The positioning performance of high-speed, high-accuracy light-weight motion control systems is usually restricted by the structure flexibility and model parameter-varying caused by load mass variation. It needs to develop novel motion control algorithm to eliminate the residual vibration in the end-effectors, as well as to be robust over the load mass variation. This paper addresses the first and crucial step of this problem, modeling and identification technique. The linear parameter-varying model of the system is constructed and analyzed. The parameters and affine function identification method based on nonlinear least-squares and principle component analysis technique is proposed. The validity of the proposed method is demonstrated through a lightweight machine experimental setup. It is general enough to be applicable to the dynamic behaviors analysis and gain-scheduling robust control design for industrial lightweight vibration suppression and motion control systems that possess flexible elements and variable loads.