Fractional-Order Modeling of Pneumatic Transmission Dynamics in Soft Robotic Actuation

Abstract

Pneumatic actuation is fundamental to soft robotic systems, yet airflow dynamics in thin, elongated pipelines are difficult to model due to transport delays, boundary-dependent transients, and long-memory effects. In such regimes, classical integer-order (IO) models often fail to capture slow relaxation, non-exponential transients, and distributed damping arising from compressibility, friction, and wave propagation. This paper presents an experimental comparison of IO and fractional-order (FO) time-domain models for pneumatic pipeline dynamics in a closed-end configuration, identified from step-response measurements obtained on a 13.2 m nylon pipeline. Control-oriented model structures are formulated for both modelling paradigms, with FO models implemented using the Grünwald-Letnikov (GL) state-space discretisation. A unified identification framework is employed in which an effective time delay is estimated, dynamic parameters are identified by minimising a weighted root-mean-square error emphasising early-time transients, and the static gain is computed analytically by least squares. The estimated delay includes both pressure-transport effects and the experimental triggering offset. Experimental results show that FO models consistently achieve lower fitting errors than IO counterparts while providing a more compact representation of long-memory relaxation and distributed damping effects. Simulink validation further supports the experimental findings, with the fractionalorder models achieving lower root-mean-square error than the tested integer-order models across all reported comparisons.