Flexible Single-Link Manipulators Control Based on a Full-Order Transfer Function Model

This article presents a solution for the problem of flexible single-link robotic manipulators control in the frequency domain based on a full-order transfer function model. A transfer function model is derived from the partial differential equations of the flexible single-link manipulator system without any model order reduction. Conditions are obtained for the stability of the derived model that takes into account the payload mass changes. Employing these conditions, desired regions are obtained for the parameters of an output feedback controller which guarantee the stability and prescribed phase and gain margins as the design criteria. The regions consist of three types of boundaries of which two types provide necessity and sufficiency for the design criteria and the other provides sufficiency. A numerical example is given to demonstrate the suggested approach, showing it is less conservative than the other existing methods using reduced-order models.