Causal inversion of nonminimum phase systems

Inversion of nonminimum phase systems is a challenging problem. The classical causal inverses proposed by Hirschorn (1979) result in unbounded solutions to the inverse problem where the zero dynamics axe unstable. Stable inversion introduced by Chen and Paden (1992) obtains bounded but noncausal inverses for nonminimum phase systems. As a first step, the paper addresses bounded causal inversion of nonlinear nonminimum phase systems. It is shown that an optimal causal inversion problem is equivalent to a minimum energy control problem of the zero dynamics driven by a causal reference output profile. A causal inversion solution for nonlinear systems and an optimal causal inversion solution for linear systems are also proposed. Simulation results demonstrate the effectiveness of the new causal inversion approach in output tracking.