  A mechanical system can be optimally controlled through continuous
measurements of its position followed by feedback. We revisit the complete
formalism for predicting the performance of such as system without invoking the
standard rotating wave approximations and the adiabatic approximation. Using
this formalism we deduce both the conditional and unconditional state of a
mechanical oscillator using the optimal control and feedback that leads to
mechanical cooling and mechanical squeezing. We find large discrepancies
between the exact solutions and the approximate solutions stressing the
importance of using the complete model. We also highlight the importance of
distinguishing between the conditional and unconditional state by demonstrating
that these two cannot coincide in a typical control scheme, even with infinite
feedback strength.
