Closed loop control of the planar flexible manipulator via Youla-Kucera parameterization

This work treats the problem of controlling a flexible robotic manipulator. The case study is a planar manipulator with a single flexible arm together with a clamped-free end and a tip lumped mass. To control the angular position of the flexible arm using an actuator, a controller method is developed which is based on Youla-Kucera parameterization. The main challenge in this approach is to obtain a Youla parameter with infinity dimensions. This parameter is approximated by a subspace with finite dimensions which makes the problem tractable. The developed approach exhibit advanced theoretical properties and good numerical convergence. In this paper, two sets of orthogonal bases such as FIR and Laguerre bases are used for system identification. The results of the present case study indicate that the proposed method is very efficient and robust for the time-continuous instances. The characteristics of an optimization problem are finally formulated for larger systems with hundreds of variables and solved with the interior point method.