A numerical algorithm for stability testing of fractional delay systems
Automatica (Journal of IFAC)
Fractional order calculus in control theory
ACMOS'11 Proceedings of the 13th WSEAS international conference on Automatic control, modelling & simulation
Computers & Mathematics with Applications
Fractional models for modeling complex linear systems under poor frequency resolution measurements
Digital Signal Processing
Fractional-order control of a micrometric linear axis
Journal of Control Science and Engineering
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In this paper, a simple and effective stabilization method for integrating time delay systems using fractional order PD controllers C(s)=k"p+k"ds^@m 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^@m 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^@m controllers can provide larger stability regions than the integer order PD controllers.