Time Response Computation of Control Systems with Fractional Order Lag or Lead Controller

In recent years, there have been many studies in the field of fractional order control systems. Many results have been published related with the frequency and time domains analysis of closed loop fractional order control systems. However, obtaining exact time response of a fractional order system is a difficult problem since it is not possible to derive analytical inverse Laplace transform of a fractional order transfer function. In this paper, an exact method is presented for computation of the time response of a closed loop control system with a fractional order lag or lead controller using frequency response data of the closed loop system. The presented method is based on the results, which use Fourier series of a square wave and inverse Fourier transform of frequency response information, previously derived by the authors. Numerical examples are provided to show the success of the presented method.