| In this dissertation, a preview-based system-inversion technique for output tracking is developed. This preview-based approach addresses the problem of quantifying the importance of the future desired trajectory in determining the current input needed for output-tracking. This problem arises, because for nonminimum-phase system, computing the exact-output-tracking input—which can be done by using the system-inversion method—requires the information of the entire future desired trajectory (such input, obtained from the system-inversion method, is called the inverse input). However, it is intuitive that the effect of the desired output's distant-future values, on the current output-tracking input, should be small. Therefore, preview information of the desired output in a finite-time window [tc, t c + Tp] (where Tp is called the preview time) should be sufficient to compute such input at current time instant (tc). In this dissertation, we show that the error in computing the current input (due to finite preview time Tp) decays exponentially with the increase of preview time, and thus can be made arbitrarily small by having a large-enough (but finite) preview time. More importantly, for given precision in computing the inverse input, we quantify the required preview time in terms of the nonminimum-phase characteristic of the system. For example, for linear time invariant system, the preview time is quantified by the minimum gap between the imaginary axis and the nonminimum-phase zeros of the system. In addition, to address the problems of model uncertainties and actuator saturations, this idea of “preview” is integrated with the optimal-inversion technique to develop the preview-based optimal-inversion technique. Such preview-based approach, enabling the system-inversion techniques to track online generated trajectory for nonminimum-phase system, is developed for: (1) linear time invariant (LTI) systems; (2) periodic-switching systems; (3) nonlinear systems. In addition, we implement these preview-based techniques in both simulations and experiments. The experimental work includes the output tracking of a flexible structure and the high-speed atomic-level imaging on a scanning tunneling microscope (STM), and the simulation study includes the precision output-tracking of an Inchworm-type piezo-positioning system and the guidance of a vertical take off and landing (VTOL) aircraft model. |
