Theory of fractional integrals and derivatives: application to motion control

The theory of fractional derivatives and integrals (FDI's) is still in a research stage but recent progresses in the area of chaos reveal promissing aspects for future developments. In the field of automatic control systems some preliminary results are restricted to the frequency domain. In this paper a novel method for the FDI approximation is presented. The proposed algorithms adopt the time domain which makes them well suited for z-transform analysis and digital implementation. Based on the new concepts the paper shows that classical P, I and D actions are special cases of a broader paradigm.N/