Model inversion for a particular class of nonlinear non-minimum phase systems: an application to the two-link flexible manipulator

Concerns the output trajectory tracking for a class of nonlinear nonminimum-phase systems, namely, systems described by Lagrange equations of motion. In the nonminimum-phase case, the direct application of classical input-output inversion procedure fails, due to the unacceptable nature of internal dynamics. The paper concerns the inversion of those internal dynamics. Inversion yielding a bounded state permits then to achieve exact output tracking (or asymptotic tracking), without control saturation. The inversion scheme deals equally with systems having hyperbolic or nonhyperbolic equilibrium points of zero dynamic. This is a consequence of a different formulation of the stable inversion problem. The nonlinear internal dynamics are inverted, without any noncausal computation and are fully based on nonlinear terms, without local dynamic linearization. The performance is demonstrated through application to the tip trajectory tracking for a two-link flexible manipulator