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Öğe Analysis of uncertain transfer functions in factored form(Ieee, 2002) Tan, N; Atherton, DPIt is well known that the mathematical representations of real physical systems suffer from parametric uncertainty due to modelling errors, nonlinearities, manufacturing tolerances and operating conditions. Therefore, it is very important to take parametric variations into account while analysing and designing control systems. This paper presents some results for computation of the robust stability of control systems with an uncertain transfer function in factored form which is the form of most real physical systems. The technique presented uses the narrowest possible Bode envelopes, which are constructed from new results obtained by the authors, and therefore it can be used for the stability analysis and design of robust controllers to meet certain closed loop stability and performance requirements for such systems less conservatively than other methods. The importance of the method for the computation of stability is discussed and illustrative examples are given.Öğe Computation of stabilizing PI and PID controllers(Ieee, 2003) Tan, N; Kaya, I; Atherton, DPIn this paper, a simple method for the calculation of stabilizing PI controllers is given. The proposed method is based on plotting the stability boundary locus in the (k(p),k(i))-plane and then computing 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. Beyond stabilization, the method is used to shift all poles to a shifted half plane that guarantees a specified settling time of response. Furthermore, computation of stabilizing PI controllers which achieve user specified gain and phase margins is studied. It is also shown via an example that the stabilizing region in the (k(p), k(i)) -plane is not always a convex set. The proposed method is also used to design PID controllers. The limiting values of a PID controller which stabilize a given system are obtained in the (k(p), k(i)) -plane, (k(p), k(d)) -plane and (k(i), k(d))-plane. Examples are given to show the benefit of the method presented.Öğe Exact parameter estimation from relay autotuning under static load disturbances(Ieee, 2001) Kaya, I; Atherton, DPObtaining the parameters for PID controllers based on limit cycle information from the process in a relay controlled feedback loop has become an accepted 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 the parameter values. In the literature to date the solutions have only been considered for odd symmetrical limit cycles which will not be the situation when constant disturbances exist. Use of these expressions will lead to errors when the limit cycle is not odd symmetrical. This paper reports on exact parameter estimation for stable and unstable FOPDT or SOPDT plant transfer functions from relay autotuning under static load disturbances where the limit cycles are asymmetrical.Öğe Extensions of classical methods to uncertain systems: An educational perspective(Pergamon-Elsevier Science Ltd, 2001) Tan, N; Atherton, DPMuch of the material being taught in a first course on control appears to have changed little over the last two decades. Whilst the basic theories on classical control in textbooks remain unchanged, there have been many new developments in the field of control theory in recent years. One such topic is the relatively recent development in methods to analyse systems with parametric uncertainty. The purpose of this paper is to show how some of these methods can be easily introduced into a typical first course on classical control. Copyright (C) 2000 IFAC.Öğe New approach to assessing the effects of parametric variations in feedback loops(Iee-Inst Elec Eng, 2003) Tan, N; Atherton, DPA method for the computation of the magnitude and phase envelopes of uncertain transfer functions is presented. The idea is to factor the transfer function into its real and complex pair roots and find the maximum and 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 the narrowest Bode envelopes and therefore can yield improved controller designs. The describing function analysis and the absolute stability problem of nonlinear systems with variable plant parameters are also studied. An approach which enables one to predict the existence of limit cycles in a control system which simultaneously contains nonlinearities and parametric uncertainties is given. The proposed method makes use of the popular describing function technique and these narrowest possible Bode envelopes of linear uncertain transfer functions in factored form. The technique can be used to cover the cases of linear elements, which have a multilinear or nonlinear uncertainty structure, and a nonlinear element with or without memory. New formulations of the circle and off-axis circle criteria are given for use with Bode diagrams so that the absolute stability of nonlinear systems with variable plant parameters can be studied. Examples are given to show how the proposed method can be used to assess the effects of parametric variations in feedback loops.Öğe A new approach to the stability of nonlinear systems with uncertain plant parameters(Ieee, 2003) Tan, N; Atherton, DPThe purpose of this paper is to study the problem of the stability of nonlinear systems with variable plant parameters. A new approach which enables one to predict the existence of limit cycles in a control system which simultaneously contains nonlinearities and parametric uncertainties is given. The proposed method makes use of the popular describing function technique and the Bode envelope of linear uncertain transfer functions. The narrowest possible Bode envelopes are obtained from new results obtained by the authors where the plant transfer function is taken in factored form. The technique can be used to cover the cases of linear elements, which have multilinear or nonlinear uncertainty structure, and a nonlinear element with or without memory. Examples are given to show how the proposed method can be used to assess the stability of nonlinear systems with uncertain plant parameters.Öğe A refinement procedure for PID controllers(Springer, 2006) Kaya, I; Tan, N; Atherton, DPProportional-Integral-Derivative (PID) controllers are still extensively used in industrial systems. In the literature, many publications can be found considering PID controller design for processes with resonances, integrators and unstable transfer functions. However, due to structural limitations of PID controllers, generally, a good closed-loop performance cannot be achieved with a PID, for controlling the aforementioned processes, and usually a step response with a high overshoot and oscillation is obtained. PI-PD controllers provide very satisfactory closed-loop performances in the case of controlling processes with resonances, integrators and unstable transfer functions. This paper introduces a simple approach to get parameters of a PI-PD controller from parameters of a PID controller so that a good closed-loop system performance can be realized. Extensive simulation examples are given to illustrate the value of the approach proposed.Öğe Robust stability of multilinear affine polynomials(Ieee, 2002) Tan, NR; Atherton, DPThis paper deals with the robust stability problem of multilinear affine polynomials. By multilinear affine polynomials, we mean an uncertain polynomial family consisting of multiples of independent uncertain polynomials of the form P(s,q) = l(0)(q)+l(1)(q)s+. -.+l(n)(q)s(n) whose coefficients depend linearly on q = [q(1),q(2),...,q(q)](T) and the uncertainty box is Q = {q : qiis an element of[(q(i)) under bar,(q(i)) over bar],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 value set of multilinear affine polynomials. In order to construct the value set of a multilinear affine polynomial, the mapping theorem can be used. However, in this case, it is necessary to find the images of all vertex polynomials and then taking the convex hull of the images of the vertex polynomials in the complex plane which is a computationally expensive procedure. On the other hand, the approach of the present paper greatly reduces the number of the images of vertex polynomials which are crucial for the construction of the value set. Using the proposed approach for construction of the value set of multilinear affine polynomials together with the zero exclusion principle, a robust stability result is given. The proposed stability result is important for the robust stability of control systems with multilinear affine transfer functions.Öğe Robustness analysis of control systems with mixed perturbations(Sage Publications Ltd, 2003) Tan, N; Atherton, DPThe 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) = l(0) (q) + l(1) (q) s +... + l(n) (q)s(n) where the coefficients depend linearly on q = [q(1), q(2),., q(q)](T) and the uncertainty box is Q = {q: q(i)is an element of[(q(i)) under bar, (q(i)) over bar], i = 1, 2,., q}. The unstructured uncertainty is modelled as H-infinity 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. Numerical examples are given to illustrate application of the proposed methods.Öğe A simple procedure for improving performance of PID controllers(Ieee, 2003) Kaya, I; Tan, N; Atherton, DPProportional-Integral-Derivative (PID) controllers are still extensively used in industrial systems. In the literature, many publications can be found considering PID controller design for processes with resonances, integrators and unstable transfer functions However, due to structural limitations of PID controllers, good closed loop performance cannot be achieved with a PID controller for the aforementioned processes and usually a step response with a high overshoot and oscillation is obtained. The PI-PD controller has been shown to provide very satisfactory closed loop performance for controlling processes with resonances, integrators and unstable transfer functions. This paper introduces a simple approach to get parameters of a PI-PD controller from parameters of a PID controller so that a good closed loop system performance is obtained. Extensive simulation examples are given to illustrate the value of the approach proposed.Öğe A user friendly toolbox for the analysis of interval systems(Pergamon-Elsevier Science Ltd, 2000) Tan, N; Atherton, DPMost of the methods which are used for the analysis and design of systems with parametric uncertainty require extensive computations. Therefore, it is value to develop computer programs which enable one to deal with uncertain systems in an easy way. This paper describes a user friendly software package(AISTK-Analysis of Interval Systems Toolkit). Algorithms have been developed in the MATLAB environment by using the Kharitonov theorem and related approaches. The objective in developing AISTK was to gather these algorithms under a toolkit and make them easily usable by students or other users. Copyright (C) 2000 IFAC.
