The current tendency toward light weight and fast machines has lead to a need to suppress vibration of flexible dynamic systems. Input shaping is an efficient tool to eliminate transient and residual vibration caused by motion of these systems. This paper proposes a new formulation of the design method for multi-mode input shapers to eliminate residual vibration in flexible dynamic systems. The essence of the proposed method is to minimize the number of impulses to be n+1 for n-mode input shapers. This paper also suggests a solution procedure to solve the complexvalued nonlinear matrix equation for the input shapers. The proposed method is applied to twomode input shapers. This paper discusses characteristics of several input shapers obtained under the same condition. Simulations and experiments show that the proposed method is very useful for designing multi-mode input shapers.
