Fractional-order control of a micrometric linear axis (Q1953757)

Summary: This paper discusses the application of a particular fractional-order control scheme, the PDD\(^{1/2}\), to the position control of a micrometric linear axis. The PDD\(^{1/2}\) scheme derives from the classical PD scheme with the introduction of the half-derivative term. The PD and PDD\(^{1/2}\) schemes are compared by adopting a nondimensional approach for the sake of generality. The linear model of the closed-loop system is discussed by analyzing the pole location in the \(\sigma\)-plane. Then, different combinations of the derivative and half-derivative terms, characterized by the same settling energy in the step response, are experimentally compared in the real mechatronic application, with nonnegligible friction effects and a position set point with trapezoidal speed law. The experimental results are coherent with the nonlinear model of the controlled system and confirm that the introduction of the half-derivative term is an interesting option for reducing the tracking error in the transient state.