A common rule of thumb for controller discretization is to have "6 samples per rise time" in order to achieve a reasonable approximation of the CT controller, without wasting computing resources. Derive the effect on PM that this choice will have. Also derive the relationship of this choice to the effective Nyquist rate for the closed-loop system.

Aturning operation is performed with following conditions: rake angle of 12°, a feed of 0.35 mm/rev, and a depth of cut of 1.1 mm. the work piece is aluminum alloy 6061 with t6 heat treatment (a16061-t6). the resultant chip thickness was measured to be 1.0 mm. estimate the cutting force, fc. use shear stress of 207 mpa and coefficient of friction on the tool face of 0.6.