Modeling and control of flexible link manipulators for unmodeled dynamics effect

Abstract

Flexible link manipulators are mostly prefered in applications where energy consumption and faster operation are critically important. Since distributed nature of flexibility makes the system depend on not only time variable but also a spatial variable, the dynamics of flexible structures are expressed by partial differential equations. In the virtue of this kind of modeling, the designers encounter with infinite dimensional systems which means that the system has an infinite number of degrees of freedom. To cope with infinite dimensional systems, one of the most relevant techniques is to truncate the model into a definite order. However, this may yield the unmodeled dynamics that cause performance degradation and even instability. In this paper, the main motivation is to propose control techniques to compensate unwanted effects of unmodeled dynamics which may occur in truncation process. In order to achieve this goal, the linear quadratic Gaussian and the weighted ${\mathcal{H}}_{\infty }$ controller design are adopted. The performances of the designed controllers are demonstrated on the experimental setup. Besides this motivation, traditional lumped parameter model of the flexible link manipulator which is widely seen in the literature is considered and the superiority of the partial differential equation model is shown on the experimental setup.