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Öğe The absolute stability of uncertain nonlinear systems using new formulations of the circle criteria(2002) Atherton D.P.; Tan N.The purpose of this paper is to study the problem of the absolute stability of nonlinear systems with variable plant parameters. New formulations of the circle and off axis circle criteria are developed which enable one to assess the stability of a control system containing a nonlinearity and plant with parametric uncertainties. In contrast to the classical approach which uses the Nyquist plot, the proposed method makes use of the narrowest possible Bode envelopes obtained from new results obtained by the authors where the plant transfer function is taken in factored form.Öğe Application of fractional-order voltage controller in building-integrated photovoltaic and wind turbine system(SAGE Publications Ltd, 2019) Gül O.; Tan N.The share of electricity generation based on clean, inexhaustible and continuous energy sources, such as solar and wind, in total energy production, is rising day by day due to its significant advantages such as having the less negative impact on global climate and environmental pollution and not requiring fuel for energy production. It is reported that commercial and residential buildings correspond to about 20.1% of the world energy consumption, so it is necessary to provide energy needs of buildings with hybrid renewable energy systems. When using non-continuous energy sources such as solar panel and wind turbines, it is important to ensure ensuring a stable and quality power flow to the building while the power demands of building show very sharp variability. This work presents a voltage control system using fractional-order operators in the smart residential building-integrated hybrid renewable power plant (solar + wind). In this research article, fractional-order proportional–integral/proportional–integral–derivative controllers are proposed on a synchronous frame for a pulse-width modulation based three-phase voltage source inverter in residential building-integrated solar panel and wind turbines system (building-integrated photovoltaic/wind turbine system) in order to improve the quality of injected voltage to building. When comparing the effect of closed-loop voltage control system with integer order controllers (proportional–integral and proportional–integral–derivative) on the power quality at the building distribution by analyzing the simulation results for proposed case study, use of fractional-order voltage controllers for nonlinear system such as building integrated with hybrid renewable sources is more suitable than using integer order voltage controllers. © The Author(s) 2019.Öğe Bode envelopes of multilinear affine systems(Institute of Electrical and Electronics Engineers Inc., 2001) Tan N.; Atherton D.P.The paper deals with the problem of computing the Bode envelope of an uncertain transfer function whose numerator and denominator polynomials are multiples of independent uncertain polynomials of the form P(s, q) = l0(q) + l1(q)s +.........+ ln(q)sn whose coefficients depend linearly on q = [q1, q2,..., qq]T and the uncertainty-box is Q = {q : qi [qi, qi], i = 1,2,...., q}. Using the geometric structure of the value set of P(s, q), a powerful edge elimination procedure is proposed for computing the magnitude and phase envelopes of these uncertain systems. A numerical example is included to illustrate the benefit of the method presented. © 2001 EUCA.Öğe Computing step and impulse responses of closed loop fractional order time delay control systems using frequency response data(Springer Berlin Heidelberg, 2017) Tan N.; Atherton D.P.; Yüce A.This paper deals with the computation of accurate step and impulse responses of fractional order control systems with time delay. Two elegant methods which are extensions of the methods previously obtained by the authors for systems without a time delay are given. The first method is called the Fourier series method and the second method is the inverse Fourier transform method. The results obtained from these methods are exact since the methods use frequency domain data of fractional order transfer functions which can be computed exactly. Time response equations which are functions of the frequency response data of the fractional order PID, lag or lead controllers, and plant are derived. Numerical examples are given to illustrate the results. © 2016, Springer-Verlag Berlin Heidelberg.Öğe Decoupling control of a twin rotor MIMO system using optimization method(Institute of Electrical and Electronics Engineers Inc., 2019) Dogruer T.; Tan N.This paper presents an optimization method on the real-time decoupling control for the TRMS system. It can be stated that TRMS has a complex structure due to its nonlinear structure, cross-couplings, two inputs and two outputs. Despite its complex structure, the TRMS is widely preferred in control applications as it allows to test the controller performances. The pitch and yaw position control in TRMS has been investigated in many studies, but its decoupling control has only been discussed in a limited number of studies. In this study, the real-time decoupling control of the TRMS was performed using fractional order PID. A Genetic Algorithm based optimization method was used for determining the parameters of the fractional order PID controller. The conventional PID was compared with the fractional order PID, and the results showed that the decoupling control of the TRMS using the fractional order PID was more successful. The method applied offers a highly effective control in real-time decoupling control of the TRMS. © 2019 Chamber of Turkish Electrical Engineers.Öğe Derivation of analytical inverse Laplace transform for fractional order integrator(L and H Scientific Publishing, LLC, 2017) Yücef A.; Tan N.There is considerable interest in the study of fractional order deriva- tive/integrator but obtaining analytical impulse and step responses is a difficult problem. Therefore all methods reported on to date use approximations for the fractional derivative/integrator both for an- alytical based computations and more relevantly in simulation stud- ies. In this paper, an analytical formula is first derived for the in- verse Laplace transform of fractional order integrator, 1/s? where ? ? R and 0 < ? <1 using Stirling's formula and Gamma func- tion. Then, the analytical step response of fractional integrator has been computed from the derived impulse response of 1/s?. The ob- tained analytical formulas for impulse and step responses of frac- tional order integrator are exact results except the very small error due to the neglected terms of Stirling's series. The results are com- pared with some well known integer order approximation methods and Grunwald-Letnikov (GL) approximation technique. It has been shown via numerical examples that the presented method is very suc- cessful according to other methods. © 2017 L&H Scientific Publishing, LLC.Öğe Design of PI and PID controllers for fractional order time delay systems(IFAC Secretariat, 2010) Özyetkin M.M.; Yero?lu C.; Tan N.; Ta?luk M.E.This paper deals with the computation of rational approximations of fractional derivatives and/or integrals. All rational approximations for fractional order of 0.1, 0.2,0.9 are obtained using continued fraction expansion (CFE) method. Extension of the stability boundary locus approach to control systems with a fractional order transfer function is given for the computation of stabilizing PI and PID controllers using continuous approximations of fractional orders. Numerical examples are provided to illustrate the results and to show the effect of the order of approximation on the stability region.Öğe Design of robust controllers for uncertain transfer functions in factored form(IFAC Secretariat, 2002) Atherton D.P.; Tan N.The paper presents a new method for computations of the magnitude and phase envelopes of uncertain transfer functions. The idea is to factor the transfer function into its real and complex pair roots and find the maximum and the minimum magnitudes of the gain and phase of each factor. The Bode envelopes of the given uncertain system are then found from those of the individual factors. This approach, which is different from those based on the interval polynomial method of Kharitonov, has the major advantage that the representation is more applicable to practical situations where typically the coefficients of the various factored terms relate to physical parameters of a mathematical model. Further the method results in narrower envelopes and therefore improved designs as illustrated in the examples which consider, lead, PI and PID controller designs. Copyright © 2002 IFAC.Öğe Design of Robust Integer/Fractional Order PID Controller Based on Bode's Ideal Transfer Function and H-Infinity Robust Performance Condition(Institute of Electrical and Electronics Engineers Inc., 2023) Menak R.; Tan N.In this paper, we proposed a new fitness function that is minimized by optimization algorithms to tune the parameters of the integer/fractional order PID (proportional-integral-derivative) controllers. The fitness function has been designed by combining H-robust performance condition constraint and Bode's ideal transfer function as a reference model. Two weighting functions have been used for robust performance condition; multiplicative uncertainty weighting function as a fixed parameters structure, and performance weighting function both as a fixed parameters structure, and optimized adjustable parameters structure. The parameters of the Bode's ideal transfer function are selected based on desired time response specifications. The particle swarm optimization (PSO) algorithm has been used as an optimization tool to minimize the proposed fitness function to tune the parameters of integer/fractional order PID controllers. The parameters of the controllers are obtained for the given second-order transfer function system as an example. The performance of the systems with obtained controllers has been compared in terms of the reference tracking ability, disturbance rejection capability, and robustness performance against parameter changes in the system. The simulation results have revealed that the proposed fitness function can be used with the aim to tune the parameters of the robust fixed structure controllers such as integer/fractional order PIDs by using any optimization algorithm while retaining the H-robust performance condition. © 2023 IEEE.Öğe Exact time response computation of control systems with fractional order lag and lead compensators(North Atlantic University Union, 2016) Tan N.; Atherton D.P.; Yuce A.; Deniz F.N.In this paper, two exact methods are developed for the computation of unit step and unit impulse responses of closed loop control systems with fractional order lag and lead compensators. The methods are based on using the frequency response data of the closed loop fractional order control system. It is shown that the unit step and unit impulse responses of a feedback control system including a fractional order lag or lead controller can be computed exactly using Fourier series of a square wave and inverse Fourier transform of frequency response information namely gain and phase values. Time response equations which are the function of controller parameters are derived. A design procedure is given for estimating the parameters of a fractional order lag or lead compensator which give specified performance values of the closed loop system. Numerical examples are provided to show the success of the presented method. © 2016, North Atlantic University Union. All rights reserved.Öğe A graphical method for computation of all stabilizing PI controllers(IFAC Secretariat, 2005) Tan N.; Kaya I.; Atherton D.P.in this paper, a new method for the calculation of all stabilizing PI controllers is given. The proposed method is based on plotting the stability boundary locus in the ( kp , ki )-plane and then computing the stabilizing values of the parameters of a PI controller. The technique presented does not require sweeping over the parameters and also does not need linear programming to solve a set of inequalities. Thus it offers several important advantages over existing results obtained in this direction. Computation of stabilizing PI controllers which achieve user specified gain and phase margins is also studied. Furthermore, the proposed method is used to compute all the parameters of a PI controller which stabilize a control system with an interval plant family. Examples are given to show the benefits of the method presented. Copyright copy; 2005 IFAC. Copyright © 2005 IFAC.Öğe Integer order approximation of fractional order systems(2010) Özyetkin M.M.; Tan N.This paper deals with the computation of rational approximations of fractional derivatives and/or integrals and time domain analysis of fractional order systems. The objective is to compute the output signals of systems which represented by fractional order transfer functions. Therefore, all rational approximations for fractional order of 0.1, 0.2,..., 0.9 are obtained using continued fraction expansion method (CFE). Simulink block diagrams of a control system with time delayed fractional order transfer function, which controlled by a PI? D? controller, are constructed using continued fraction expansion method and unit step responses of the system are investigated for different values of ? and ?. ©2010 IEEE.Öğe Limit cycle prediction for fractional order systems with static -onlinearities(IFAC Secretariat, 2010) Yeroglu C.; Tan N.This paper deals with limit cycle prediction for nonlinear systems which have fractional order transfer functions. Describing function method is used for the analysis of fractional order nonlinear systems. It is observed that the limit cycle frequencies obtained from the simulation of the fractional order nonlinear systems, agree with the theoretical values of the limit cycle frequencies obtained from Nyquist plots of the fractional order plant and complex plot of the negative inverse of describing function. The critical gain of the system is estimated from Nyquist plot. The fractional order nonlinear system becomes stable for the gain smaller than the critical gain value. System starts to oscillate for the gain bigger than the critical gain value. © 2010 IFAC.Öğe A new tuning method for PI?D? controller(2009) Yeroglu C.; Onat C.; Tan N.The paper presents development of a new tuning method for fractional order PID controller for the systems which have integer order transfer functions. AU the parameters of the controller, namely proportional gain kp, integral gain ki, derivative gain kd, fractional order of integrator k and fractional order of differentiator ? can be obtained by using this method. It is clearly shown that the fractional order controller, which the parameters obtained by the proposed method, gives better response than the integer order one for the same system.Öğe Note on describing function analysis of fractional order nonlinear control systems(Systems Research Institute, 2015) Yeroglu C.; Tan N.This paper presents extensions of some results, obtained for the analysis of classical nonlinear control systems, to the nonlinear fractional order systems. It is shown that the results related to limit cycle prediction using describing function method can be applied to the fractional order plants. The frequency and the amplitude of the limit cycle are used for auto-tuning of the PID controller for nonlinear control systems with fractional order transfer functions. Fractional order control system with parametric uncertainty is also considered for the nonlinear case. On the other hand, a new method is provided for stability margin computation for fractional order nonlinear control system with parametric uncertainty structure using the Nyquist envelopes of the fractional order uncertain plant and the describing function that represents the nonlinearity of the system. Maximum perturbation bounds of the parameters of the fractional order plant are computed. Numerical examples are included to illustrate the methods presented.Öğe Root-locus analysis of fractional order transfer functions using LabVIEW: An interactive application(Institute of Electrical and Electronics Engineers Inc., 2018) Yuce A.; Tan N.; Dogruer T.The 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. © 2018 IEEE.Öğe Smith Predictor Based PID Controllers Design with Bode's Ideal Transfer Function Reference Model for High Order Time Delay Systems(Institute of Electrical and Electronics Engineers Inc., 2023) Irgan H.; Tan N.In this study, a Smith predictive control scheme is proposed for high order time delay systems. Here, Bode's ideal transfer function is used as the reference model and its two adjustable parameters ? and ?c are chosen according to the desired step response. Then, PID control is provided so that the output of the high order time delay model can follow the response of this adjusted reference system. Genetic Algorithm optimization method was used to obtain PID parameters. The contribution of the obtained results to the literature is to show the efficiency of the controller design using the Bode's ideal transfer function of the fractional order for high order time delay systems. © 2023 IEEE.Öğe Some results on control systems with mixed perturbations(IFAC Secretariat, 2002) Tan N.; Atherton D.P.The paper considers control systems with parametric as well as unstructured uncertainty. Parametric uncertainty is modelled by a transfer function whose numerator and denominator polynomials are independent uncertain polynomials of the form of P(s, q) = l0(q) + l1(q)s +? + ln(q)sn where the coefficients depend linearly on q = [q1,q2,?,qq]T and the uncertainty box is Q = {q: qi?[qi,qi¯],i = 1, 2,?,q}. The unstructured uncertainty is modelled as H? norm bounded perturbations and perturbations consisting of a family of nonlinear sector bounded feedback gains. Using the geometric structure of the value set of P(s, q), some results are presented for determination of the robust small gain theorem, robust performance, strict positive realness and absolute stability problem of control systems with parametric as well as unstructured uncertainty. Copyright © 2002 IFAC.Öğe Stability margin computation for nonlinear systems: A parametric approach(IFAC Secretariat, 2002) Tan N.; Atherton D.P.This paper studies the existence of limit cycles in a control system which contains nonlinearities and parametric uncertainties. The existence of limit cycles in a control system with a separable nonlinearity can be predicted using the describing function. In this paper, some of the well-known results developed in the area of parametric robust control are used together with the describing function method to analyze the stability problem of uncertain nonlinear systems. Based on the segment lemma, a stability result for a control system with an uncertain nonlinear element and a fixed linear element is first derived. Then, a polynomial method and a graphical method are proposed to determine how much one can perturb the coefficients of the linear element without causing the nonlinear system to have a limit cycle. Examples are given to illustrate the method presented. Copyright © 2002 IFAC.Öğe Systems with variable parameters; classical control extensions for undergraduates(IFAC Secretariat, 2003) Tan N.; Atherton D.P.; Dormido S.Recently a method has been introduced for finding the minimum bounds of the frequency response of a system with variable parameters on Bode gain/phase diagrams. The results are easily derived from classical control frequency response concepts and provide a simple way of introducing the concepts of control system design under parameter uncertainty to undergraduates. This paper describes the method and shows how it can be used for investigating stability and the design of simple classical compensators. Use of the method for interactive education is also discussed. Copyright © IFAC Advances in Control Education Oulu, Finland, 2003
