Calculation of all stabilizing fractional-order PD controllers for integrating time delay systems

In this paper, a simple and effective stabilization method for integrating time delay systems using fractional order PD controllers μ s k k s C d p + = ) ( is proposed. The presented method is based on finding the stability regions according to the fractional orders of the derivative element in the range of (0, 2). These regions are computed by using three stability boundaries: Real Root Boundary (RRB), Complex Root Boundary (CRB) and Infinite Root Boundary (IRB). The method gives the explicit formulae corresponding to these boundaries in terms of fractional order PD controller (PD controller) parameters. Thus, the complete set of stabilizing controllers for an arbitrary integrating time delay system can be obtained. In order to demonstrate the effectiveness in solution accuracy and the simplicity of this method, two simulation studies are given. The simulation results indicate that the PD controllers can provide the larger stability regions than the integer order PD controllers.