Implementation of discrete-time fractional-order derivative controller for a class of double integrating system

In this paper, a fractional-order derivative controller has been designed to control a double integrator plant towards satisfying the specific design criterions of frequency domain. The design approach employs a reference model. The open loop transfer function of the reference model is given by the Bode's ideal transfer function. The design is accomplished in two stages. At first, the reference model is obtained from the given design specifications and the transfer function of the continuous-time fractional-order derivative controller is derived subsequently. In the next stage, the fractional-order controller (FOC) has been realised in delta-domain involving continued fraction expansion method. The efficacy of the presented design methodology has been established through a comparative study with one of the conventional approaches pertaining to discrete-time implementation of FOC. The robustness of the closed loop controlled system is also tested against the uncertain plant gain. The essential simulation results have been presented using MATLAB.