Create a Controller for a Lathe by Approximating the Time Delays

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: