柔軟構造物のデジタル制御による振動抑止におけるサンプリング間隔のスピルオーバに対する影響 第１部 近似理論解析とシミュレーション計算１

Abstract

The present paper discloses the influence of sampling period on the occurrence of the spillover by approximate theoretical analysis and numerical simulation. The fundamental equation of the system is formulated about a beam-structure. The control law, so called “Direct Output Feedback” is used. Taking the first mode of an uniform cantilever beam as a control mode and the second and third modes as residual modes, numerical simulation has been carried out about many values of the sampling period. Sensor and actuator are collocated at the tip of the cantilever beam. The equation of the present approximate analysis is derived through dropping the terms of coupling and of the feedback of displacement. The formula of stability criterion for each mode is derived through the calculation of the work done by the control force and the structural damping force during the sampling period. The approximate analysis and the numerical simulation disclose the occurrence of a resonant type of spillover in the case where the sampling period is very close to (2m-1)/2 of the natural period of a normal mode. The result of numerical simulation is in good agreement with that of approximate analysis about the ranges of the sampling period which produces the spillover.