Residual vibration reduction in low damping systems. Generation of regular piecewise algebraic polynomial inputs

This paper presents a feedforward technique to generate command inputs to reduce residual vibration after transient maneuvers in mechanical systems. Synthesized inputs base their vibration reduction in zero-frequency content at the system resonances and are obtained taking advantage of the convolution theorem of the Fourier transform (FT). The analyzed systems are those that can be modeled as discrete linear systems with n vibratory degrees-offreedom, and can be described with constant parameter motion equations. Although the complete cancellation of residual vibrations occurs for null damping ratios, the results obtained for low damped systems are quite acceptable. The method is particularized for rest-to-rest maneuvers and is compared to other literature methods. The new profiles present an optimal shape in terms of minimum acceleration fluctuation, which is useful to reduce the fatigue strength of the mechanical parts. By using a pulse as a base signal, the inputs obtained follow piecewise algebraic polynomial functions easily implementable through a B-spline scheme. The development includes a robust approach against the variation of the system parameters and a constraint determination aid for symmetric functions. Finally, some experimental results are presented using a two vibratory degrees-of-freedom test bed.