Lifted time stable inversion based feedforward control for linear non-minimum phase systems

The feedforward control strategy exhibits substantial capability and high-precision control for output tracking tasks. However, the feedforward control action obtained through solving the inverse problem is unstable for non-minimum phase systems. In this paper, a novel stable inversion method is presented, termed lifted time stable inversion. Compared to the existing method, the proposed method does not necessitate infinite window to accomplish the tracking tasks. A comprehensive analysis of the developed method is provided, focusing on analysis of finite time stability and input–output finite time stability, aspects that have garnered limited attention in the literature on feedforward control. Furthermore, the relationship with existing stable inversion method is illustrated by constructing a linear transformation of the initial conditions for both inversions. Simulation results substantiate the validity of the finite time bounds and demonstrate the superior tracking advantage of the proposed method relative to the existing method. The performance of the proposed method is further displayed experimentally on a piezoelectric ceramic positioning platform.