Fractional-order PI^λ D^μ controller design

This paper introduces a new design method of fractional-order proportional-derivative (FOPD) and fractional-order proportional-integral- derivative (FOPID) controllers. A biquadratic approximation of a fractional-order differential operator is used to introduce a new structure of finite-order FOPID controllers. Using the new FOPD controllers, the controlled systems can achieve the desired phase margins without migrating the gain crossover frequency of the uncontrolled system. This may not be guaranteed when using FOPID controllers. The proposed FOPID controller has a smaller number of parameters to tune than its existing counterparts. A systematic design procedure is identified in terms of the desired phase and the gain margins of the controlled systems. The viability of the design methods is verified using a simple numerical example.