Modelling and H∞ control of a single-link flexible manipulator

The aim of this study is to investigate motion in the horizontal and the vertical planes of a single-link flexible manipulator. The manipulator is modelled including gravity terms, and it is verified experimentally that the horizontal and the vertical motions are decoupled for a cylindrically symmetrical link and payload. The mathematical model is used to design a mixed-sensitivity H∞ contrlllerr. The sensitivity weighting function is used to obtain the required disturbance rejection properties, including zero sensitivity to a force disturbance in the steady state (i. e. integral action control). The control sensitivity weighting function is chosen to guarantee stability despite variation in the payload mass. The controller is compared experimentally with a proportional-plus-integral controller with velocity feedback and shown to give improved vibration control performance in the vertical plane.