Order Pade Approximation Research Articles

Continuous-time identification of SISO systems using Laguerre functions

This paper looks at the problem of estimating the coefficients of a continuous-time transfer function given samples of its input and output data. We first prove that any nth-order continuous-time transfer function can be written as a fraction of the form /spl Sigma//sub k=0//sup n/b~/sub k/L/sub k/(s)//spl Sigma//sub k=0//sup n/a~/sub k/L/sub k/(s), where L/sub k/(s) denotes the continuous-time Laguerre basis functions. Based on this model, we derive an asymptotically consistent parameter estimation scheme that consists of the following two steps: (1) filter both the input and output data by L/sub k/(s), and (2) estimate {a~/sub k/, b~/sub k/} and relate them to the coefficients of the transfer function. For practical implementation, we require the discrete-time approximation of L/sub k/(s) since only sampled data is available. We propose a scheme that is based on higher order Pade approximations, and we prove that this scheme produces discrete-time filters that are approximately orthogonal and, consequently, a well-conditioned numerical problem. Some other features of this new algorithm include the possibility to implement it as either an off-line or a quasi-on-line algorithm and the incorporation of constraints on the transfer function coefficients. A simple example is given to illustrate the properties of the proposed algorithm.

On Identification of time Delay Via the Approximatione-TS≃1-sT/21+sT/2

This paper considers the identification of time delay, T, in the system, y(t) = u(t-T) by using the first order Padé approximation, [ 1 − sT / 2 1 + sT / 2 ] to e -Ts and a Luenberger observer or a Kaiman filter algorithm.

RESEARCH ON THE ACCELERATION WAVEFORM CONTROL OF ELECTRO-HYDRAULIC SERVO SYSTEM USING LINEAR MODEL FOLLOWING CONTROL

In this work, a control method to reproduce input waverorm is discussed. The acceleration waverorm of an electrohydraulic servo system is controlled by means or Linear Model Following Control (1MUC) with a timedelay reference model. This control system makes the signal transfer characteristics or forward path equivalent to that of the 2nd order Pade approximation or the timedelay characteristics. The difference signal between the output signal or the timedelay model and the output acceleration signal of the hydraulic servomotor, which is called acceleration error signal, is red back. Then, the acceleration error signal reedback makes the signal transfer characteristics or the servomotor more exact to that of the timedelay reference model. The performance or this control system is confirmed by experiments.

Nonlinear Methods in Numerical Analysis.

I. Continued Fractions. Since these play an important role, the first chapter introduces their basic properties, evaluation algorithms and convergence theorems. From the section dealing with convergence it can be seen that in certain situations nonlinear approximations are more powerful than linear approximations. The recent notion of branched continued fraction is introduced in the multivariate section and is later used for the construction of multivariate rational interpolants. II. Pade Approximants. A survey of the theory of these local rational approximants for a given function is presented, including the problems of existence, unicity and computation. Also considered are the convergence of sequences of Pade approximants and the continuity of the Pade operator which associates with a function its Pade approximant of a certain order. A special section is devoted to the multivariate case. III. Rational Interpolants. These rational functions fit a given function at some given points. Many results of the previous chapter remain valid for this more general case where the interpolation conditions are spread over several points. In between the rational interpolation case and Pade approximation case lies the theory of rational Hermite interpolation where each interpolation point can be assigned more than one interpolation condition. Some results on the convergence of sequences of rational Hermite interpolants are mentioned and multivariate rational interpolants are introduced in two different ways. IV. Applications. The previous types of rational approximants are used here to develop several numerical methods for the solution of classical problems such as convergence acceleration, nonlinear equations, ordinary differential equations, numerical quadrature, partial differential equations and integral equations. Many numerical examples illustrate the different techniques, and it is seen that nonlinear methods are very useful in situations involving singularities. Subject Index.

Thermodynamic properties of NaCl on its P-V-T surface

Various state equations derived by expanding energy as function of volume in a Taylor series and using the difference order Pade approximants have been combined with the quasi-harmonic approximation for free energy to reproduce the thermodynamic properties of the crystal on its P-V-T surface. The authors have used these state equations to compute the pressure-volume behaviour, the isothermal bulk modulus, the pressure derivative of bulk modulus and the Anderson-Gruneisen parameter of NaCl at high pressure (up to 80 kbar) and various temperatures (T=298, 550 and 800K). The results obtained are reasonably good, lending support to the state equations and the method used to extend their applicability at elevated temperatures. The significant results obtained in the present study include the unified reduced equation of state for NaCl which generates a single curve for the P-V behaviour at all temperatures.

On the Continuity of the Padé Operator

Let $r_{m,n} $ be the Pade approximant of order $(m,n)$ for a given power series f. Let $T_{m,n} $, be the operator that maps f on $r_{m,n} $. It is known that $T_{m,n} $ satisfies a (local) Lipschitz condition in case $r_{m,n} $ is normal, but may fail to be continuous if $r_{m,n} $ is not normal.In this paper we prove that $T_{m,n} $ is continuous if and only if $r_{m,n} $ has defect zero. We also prove a convergence result for Pade approximants in the case where the defect is positive.

Theory and recursive computation of 1-D matrix Pade approximants

Given a matrix power series, it is shown that (except possibly in certain derogatory cases) a recurrence relation relates the [L+ l/M+1} [L/M], [L- l/M- 1] order Pade approximants, the existence of each of which is guaranteed from validity of a certain rank condition on the corresponding set of characterizing matrices possessing a block-Hankel structure.