  We propose a feedback control mechanism for the squeezing of the phononic
mode of a mechanical oscillator. We show how, under appropriate working
conditions, a simple adiabatic approach is able to induce mechanical squeezing.
We then go beyond the limitations of such a working point and demonstrate the
stationary squeezing induced by using repeated measurements and
re-initialisation of the state of a two-level system ancilla coupled to the
oscillator. Our non-adaptive feedback loop offers interesting possibilities for
quantum state engineering and steering in open-system scenarios.
