申論題

PROBLEM 1 (40%)
 A DC motor drives a machine-tool spindle and workpiece, and its dynamic equation is described 

by
where ω is the angular velocity in units of rad/s, I is the input current, and Tt is the external torque generated by the cutting forces acting on the workpiece. There is an input delay of 0.092 s. The motor's torque constant K is found to be 0.1 by referring to the motor data sheet; but the moment of inertia J and the damping ratio B are unknown. Temporarily removing the workpiece (i.e., Tz=0), and doing the frequency response test by sweeping the frequency of the input current I, we can obtain the Bode plot of the transfer function between input current I and angular velocity w, as displayed in Fig. 1.