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A New Approach to Rational Discrete-Time Approximations to Continuous-Time Fractional-Order Systems

Abstract : In this paper a new approach to rational discrete-time approximations to continuous fractional-order systems of the form 1/(sα+p) is proposed. We will show that such fractional-order LTI system can be decomposed into sub-systems. One has the classic behavior and the other is similar to a Finite Impulse Response (FIR) system. The conversion from continuous-time to discrete-time systems will be done using the Laplace transform inversion integral and then applying the Bilinear transformation to obtain the corresponding discrete-time system and the corresponding frequency response. An optimization algorithm will be used to find the FIR type parameters that best approximate the discrete-time system.
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Carlos Matos, Manuel Ortigueira. A New Approach to Rational Discrete-Time Approximations to Continuous-Time Fractional-Order Systems. 3rd Doctoral Conference on Computing, Electrical and Industrial Systems (DoCEIS), Feb 2012, Costa de Caparica, Portugal. pp.251-258, ⟨10.1007/978-3-642-28255-3_27⟩. ⟨hal-01365592⟩

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