[(cas/pen)] 15 o 0 0.8 0.6 >0.4 02 0 0.005 0.01 Velocity Loop Step Response 0.015 0.02 0.025 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 time [sec] Figure 2: Step Response of a CNC's Axis The step response of a CNC Machine's axis is shown in Figure 2. V.[V] is the voltage command input, and [rad/sec] is motor's angular velocity. a) The mechanical dynamics can be represented by a first order system (s)/V(s) = K₂/(1,5+1). Determine the velocity loop gain K, and time constant r from Figure 2 above. (10pts) 0.03 0.035 0.04 b) Assume that the axis is driven by a ball-screw mechanism that has a pitch of h=10[mm]. The feedback measurement (encoder measurement) is taken from the table. Design a proportional (P) feedback position controller. The performance target is to achieve 5% overshoot. Calculate the appropriate K, gain value. (10pts) Some assistive formula: t c) Compute the steady state tracking error [mm] for a feedrate command of f = 120 [mm/sec]. (5pts) -tan √₁-2²₁ -√1-² and (== -log, M ²+log (M₂)

Fig: 1