Partial eigenstructure assignment of the vibration system based on multi-input PID active control

Abstract

We propose a multi-input active control method to enable targeted assignment and suppression of closed-loop zeros and poles in a vibration system, while preventing system singularities. This approach integrates integral feedback into the dynamic flexibility matrix control framework. The method begins by introducing multi-input PID feedback into the free vibration equation of a multi-degree-of-freedom linear system. The Laplace transform is then applied to decompose and solve the resulting linear equations using LU decomposition, yielding the closed-loop system’s transfer function matrix. When the preset zeros and poles are self-conjugate with negative real parts, the gain vector for multi-input PID feedback eigenstructure assignment is determined using the Levenberg–Marquardt method. The effectiveness of this method is demonstrated through third- and sixth-dimensional examples. Numerical results confirm its efficacy in multi-input active control with partial eigenstructure assignment, while a robustness analysis further supports its practical applicability.