State-space representation for fractional order controllers
State-space representation for fractional order controllers
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DOI：
10.1016/s0005-1098(00)00011-x
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发表时间：
2000-07-01
期刊：
影响因子：
6.4
通讯作者：
Zergaïnoh, A
中科院分区：
文献类型：
--
作者：
Raynaud, HF;Zergaïnoh, A
本文提出了具有传递函数C-d(s)的线性滤波器的无限维状态空间实现，对应于c (o)((1 + s/omega(b))/ (1 + s/omega(h)))(d)，其中0 < omega(b) < omega(h)且0 < d < 1。这种指数稳定的表示是由函数（1 - z）(d)在零点处的泰勒展开式导出的，它由无数个一阶常微分方程组成。截断这种表示得到的有限维近似在h∞处收敛于C-d。给出了一个包含这种近似C-d（汽车悬架）的反馈回路示例，该示例实现了闭环谐振和阶跃响应超调对车辆质量变化的鲁棒性。(C) 2000 Elsevier Science Ltd.版权所有。
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.