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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 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 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 Exact parameter estimation using relay feedback control(IFAC Secretariat, 2005) Kaya I.; Atherton D.P.Obtaining the parameters for PID controllers based on limit cycle information from the process in a relay controlled feedback loop is, in many cases, an acceptable practical procedure. If the form of the plant transfer function is known, exact expressions for the limit cycle frequency and amplitude can be derived in terms of the plant parameters, so that their measurements, assumed error free, can be used to calculate two unknown plant parameter values. in the literature to date the solutions have been considered for stable or unstable first order plus dead time (FOPDT) or second order plus dead time (SOPDT) plant transfer functions. This paper reports on exact parameter estimation for an SOPDT plant transfer function with the further addition of a , stable or unstable, zero by a single relay feedback test. Copyright © 2005 IFAC.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 Smith predictor design by CDM(Institute of Electrical and Electronics Engineers Inc., 2001) Hamamci S.E.; Kaya I.; Atherton D.P.Good control of processes with a long dead time is often achieved using a Smith predictor structure. Typically a PI or PID controller is used in this configuration. In this paper, controller design is considered for a recently proposed modified form of the Smith predictor. The design is done using the Coefficient Diagram Method (CDM) to achieve a good step response to a set point change. The proposed method is compared with some other existing methods to illustrate its value. © 2001 EUCA.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
