Question

A computer uses a printer as a fast output device. We desire to maintain accurate position control while moving the paper rapidly though the printer. Consider a system with unity feedback and a transfer function for motor and amplifier of 0.15 G(S) Design a lead network compensator so that the system bandwidth is 0.75 rad/s and the phase margin is 30. Use a lead network with a 0.

Answer 1

Solurtion The gWen txansfer 혹unctionis G(s) 015 -O we Know that, lead compenSator is os follows G(s)- ItaT calculate the forwad Tls Now, Substitute the ea 04 ー② in abo ve then leed Let us aSSume that e to, then From equodion O → The aan crossover frequency is given o15

The nagnitude is 7'ven as, D15 Nlouw eaua te the akoke equa tion, we get then o-15 Nou, 0495 4995 0-1259; 125 the above Values ave h-Velues to Solue th above equation

① consider the real positie value. Ws 01259, then the cross ovey trnuencyis we 0.1259 Yoalsec Dd ermine ttu phase of di(jw) し6Gw') is given as: → ket us consider W-NC, in phase of w' Substitute b then he ae t L Ge(175)-(a 04) hiwe)129.9 phase masgin is aiven as Phase margin-180..(LGGwe 1 to (-12990) CS

Draw the blode plot ,fh15): 50 Madtlab code num o-15: Now lead com or i's given as CItTs canned wit amscanner

Ne Know that phole naYan ะ 5004. maximum phase leadso6 -2o) Cadd incre ment ot) then Moxinum phase lead -. The max. load comperdlotbs is aiven as ot since in-sin-246 0.198 3 0.6147드t-S883 b. 6147 1-3883

The maximun magnit ude to 101" ะเ0 1090 4427 3 539 The motinn ma gritude of lead compens.ator is -3518 CS