On-off nonlinear active control of floor vibrations

Human-induced floor vibrations can be mitigated by means of active control via an electromagnetic proof-mass actuator. Previous researchers have developed a system for floor vibration comprising linear velocity feedback control (LVFC) with a command limiter (saturation in the command signal to avoid actuator overloading). The performance of this control is highly dependent on the linear gain utilised, which has to be designed for a particular excitation and might not be optimum for other excitations. This work explores the use of on-off nonlinear velocity feedback control (NLVFC) as the natural evolution of LVFC when high gains and/or significant vibration level are present together with saturation in the control law. Firstly, the describing function tool is employed to analyse the stability properties of: (1) LVFC with saturation, (2) on-off NLVFC with a dead zone and (3) on-off NLVFC with a switching-off function. Particular emphasis is paid to the resulting limit cycle behaviour and the design of appropriate dead zone and switching-off levels to avoid it. Secondly, experimental trials using the three control laws are conducted on a laboratory test floor. The results corroborate the analytical stability predictions. The pros of on-off NLVFC are that no gain has to be chosen and maximum actuator energy is delivered to cancel the vibration. In contrast, the requirement to select a dead zone or switching-off function provides a drawback in its application.