Determination of optimal positive position feedback parameters by using nonsmooth H∞ synthesis

This article presents a method for determining optimal parameters of positive position feedback controllers used for suppressing vibration of flexible structures. The method is based on solving the H∞ synthesis problem with additional constraints on the controller structure. The method allows for independent control of damping added to each mode. Moreover, optimal parameters for both simple input simple output and multiple input multiple output control formulations can be obtained. The effectiveness of the method is shown by comparing the results of both multiple input multiple output and simple input simple output positive position feedback controllers designed by the proposed method, with the simple input simple output positive position feedback controller designed by analytically derived optimal parameters. Moreover, results of controllers designed with the fixed-order transfer function control structure are also presented to emphasize the advantages offered by the positive position feedback control structure.