Improved clipped periodic optimal control for semi-active harmonic disturbance rejection

This paper presents a new approach for harmonic disturbance rejection using semi-active vibration control. The approach is illustrated through application to the problem of maximizing the energy dissipated by a semi-active damper under harmonic excitation. In order to establish a baseline for the evaluation of the performance of the semi-active damper, the effectiveness of the optimal passive and active cases are first presented. The study then examines the ability of the clipped optimal control (or clipping control) approach to improve the energy dissipation capacity of the semi-active damper over the optimal passive damper. An approximate solution to the nonlinear dynamic problem, obtained using the method of averaging, and a time integration based numerical method indicate that this approach improves the energy dissipated by the semi-active damper over the optimal passive damper. The approach presented in this paper intends to further “improve”, or “fine tune”, the control parameters given by the clipped optimal control approach. This is done using an approximated solution of the problem and an appropriate optimization algorithm. Results clearly indicate that this new approach provides significant improvement on energy dissipation over the clipped optimal control approach for the semi-active damper.