LQR control with frequency-dependent scheduled gain for a semi-active floor isolation system

SUMMARY: Floor isolation is an alternative to base isolation for protecting a specific group of equipment installed on a single floor or room in a fixed-base structure. The acceleration of the isolated floor should be mitigated to protect the equipment, and the displacement needs to be suppressed, especially under long-period motions, to save more space for the floor to place equipment. To design floor isolation systems that reduce acceleration and displacement for both short-period and long-period motions, semi-active control with a newly proposed method using the linear quadratic regulator (LQR) control with frequency-dependent scheduled gain (LQRSG) is adopted. The LQRSG method is developed to account for the frequency characteristics of the input motion. It updates the control gain calculated by the LQR control based on the relationship between the control gain and dominant frequency of the input motion. The dominant frequency is detected in real time using a window method. To verify the effectiveness of the LQRSG method, a series of shake table tests is performed for a semi-active floor isolation system with rolling pendulum isolators and a magnetic-rheological damper. The test results show that the LQRSG method is significantly more effective than the LQR control over a range of short-period and long-period motions.