Youla-Parameterized Adaptive Switched Control of a Magnetic Negative Stiffness Isolator

Unknown time-varying narrowband direct disturbances caused by the moving parts will reduce the accuracy of the ultraprecision machining system. As a typical high static and low dynamic stiffness isolator (HSLDS), the magnetic negative stiffness isolator (MNSI) improves the low-frequency base vibration isolation performance, but reduces the resistance to direct disturbances. In this article, a MNSI with nonlinear characteristics is designed, which is modeled as a switched system with fixed error-dependent switching signal by piecewise linearization, and then a Youla-parameterized adaptive switched controller is proposed to realize output regulation. The conservativeness and computational expense of controller design are reduced by using linear matrix inequalities to replace the bilinear matrix inequalities. The unknown time-varying narrowband disturbance is controlled by adaptively adjusting Youla parameters by the recursive least square algorithm. The experimental results show that the problem of narrowband vibration control of HSLDS is solved by introducing a Youla-parameterized adaptive switched controller into the nonlinear system through piecewise linearization.