部分空間法と周波数頸域最小二乗近似を用いた除振台の低次元システム同定

摘要

近年の目覚ましぃ技術進歩に伴って製品の精密化がrn進んだことにより，半導体製造装置や検査装置のようrnな精密な計測や加工を伴う装置はさらなる高精度，高rn性能が求められることとなった．高精度なァクティブrn除振制御を行うためには制御対象の高精度な数学モデrnルが必要不可欠である．システムの入出力関係を用ぃrnてモデリングを行う手法がシステム同定であり．現在rnまで様々な条件，用途に応じて様々な同定手法が提案rnされてぃる（1）～（4）．%A system identification technique for a vibration isolation table is studied in this paper. The vibration isolation table is supported by four pneumatic actuators at corners of the square rigid table. A 3 DOF mathematical model of the vibration isolation table is constructed. The regulator for the pneumatic actuator is driven by a stepping motor. Proposed procedure to obtain the minimum-order model is described as follows : First, the state space model is identified from input-output data by subspace method. Next, the low order curve fitting model is calculated by Frequency-Domain Least-Squares Approximation (FDLSA). And then, the characteristic eigenvalues near the eigenvalues of FDLSA model is picked out from the N4SID model, and the minimum order system that has the characteristic eigenvalues of N4SID model is reconstructed. And the procedure can be fully automated. Effectiveness of this approach is examined by experiments.