Inversion-based optimal output tracking–transition switching with preview for nonminimum-phase linear systems

In this article, the problem of nonperiodic tracking–transition switching with preview is considered. Such a control problem exists in applications including nanoscale material property mapping, robot manipulation, and probe-based nanofabrication, where the output needs to track the desired trajectory during the tracking sections, and rapidly transit to another point during the transition sections with no post-transition oscillations. Due to the coupling between the control of the tracking sections and that of the transition ones, and the potential mismatch of the boundary system state at the tracking–transition switching instants, these control objectives become challenging for nonminimum-phase systems. In the proposed approach, the optimal desired output trajectory for the transition sections is designed through a direct minimization of the output energy, and the needed control input that maintains the smoothness of both the output and the system state across all tracking–transition switching is obtained through a preview-based stable-inversion approach. The needed preview time is quantified by the characteristics of the system dynamics, and can be minimized via the recently developed optimal preview-based inversion technique. The proposed approach is illustrated through a nanomanipulation example in simulation.