Task priority based mode shaping method for in-phase design of flexible structures aiming at high speed and accurate positioning

The flexibility of the mechanical system is one of the factors of the bandwidth limitation. Especially, it is known that an out-of-phase vibration mode makes the closed loop unstable with the negative feedback of the positioning error. In this paper, a novel mode shaping method for in-phase design of flexible structures is proposed. From the relation between the modal analysis and the state-space representation, we classify in-phase mode shaping into two types based on the boundary which is passed across during the shaping process. By the proposed method, the out-of-phase modes are shaped into in-phase in order of the natural frequencies applying a task priority based modification scheme. We also propose a method of selecting the boundary, so that the vibration mode is shaped into the arbitrary type of in-phase design.