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:
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The uncontrolled system is unstable:
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Creating a delay-free approximation for a time-delay system allows for all of the standard controller design techniques:
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Design an estimator-regulator by moving the unstable open-loop poles:
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The closed-loop system response is stable:
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