Question

Figure Q1(b) shows the simplified diagram of the armature controlled D.C. b) servomotors used in instruments and employed a fixed permane nt magnet field. The control signal is app lied to the amature terminals. The inductance of armature winding is negligible. Obtain the transfer function of the servo mot or (assume K, K, and K, are constant) i) (10marks) Derive a state spa ce model for the servomotor (armature resistance is 0.2) (5marks) i) La Fixed field (if) Ra ww00 Ceq J ea ев(Т ia Figure Q1(b) The amature resistance () The amature inductance (H) The armature current (A) The field aurrent (A) The applied armature voltage (V) The back emf (V) Angular displacement of motor shaft, in radians L i, e T The torque delivered by motor, in newton-meter (N-m) Equivalent moment of inertia of motor and load refered to motor shaft (kg-m2) Equivalent viscous-friction coefficient of the motor and load refeed to motor shaft Cea (N-m/rad/s) Field current constant K Electromagnetic force constant of the motor Motor torque constant Кр Kt

Answer 1

Transter funchion ot ATmalure ontrolled DC motor V Armalare Voltage AImelure Guyren La Amdlive induchan ce Vb Ras Armalinre Resistance V aL inerhia g-m rad J moment of Frichon tdque T - En back emt in v IcT Taqne Constant Ch Back emt Consrant v/adl sec) This system hay N-mIA Sustems ele cl-n tel Sstem 2 v mechani Cad 54stem 4item electrical mechanicel stem Eb applzy loep Analysis Vas iaRa La dia Eh de applz tepla ce anstorm bolBsides apply leplace transtorm Va)=Ra Ta las Ta+ E) TO) +Bs 0U T) veS)=Tas) Ratsla) E) O 4 TU)-G s) U) (y Constant T8que Ia Na Eb T d La ( Constoant) NO Eb Eb do dh cPphu Leplace Hanstorm EbKh d appl2 leplace transtorm ein KEIaSJ B1)0 ) Tau)= (tBJ) pu) eq in eq D V()Tas) (Ratsla) t KhsOG e g in eq (JS+BS)(Ratsla) e0) tes eu Va) (TsB (Rat s la) +Kbr Transter tunchion TE 0s) (Js+B)(RatSla) t Kl

3) Determine the stata Model of armature contrelkd oCMolor AN The speed of De MoGr il directy progor trinas t armalare Voltage and invenly Proportainal flur In amalire cantrled Dc Molsr the detired peed obtained b hanw cont the amatire voltage. thi jeed cantrol yten $ytem. The electrical (yrtem contib of the amalire and the feld tircuit but for onalys puipole, only the armatire ciicuit h contidered be couie the field crcilid by a convtant voltage The Mechanical ythem conwit of the rotaling tort of the molsr and toad connectid t the shaft of the Mobr is an electro mecha Load Yg in put J,B elautput)

Leb la-Armature renitanee, n La-Armalure indutance, H ia Armalüre cunent,A Va Armalure Voltage V Bact emf i KE = Torque contant, N-m/A T 1omue develop ed by Mols, M-m - Angular diplacement of thaft, rad s- deldt 3 Moment of inertra of M.ir and toad N-m/radhee Kace emf convont, vfad lie) Angulas vetocily of the shott, radliee Ro La AIply kvi t the cirtuit m + o Ra tha diaes Va0 Va dt Torgueit)pin 1to 1- Kt ia The differenlial equation ova ning Hhe mechanical ytem of Molar +tp The bock cmof DC Machine i proportional As specd (angular velocity) of tha t d1-

Cdo -1P Cb-kyde Subiti e e in e0 ialo tLadia+k de Va P Subctlal Tin eg d+6deKla

eq& eg are the differcnti equation 1ovening Controlled DC Mol Lct u tabe stall vaviable the arma u-Va 3P de dP dev FYom eqo u-xi Rat La, k6 Ra TI La La La FYom c Kt, 3d +41p ktJ , 71 Diftere nliali bo th des wr.s t do dz3 dt Ra LA elr eqdation I2w-de Ya=9-79