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This paper presents reduced integer order models of fractional differentiators. A two step procedure is followed. Using the Carlson method of approximation, approximated second iteration models of fractional differentiators are obtained. This method yields transfer function of high orders, which increase the complexity of the system and pose difficulty in realization. Hence, three reduction techniques, Balanced Truncation method, Matched DC gain method and Pade Approximation method are applied and reduced order models developed. With these models, fractional Proportional-Derivative and fractional Proportional-Integral-Derivative controllers are implemented on a fractional order plant and closed loop responses obtained. The authors have tried to reflect that the Carlson method in combination with reduction techniques can be used for development of good lower order models of fractional differentiators. The frequency responses of the models obtained using the different reduction techniques are compared with the original model and with each other. Three illustrative examples have been considered and their performance compared with existing systems.

Implementation of Carlson based Fractional Differentiators in Control of Fractional Order Plants