A low-order approximation method for fractional order PID controllers

The control community recognizes the improved performance, stability and intrinsic robustness brought by fractional orders of differentiation and integration. However, the full potential of Fractional Order Proportional Integral Derivative (FOPID) controllers is yet to be grasped in the modern industrial setting. Mass adoption is hindered by implementation difficulties associated to fractional order terms. Available approximation methods usually obtain high order equivalent integer order transfer functions that could be difficult to implement. The present study introduces a novel frequency-domain approximation strategy based on non-linear least squares optimization routine. The result is an alternative approximation strategy that obtains an accurate frequency domain approximation with a reduced order transfer function. Validations are performed on various numerical examples, also highlighting the efficiency of the method for fractional orders greater than 1.