Two-scale command shaping for feedforward control of nonlinear systems

Abstract

This research proposes a two-scale command shaping (TSCS) approach for tailoring control inputs to nonlinear, flexible systems aimed at reducing undesirable residual vibrations. These systems exhibit control complexities not present in traditional linear systems. The TSCS approach employs problem scale decomposition using an asymptotic method, command shaping of a linear subproblem, and cancellation of a remaining nonlinear subproblem. For traditional and nontraditional Duffing-like nonlinear systems, TSCS is shown herein to outperform other command shaping strategies recently presented in literature. Following initial development, the TSCS approach is further extended to nonlinear systems with uncertain parameters through the implementation of robust command shaping strategies and parameter estimation techniques. Undesirable vibrations arising from internal combustion engine (ICE) restart/shutdown, which occurs in both hybrid electric and conventional vehicles, provides a contemporary motivating problem ideal for TSCS application due to nonlinearities arising in ICE geometry and friction. Using analytical, computational, and experimental means, TSCS applied to this problem is shown to significantly reduce undesirable vibrations while leveraging existing vehicle components. It is anticipated that the developed TSCS approach can be applied to a wide array of nonlinear, flexible systems with little to no additional cost and complexity, making it attractive for further study and adoption.