P9.26 A specialty machine shop is improving the effi

ciency of its surface-grinding process [21]. The existing machine is mechanically sound, but manually oper

ated. Automating the machine will free the operator for other tasks and thus increase overall throughput of the machine shop. The grinding machine is shown in Figure P9.26

(a) with all three axes automated with motors and feedback systems. The control system for the y-axis is shown in Figure P9.26(b). To achieve a low steady-state error to a ramp command, we choose

K = 2. Sketch the Bode plot and Nichols chart.

Determine the gain margin and phase margin of the system and the bandwidth of the closed-loop system.

Estimate the damping ratio of the system and the pre

dicted percent overshoot and settling time. 

x-axis motor z-axis motor Grinding wheel y-axis motor (a) Safety guard K R(s) Y(s) s(0.4s+ 1)(0.5s+1) FIGURE P9.26 Surface-grinding wheel control system. (b)