Proportional-Integral-Derivative (PID) control is used for automatically regulating a measurable quantity to a desired setpoint. It is widely used in different types of classical control electronics. Here, we show how generalizing the feedback term in quantum systems to include derivative and integral components influences both the transient and steady-state behavior of the amplitude and squeezing of a mechanical quadrature in an optomechanical system. We show that, the derivative feedback leads to enhanced unconditional squeezing. Furthermore, we demonstrate how feedback may be employed to drive a mechanical quadrature to a desired setpoint, and to track an external force. Our findings offer new routes for an improved quantum state control and measurement precision.