B-spline-decomposition-based output tracking with preview for nonminimum-phase linear systems

This article proposes a B -spline-decomposition-based approach to output tracking with preview for nonminimum-phase (NMP) systems. It has been shown that when there exists a finite (in time) preview of future desired trajectory, precision output tracking of NMP systems can be achieved by using the preview-based stable-inversion technique. The performance of this approach, however, can be sensitive to system dynamics uncertainty, and the computation involved can be demanding. We propose to address these challenges by integrating the notion of trajectory decomposition with the iterative learning control (ILC) technique. Particularly, the B -splines are used to construct a library of output elements and the corresponding input elements a priori, and the ILC techniques are used to obtain the input elements for precision tracking of the output elements. During the tracking with preview, the previewed future desired trajectory is decomposed by using the output elements, and the input is synthesized by using the corresponding input elements with chosen pre- and post-actuation times. The required pre-/post-actuation times are quantified based on the stable-inversion theory. The use of B -splines substantially reduces the number of output elements in the library, and the decomposition-synthesis occurs only at time instants separated by the difference between the preview time and pre-actuation time. The proposed approach is illustrated through a simulation study of nanomanipulation application using a NMP piezo actuator model.