The force on the cutting tool in a lathe depends on the cutting depth from the previous rotation of the work piece. This can be modeled as a internal delay in the system:

The uncontrolled system is unstable:

Creating a delay-free approximation for a time-delay system allows for all of the standard controller design techniques:

Design an estimator-regulator by moving the unstable open-loop poles:

The closed-loop system response is stable: