ARX System identification of a positioning stage based on theoretical modeling and an ARX model WANG Jing-shu 1 GUO Jie 2 ZHU Chang-an 2

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1 DOI: /j.cnki.jvs JOURNAL OF VIBRATION AND SHOCK Vol. 32 No ARX ARX ARX ARX TH113 A System identification of a positioning stage based on theoretical modeling and an ARX model WANG Jing-shu 1 GUO Jie 2 ZHU Chang-an 2 1. Chongqing University of Technology School of Mechanical Engineering Chongqing China 2. Department of Precision Machinery and Precision Instruments University of Science and Technology of China Hefei China Abstract In order to know the characteristics of a positioning stage a dynamic model with single input and twooutput was developed and the positioning tests were done. Based on the dynamic model and the test data after interpolating and normalizing the unknown parameters were identified with the least square method. Another identification method based on an ARX model was applied to recognize the inside stage system. The results comparison indicated that the ARX model is appropriate to describe the characteristics of the stage system while the dynamic model is meaningful for structural optimization. Key words positioning stage dynamic model system identification ARX STM ARX ARMAX Box- Jenkins 5-6 ARMA ARX

2 ARX Hz Hz s 2 1 Fig. 1 The structure of the positioning stage Fig. 2 The kinetic model of the stage 50 μm 50 μm 0 u x in = x 1 /50 μm x 1 x 2 x out = x 2 /50 μm M m x in k 2 b 2 x out k 1 b 1. Mx 1 = - k 1 x 1 - b 1 x 1 - k 2 u + x 1 - x 2 mx 2 = k 2 u + x 1 - x 2 + b 2 x 1 - x Hz Hz s x n T m = T m - t i -1 x t i - t n t i - x n t i -1 i -1 n = 1 2 x n = 1 n = 2 T m = m* t i T m t i - 1 T m x n 3 50 μm

3 M m 1 k 1 k 2 b b 2 1 Tab. 1 The known parameters of the kinetic model M m kg Hz 4 T i y i i = n min n i = 0 f T i - y i 2 n T i y i f T - matlab 2 2 Tab. 2 The unknown parameters of the kinetic model k 1 / N m - 1 k 2 / N m - 1 b 1 / Nm s - 1 b 2 / Nm s ARX ARMAX Box-jenkins 1 ARX ARX A z -1 y k = B z -1 u k - n k + ξ k ξ k n k ARX ξ k = 0 n k = 0 Rissanen [ ( ) ] min V 1 + dlogn N N d V ARX A 10 B Fig. 3 The identification results of the kinetic model 2

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