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

Abstract

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.

Design of a Fractional Order Low-pass Filter Using a Differential Voltage Current Conveyor

“…It has been noted that the practical implementation of fractance devices for microwave signals is constrained by the fact that existing approximation circuits for fractional devices may contain numerous lumped elements for a single fractional element [18]. In this area, work [19] presents model of fractional differentiators' with reduced integer order using two steps. The paper is structured in the following manner.…”