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Phase analysis of actuator response for sub‐optimal bang–bang and velocity cancellation control of base‐isolated structures

Starting with simplified models of displacement response for a base‐isolated structure supplemented with sub‐optimal bang–bang control, we formulate models of phase analysis of actuator force direction in relation to system displacements and velocities. For the case of steady‐state displacement response, we show that switching of the actuator force direction can neither be perfectly in phase with displacements, nor perfectly in phase with velocities. In practice, however, switching of the actuator force direction is ‘almost in phase’ with velocities and ‘almost orthogonal’ to sign changes in displacements. This observation suggests that a new and very simple velocity cancellation control might be effective in adding value to base isolation system responses. Numerical experiments are conducted to assess improvements in performance due to sub‐optimal bang–bang control and velocity cancellation control, and to validate the extent to which the phase analysis predictions hold in linearly elastic and non‐linear time‐domain settings. Copyright © 2007 John Wiley & Sons, Ltd.