Force control of one-link flexible arms mounted on a linear motor with PD and shear force (PDSF) feedback

In this paper we propose a robust force controller of flexible one-link arms with a linear motor. Since the tip of the flexible arm contacts with a given constraint surface, a constraint condition should be satisfied. By using Hamilton´s principle, we derive dynamic equations of the motion of the base body that the flexible arm, is mounted and the constraint force. To compensate the spillover instability a PDSF controller is constructed. The synthesis is carried out in the infinite-dimensional setting, mathematical features of which give rise to stabilizing PDSF control algorithm. Due to simplicity of the implementation, the algorithm becomes extremely attractive under limitations on the computer power in the space. The effectiveness of the proposed control strategy is supported by simulations