Numerical design of retarded fractional delay differential systems by the method of inequalities

Abstract

The class of retarded fractional delay differential systems (RFDDS) is very general and includes rational systems and retarded delay differential systems as special cases. In practice, a RFDDS can arise when the controlled plant is characterized by fractional delay differential equations and/or when the controller used is of fractional order. The primary objective of this thesis is to develop computational methods to make possible the design of RFDDSs by the method of inequalities (MoI). In the design by the MoI, design problems are usually formulated so that they are suitable for solution by numerical methods. Accordingly, the design procedure comprises two phases of computation. First, seek a stability point in design-parameter space. Second, search in the stability region for a design solution by starting at the stability point so obtained. In this thesis, for RFDDSs, a computational stability test and a method for computing the abscissa of stability of the characteristic function are devised. Moreover, fractional controllers are designed for SISO and MIMO plants by the MoI together with conventional step-response criteria, using the developed computational tools. The numerical results evidently show the effectiveness of the systematic design procedure as well as the usefulness of the tools.