Impulse response of a generalized fractional second order filter

被引：0
作者：
Zhuang Jiao
YangQuan Chen
机构：
[1] Tsinghua University,Department of Automation
[2] Utah State University,Center for Self
来源：
Fractional Calculus and Applied Analysis | 2012年 / 15卷
关键词：
generalized fractional second order filter; fractional-order signal processing; impulse response; critically stable; Primary 26A33; Secondary 33E12, 34A08, 34K37, 35R11, 60G22;
D O I：
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学科分类号：
摘要：
The impulse response of a generalized fractional second order filter of the form (s2α + asα + b)−γ is derived, where 0 < α ≤ 1, 0 < γ < 2. The asymptotic properties of the impulse responses are obtained for two cases, and within these two cases, the properties are shown when changing the value of γ. It is shown that only when (s2α + asα + b)−1 has the critical stability property, the generalized fractional second order filter (s2α + asα + b)−γ has different properties as we change the value of γ. Finally, numerical examples to illustrate the impulse response are provided to verify the obtained results.
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页码：97 / 116
页数：19
相关论文
共 54 条
  • [1] Torvik P.(1984)On the appearance of the fractional derivative in the behavior of real materials J. of Applied Mechanics ASME 51 294-298
  • [2] Bagley R.(2011)PLC implementation of a CRONE controller Fract. Calc. Appl. Anal. 14 505-522
  • [3] Lanusse P.(1983)A theoretical basis for the application of fractional calculus to viscoelasticity Journal of Rheology 27 201-210
  • [4] Sabatier J.(1999)Fractional-order systems and IEEE Trans. on Automatic Control 44 208-214
  • [5] Bagley R.(2011) controllers Fract. Calc. Appl. Anal. 14 436-453
  • [6] Torvik P.(2006)Stability analysis of fractional-order systems with double noncommensurate orders for matrix case Science in China: Series G, Physics, Mechanics and Astronomy 49 257-272
  • [7] Podlubny I.(2002)Intermediate processes and critical phenomena: theory, method and progress of fractional operators and their applications to modern mechanics Nonlinear Dynamics 29 191-200
  • [8] Jiao Z.(1971)Analytical stability bound for a class of delayed fractional order dynamic systems J. of Electro Analytical Chemistry 33 253-265
  • [9] Chen Y.(1995)An analog simulation of noninteger order transfer functions for analysis of electrode Biosensors and Bioelectronics 10 67-74
  • [10] Xu M.(1991)The linear and non-linear electrical properties of the electrode-electrolyte interface Mechanical Systems and Signal Processing 5 81-88
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