Bagley-Torvik fractional order system performance characteristics analysis

Abstract

The general Bagley-Torvik fractional order system is represented by the Bagley-Torvik equation with a real order derivative instead of 1/2 or 3/2 order derivative. This fractional order system can exhibit behaviors that range from relaxation to oscillation for different values of the real derivative order and the damping ratio-like parameters. For this reason, it is interesting to take this system as a reference model in feedback control system. The aim of this paper is then to provide analysis of the essentials of the time and frequency performance characteristics of the general Bagley-Torvik fractional order system by varying its two tuning the real derivative order and the damping ratio-like parameters. To show the effectiveness of the proposed reference model, the obtained performance characteristics have been compared to the performance characteristics of the regular second order model.