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 prove that the direction of actuator application can neither be perfectly in phase with displacements, nor perfectly in phase with velocities. In practice, however, the actuator force direction is almost in phase' with velocities and almost orthogonal' to sign changes in displacements. This observation suggests that a 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 nonlinear time-domain settings.