2点 Padé 近似による離散時間システムモデリング

抄録

In order to design control systems, it is necessary to have a mathematical model which will adequately describe the motion of a given system. Modelling problem is a significant field in control theory, and has been much studied in relation t signal processing theory.
In this paper, we concern with a modelling method using 2-point Padé approximation on discrete-time systems. The rational function of z (difference operator) obtained by usual Padé approximation preserves the first some terms of the given power series expansion at a point. When we choose z=1 (z=∞) as that point, the first parts of time moments (Markov parameters) of the model coincide with the given ones in version of discrete-time systems. On the other hand, 2-point Padé approximation provides the transfer function which fits the desired characteristics at two points respectively, hence selecting z=1 and z=∞ as these two points, we can obtain the model with both steady and transient response taken into account.
The outline of this paper is as the following: after definition of 2-point Padé approximation problem in Sec. 2.1, a few subjects on it are discussed in the next four sections. They are (1) an explicit form of 2-point Padé approximation (Sec. 2.2), (2) manimal order's reakization problem (Sec. 2.3), (3) Nuttall's compact form (Sec. 2.4), (4) relation to continued fraction expansions and numerical efficient algorithm based on it (Sec. 2.5). In Sec. 3, a numerical example of modelling via 2-point Padé approximation is shown for demonstration of its effectiveness.