Two-scale command shaping for feedforward control of nonlinear systems

This paper presents a critical analysis of the two-scale command shaping (TSCS) feedforward control technique as applied to nonlinear Duffing oscillators. TSCS is an approach for tailoring a flexible system's applied control input to reduce undesirable residual vibrations using multiple problem scales, command shaping of a linear subproblem, and cancelation of a remaining nonlinear subproblem. As shown herein, TSCS proves to be an effective method for feedforward control of nonlinear systems. The strategy outperforms conventional and nonlinearly informed command shaping strategies in traditional and non-traditional Duffing systems (e.g., Duffing systems with quadratic nonlinearity and Coulomb damping). The TSCS approach is also extended herein to nonlinear systems with uncertain parameters through the implementation of robust command shaping strategies and the extended Kalman filtering parameter estimation technique.