An introduction to the receptance method in active vibration control

Abstract

The paper gives an introduction to the inverse problem of eigenvalue assignment in active vibration control by the receptance method. Well known in passive structural modification theory, the receptance method not only provides an alternative to conventional state-space methods in active vibration control, but also possesses many significant advantages. In particular there is no need to know or to evaluate the system matrices M, C, K and no need for model reduction or the estimation of unmeasured states by an observer since the system equations, being inverted, are made complete by the measured states alone. In the case of single-input state feedback, the characteristic equations are shown to be linear in the unknown control gains, a consequence of the rank-one control provided [1]. The method is equally applicable to output feedback control, with greater freedom for pole placement, but the characteristic equations become nonlinear. Method for the assignment of eigenvalue sensitivity are described by both approaches [2, 3]. Partial pole placement and eigenstructure assignment problems are also described [3]. The method does not require The use of orthogonality relations. Numerical examples and physical experiments [4] are provided to illustrate the working of the metho