Accurate output tracking for nonminimum phase nonhyperbolic and near nonhyperbolic systems

Abstract

A new method to achieve an accurate output tracking for nonminimum phase linear systems with nonhyperbolic and near nonhyperbolic internal dynamics is presented. For the classical methods, developed in the framework of the preview based stable inversion, the nonhyperbolicity represents a rather serious inconvenience because the required preactuation time tends to be unacceptably large. Different stable inversion techniques, developed for SISO systems, are based on a proper redefinition of the desired output trajectory with the aim of canceling the undesired effects of unstable zeros. The main purpose of the new approach is to alleviate some theoretical and practical limitations inherent in the above methods. The desired output is partitioned into the transient and steady-state components. The transient input is "a priori" assumed to be given by a spline function. Once the desired output trajectory has been specified, this allows the computation of the unknown transient input as the approximate least-squares solution of Fredholm's integral equation corresponding to the explicit formula of the output forced response. The steady-state input is analytically computed exploiting the steady-state output response expressions for inputs belonging to the same set of the desired steady-state output. The main advantage of the resulting technique is that its generality does not require "ad hoc" procedures depending on the particular plant to be controlled. This allows the designer to freely specify the desired output trajectory without requiring it to depend on the unstable zeros of the plant or it to be null over an initial time interval.