Exact and Causal Inversion of Nonminimum-Phase Systems: A Squaring-Down Approach for Overactuated Systems

Nonminimum-phase zeros pose challenges for controller design, i.e., in inversion-based control approaches where inverting these zeros may result in “unstable” poles. The aim of this paper is to exploit the additional freedom in overactuated systems to eliminate these zeros, facilitating subsequent inversion. In particular, an approach for causal and exact inversion of systems with nonminimum-phase behavior is presented. In an either static or dynamic squaring-down step prior to inversion, the approach exploits the fact that nonsquare systems typically have no invariant zeros. The proposed approach is successfully demonstrated in experiments on an overactuated motion system. The method enables exact inversion for nonsquare systems without requiring preview or preactuation.