Machine tools are often automatically controlled. 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 is

where Ka= 1 and Ta = 0.4 s. The output voltage of the difference amplifier is
E()(5) = K1{X{s) - Xd(s)).
where xd(t) is the desired position input. The force on the shaft is proportional to the current i, so that F = K2i(t). where K2 = 3.0. The spring constant K, is equal to 1.5,7? = 0.1, and L = 0.2.
(a) Determine the gain K1 that results in a system with a phase margin of 30°. (b) For the gain Kx of part (a), determine Mpω, con and the closed-loop system bandwidth, (c) Estimate the percent overshoot of the transient response to a step input Xd(s) = l/.y, and the settling time (to within 2% of the final value).

Transcribed Image Text:

K, y(s)