Abstract
The emphasis on studying fractional-order controller has gradually been increasing in the area of control theory. The elementary component of a fractional-order controller is the fractional-order operator \( s^{\beta } \left( {0 < \beta < 1} \right) \), which can either be a fractional differentiator or be a fractional integrator. The discretization of \( s^{\beta } \) is central for digital realization of the fractional-order controller. In this paper, a half-order fractional differentiator is approximated to a rational transfer function by using Oustaloup approximation. The approximated continuous-time transfer function is then discretized to obtain the corresponding transfer functions in the complex \( z \)-domain and complex delta-domain. Finally, the frequency responses obtained from two discretized transfer functions of two different complex domains are compared for simulation studies with the help of MATLAB software.
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Swarnakar, J., Sarkar, P., Singh, L.J. (2018). Realization of Fractional-Order Operator in Complex Domains—A Comparative Study. In: Bera, R., Sarkar, S., Chakraborty, S. (eds) Advances in Communication, Devices and Networking. Lecture Notes in Electrical Engineering, vol 462. Springer, Singapore. https://doi.org/10.1007/978-981-10-7901-6_77
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DOI: https://doi.org/10.1007/978-981-10-7901-6_77
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