Establishment and Identification of Fractional-Order Model for Structurally Symmetric Flexible Two-Link Manipulator System

Integer-order models cannot characterize the dynamic behavior of the flexible two-link manipulator (FTLM) system accurately due to its viscoelastic characteristics and flexible oscillation. Hence, this paper proposes a fractional-order modeling method and identification algorithm for the FTLM system. Firstly, we exploit the memory and history-dependent properties of fractional calculus to describe the flexible link’s viscoelastic potential energy and viscous friction. Secondly, we establish a fractional-order differential equation for the flexible link based on the fractional-order Euler–Lagrange equation to characterize the flexible oscillation process accurately. Accordingly, we derive the fractional-order model of the FTLM system by analyzing the motor–link coupling as well as the symmetry of the system structure. Additionally, a system identification algorithm based on the multi-innovation integration operational matrix (MIOM) is proposed. The multi-innovation technique is combined with the least-squares algorithm to solve the operational matrix and achieve accurate system identification. Finally, experiments based on actual data are conducted to verify the effectiveness of the proposed modeling method and identification algorithm. The results show that the MIOM algorithm can improve system identification accuracy and that the fractional-order model can describe the dynamic behavior of the FTLM system more accurately than the integer-order model.