Prévia do material em texto
Problem 6.58PP Consider a unity-feedback system with G (s) = 1 s (i/20 + 1) (i2/1002 + O.Sj /100 + 1) ■ (a) A lead compensator is introduced with a = 1/5 and a zero at 1/T = 20. How must the gain be changed to obtain crossover at cue = 31.6 rad/sec, and what is the resulting value of Kv7 (b) With the lead compensator in place, what is the required value of K for a lag compensator that will readjust the gain to a /Cv value of 100? fcl Place the, Dole of tfie laa comoensator at 3.16 rad/sec. and determine the zero location that (c) Place the pole of the lag compensator at 3.16 rad/sec, and determine the zero location that will maintain the crossover frequency at ojc = 31.6 rad/sec. Plot the compensated frequency response on the same graph. (d) Determine the PM of the compensated design. Step-by-step solution step 1 of 5 G(s)=- f -5— +l l UOO 100 ) Step 2 of 5 K(0.05s+1) (O.Ols+l) At Ĝ —31.6, Gain —29.6dB -201og K=-29.6 => |K=30.2| K y = K = 30 .2 Step 3 of 5 b. K=Ky KforLag = 100 _ 30.2' Step 4 of 5 c. pole=3.16 rad/sec To maintam