Gain scheduling GMV using Gaussian function for nonlinear hysteretic structural systems

In this paper, a generalized minimum variance algorithm using the gain scheduling technique is presented. First, we linearize the nonlinear model of the structure around a number of desired states representing regions of evolution of the structural response. Around each state, an Auto-Regressive-Moving-Average-eXogen (ARMAX) model of the structure is determined and a local GMV control law is developed. The control consists on switching-on or switching-off a local GMV controller depending on the actual state of the system. The approach consists on using Gaussian membership functions related to the domains around the points of linearization. The control from the local GMV controllers is weighed by these functions and added together to produce the final control.