Machine tools are often automatically controlled as shown in Figure P9.10. These automatic systems are often called numerical machine controls [9]. On each axis, the desired position of the machine tool is compared with the actual position and is used to actuate a solenoid coil and the shaft of a hydraulic actuator. The transfer function of the actuator (see Table 2.7) is
where Ka = 1 and τa = 0.4 s. The output voltage of the difference amplifier is
(a) Determine the gain K] that results in a system with a phase margin of 30°. (b) For the gain K1 of part (a), determine Mpω, ωn and the closed-loop system bandwidth, (c) Estimate the percent overshoot of the transient response to a step input Xd(s) = 1/s, and the settling time (to within 2% of the final value).
