Laguerre based design of fractional-order PD controller

In this paper, a fractional-order PD controller based on Laguerre orthonormal functions is constructed for commensurate fractional order systems. The main idea is to expand the transfer functions of the fractional order plant, the desired open loop gain, and the fractional order PD controller in terms of their Laguerre basis functions. The fractional order PD controller coefficients are obtained by matching the first two coefficients of the open loop gain Laguerre series with the desired one. The optimum value of the Laguerre basis function pole is appropriately selected to minimize an integral square error performance index. The numerical simulations demonstrate the performance of the proposed Laguerre based fractional order PD controller, as well.