Adaptive forward-propagating input reconstruction for nonminimum-phase systems

Input reconstruction is a process where the inputs to a system are estimated using the measured system output, and possibly some modeling information from the system model. One way to achieve this goal is to invert the system model and cascade delays to guarantee that the inverse is proper. A standing issue in input reconstruction lies in the inversion of nonminimum-phase systems, since the inverse model is unstable. We consider two methods for achieving input reconstruction despite the presence of nonminimum-phase zeros. First, we develop an open-loop partial inversion of the system model using a finite number of frequency points, where the partial inverse is a finite impulse response model and therefore is guaranteed to be asymptotically stable. Second, we examine a closed-loop approach that uses an infinite impulse response model. We demonstrate both methods on several illustrative examples.