Question

A numerical path-controlled machine turret lathe is an interesting problem in attaining sufficient accuracy [2, 23). A block diagram of a turret lathe control system is shown in Figure P10.8. The gear ratio is n = 0.2, J = 10-3, and b = 2.0 x 10-2. It is necessary to attain an accuracy of 5 x 10-4 in., and therefore a steady-state position accuracy of 2.5% is specified for a ramp input. Design a cascade compensator to be inserted before the silicon-controlled rectifiers in order to provide a response to a step command with a percent overshoot of P.O. < 5%.A suitable damping ratio for this system is 6 0.7. The gain of the silicon-controlled rectifiers is KR 5. Design a suitable phase-lag compensator. = Silicon-controlled rectifiers Motor Gears 1 Input G.(5) KR 0.2s +1 s(Js+b) FIGURE P10.8 Path-controlled turret lathe.

Answer 1

KR Input Ge(s) 0.25 + 1 s(js+b) o xn. KR 0.28t1 Transfer function Gls) - - I sejs +b) Gis) = n KR SlSj +6) (0.25 +1) Given data → n=0.2,J=10-3, 6= 2x 10-2 KR=0.59-0.7. G(s) = 510-28+1) (10-35 + 2x102) G(s) 505+5)(8 +20 - 0.2 x 5 5000 steady state posit'on accuracy = 2.5. for ramp input. ㅗ ess Kv, comp kv, comp 7. -40 0.025 [Kv comp=40 Uncompensate velocity constant: + Kv comps.ht SGS) S70

ht S'K_5000 So 818+5)(8 +20) sok Sook 5 x 20 uncomp² > 50k for (20.7 Kv. the required ratio of zero to pole of the compensator is kucomp ca. Kyuncomp k=0.0395 Kyuncomp 1.975 50X 0.0395 zero to pole ratio is, da #vcomp 40 2 20.25 do 20:25 Kv uncomp 1.975 zero location 222 p. Assume zao zero is located at oil on the left side. The pole is . I 0.0049 20.25 G (CS) = K * (***) 1-0 0.0395 3+0.) S+0.0049) Lag Compensator is Gęs)z 0.0395 S+ 0.1 sto-0049 pol 그

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