control Systems with Fractional Order PID from Frequency Responses(Ieee, 2015) Yuce, Ali; Deniz, Furkan Nur; Tan, Nusret; Atherton, Derek P.The paper deals with obtaining the time response of closed loop control system with fractional order PID controller using frequency response data. For this aim, a feedback control system with an integer order plant and a fractional order PID controller are studied. The real and imaginary parts of the closed loop transfer function are obtained which depend on the parameters K-p, K-i, K-d, lambda and mu of fractional order PID controller and real and imaginary parts of the plant. Then the time domain responses of the closed loop control system with fractional order PID controller are plotted by using Inverse Fourier Transform Method (IFTM) or Fourier Series Method (FSM). The presented idea is supported by some numerical examples.Öğe On the approximate inverse Laplace transform of the transfer function with a single fractional order(Sage Publications Ltd, 2021) Yuce, Ali; Tan, NusretThe history of fractional calculus dates back to 1600s and it is almost as old as classical mathematics. Although many studies have been published on fractional-order control systems in recent years, there is still a lack of analytical solutions. The focus of this study is to obtain analytical solutions for fractional order transfer functions with a single fractional element and unity coefficient. Approximate inverse Laplace transformation, that is, time response of the basic transfer function, is obtained analytically for the fractional order transfer functions with single-fractional-element by curve fitting method. Obtained analytical equations are tabulated for some fractional orders of alpha is an element of {0.1, 0.2, 0.3, ... , 0.9}. Moreover, a single function depending on fractional order alpha has been introduced for the first time using a table for 1=(s(alpha) + 1). By using this table, approximate inverse Laplace transform function is obtained in terms of any fractional order of a for 0 < alpha < 1. Obtained analytic equations offer accurate results in computing inverse Laplace transforms. The accuracy of the method is supported by numerical examples in this study. Also, the study sets the basis for the higher fractional-order systems that can be decomposed into a single (simpler) fractional order systems.Öğe Root-Locus Analysis of Fractional Order Transfer Functions Using LabVIEW: An Interactive Application(Ieee, 2018) Yuce, Ali; Tan, Nusret; Dogruer, TufanThe analysis of the open loop system in the design of the closed loop control systems is very important and useful in terms of being able to learn how the closed loop system will behave. In this paper, root locus graph of fractional order transfer function is plotted with the developed application using LabVIEW graphical programming language. A user panel has been designed using the LabVIEW graphical programming language. Interactive user panel is basic and user friendly for the computation and analysis. The root locus graph of the fractional order transfer function can interactively be plotted. Matsuda method is preferred for integer order approximation. With the interactive feature of developed application, the unit step response of closed loop control system can be plotted for a selected gain on the root locus graph panel. The application which has a rich graphical interface and interactive feature can also be used in teaching of fractional order control theory.Öğe Time Response Computation of Control systems with Fractional Order Lag or Lead Controller(Ieee, 2015) Tan, Nusret; Yuce, Ali; Atherton, Derek P.; Deniz, Furkan NurIn recent years, there have been many studies in the field of fractional order control systems. Many results have been published related with the frequency and time domains analysis of closed loop fractional order control systems. However, obtaining exact time response of a fractional order system is a difficult problem since it is not possible to derive analytical inverse Laplace transform of a fractional order transfer function. In this paper, an exact method is presented for computation of the time response of a closed loop control system with a fractional order lag or lead controller using frequency response data of the closed loop system. The presented method is based on the results, which use Fourier series of a square wave and inverse Fourier transform of frequency response information, previously derived by the authors. Numerical examples are provided to show the success of the presented method.Öğe Tuning of Fractional Order PID Controllers Based on Integral Performance Criteria Using Fourier Series Method(Elsevier, 2017) Deniz, F. Nur; Yuce, Ali; Tan, Nusret; Atherton, Derek P.This paper presents a time domain tuning technique for a fractional order PID controller based on optimizing an integral performance criterion. A Fourier series based method (FSM) is used to calculate accurately the step response of the closed loop control systems so as to determine the exact value of the error function performance criterion. The initial guesses for the FOPID controller parameters to be optimized are found using the analytical solution for integral squared error optimization for an integer order PID controller. The proposed method is used for two test plant transfer functions by comparing different optimal FOPID controllers. The results show that the design technique based on optimization of different integral performance criteria give good step responses for FOPID controller. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
