Stable inversion of SISO nonminimum phase linear systems through output planning: an experimental application to the one-link flexible manipulator

In this paper, we introduce a new technique that allows for causal stable inversion of linear nonminimum phase systems. This approach is presented through its application to a flexible arm robot. In contrast with the available techniques, which amounts to finding a particular initial value for the inverse system to have bounded state trajectories, the presented scheme starts from any free initial conditions of the inverse dynamics, and searches for proper output trajectories with a polynomial form. Those output trajectories are computed such that the effect of the unstable zeros are completely cancelled. Furthermore, the scheme deals equally with hyperbolic as well as nonhyperbolic systems. The stable inverse is then incorporated into an output tracking controller, using a classical static state feedback. This global controller permits an exact tracking of the planned output. Experiments for a one-link flexible arm show good end-effector tracking results.