State-space representation for fractional order controllers

This article proposes an infinite-dimensional state-space realization for linear filters with transfer function C-d(s)corresponds toC(o)((1 + s/omega(b))/ (1 + s/omega(h)))(d), where 0 < omega(b) < omega(h) and 0 < d < 1. This exponentially stable representation is derived from the Taylor expansion at zero of the function (1 - z)(d), and is made up of an infinite number of first-order ordinary differential equations. Finite-dimensional approximations obtained by truncating this representation are shown to converge towards C-d in H-infinity. An example of feedback loop incorporating this approximation of C-d (car suspension) is presented, for which robustness of closed-loop resonance and step response overshoot vis-g-vis a Variation in the vehicle mass is achieved. (C) 2000 Elsevier Science Ltd. All rights reserved.