Modelling and Control Synthesis of Flexible Multibody Systems
In the last two decades, several models have been developed for the simulation of gross nonlinear motions of multibody systems which incorporate elastic members with small deformations. Although these models represent the real system sufficiently well for simulation, a closed-loop controller designed on the basis of such models may result in instability if applied to the real system.
In this paper, the value of a model consisting of superelements for control synthesis is investigated. The superelements approximating flexible bodies with beam like structures are composed of a series of rigid bodies interconnected by joints and springs. As an example, the nonlinear equations of motion of a plane flexible robot with two links are derived and linearized for control synthesis. A first controller is synthesized by using the pole placement method. Applied to the ‘real system’ represented by a highly accurate finite element model, the controller leads to instability. Therefore, a second robust controller is synthesized by using left coprime factorization and H∞ minimization.
KeywordsMultibody System Control Synthesis Robust Controller Open Loop Control Flexible Body
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