H-infinity optimal control based on output feedback for nonlinear two-degree-of-freedom vibration isolator with quasi-zero stiffness

Nonlinear vibration isolators can offer a high static stiffness alongside a low dynamic stiffness and so they have better isolation performance than conventional linear devices. In this paper, the models of the one-degree-of-freedom (DOF) and two-DOF bottom-springs grounded (BG) nonlinear vibration isolators with quasi-zero stiffness (QZS) characteristic are analyzed. In order to further improve the isolation performance of the 2-DOF BG nonlinear QZS vibration isolator, the H-infinity optimal control problem based on output feedback is studied. The nonlinear element of the vibration isolator is linearized by Taylor series expansion and ignoring the higher order term and then the whole nonlinear system is decomposed into linear part and nonlinear part. The output feedback H-infinity optimal controller designed for the linear part is proved to be the H-infinity optimal controller of the original nonlinear system. The controller has constraints, and the constraint equation contains input-related terms. The solution methods recorded in the existing literature are invalid for this situation. Therefore, a new linear matrix inequality for solution is given in this paper. To test the performance of the controller, numerical simulation is studied under the typical harmonic excitation. The results show that the designed controller for the 2-DOF BG nonlinear QZS vibration isolator has a good vibration isolation effect.