Dynamics-based nonsingular interval model and luffing angular response field analysis of the DACS with narrowly bounded uncertainty

Abstract

This paper develops a dynamics-based nonsingular interval model and proposes a first-order composite function interval perturbation method (FCFIPM) for luffing angular response field analysis of the dual automobile cranes system (DACS) with narrowly bounded uncertainty. By using the nonsingular interval model to describe a structure parameter with bounded uncertainty, the reasonable lower and upper bounds can be obtained, which is quite different from the traditional interval model with approximate bounds only from a large number of samples. Firstly, for the DACS with deterministic information, the inverse kinematics is analyzed, and the dynamic model of the DACS is established based on the virtual work principle and the inverse kinematics. Secondly, considering the nonsingularity of the dynamic response curves, a dynamics-based nonsingular interval model is introduced. Based on the nonsingular interval model, the interval luffing angular response vector equilibrium equation of the DACS is established. Thirdly, a first-order composite function interval perturbation method is proposed. In the FCFIPM, the composite function vectors are expanded by using the first-order Taylor series expansion, based on the differential property of composite function and monotonic analysis technique, the lower and upper bounds of the interval luffing angular response vector of the crane 1 and crane 2 of the DACS are determined. The first case is to investigate the deterministic kinematics and dynamics of the DACS with a given trajectory. The second case is provided to illustrate the detailed implementation process of constructing a dynamics-based nonsingular interval model. Finally, some numerical examples are given to verify the feasibility and efficiency of the FCFIPM for solving the luffing angular response field problem with narrowly interval parameters.