Separated-Form Equations of Motion of Controlled Flexible Multibody Systems

Abstract

This paper introduces a method leading to separated-form formulation of dynamic equations of multibody systems subject to control. The algorithm is derived from the virtual work principle and includes the moving base effects. The elastic members are treated as Euler-Bernoulli beams. Equations of motion are expanded using generalized coordinate partitioning and a Jacobian matrix expansion. The formulation of each physical term is separated, i.e., the inertia matrix, nonlinear coupling vector, generalized force vector and base motion-induced terms are established individually. The formulation is implemented on a workstation using MAPLE. Nonlinear and linearized equations with control are generated in FORTRAN format. The control design adopts second-order models directly. Several examples including a spin-up cantilever beam, an elastic vehicle with active suspensions and an elastic slider-crank mechanism are given. Numerical results for nonlinear and linear spin-up beam models are provided. Simulation for the active vehicle model using second-order control theory is presented.