Tutorial 5 Drive dynamics & control

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1 UNIVERSITY OF NEW SOUTH WALES Electic Dive Sytem School o Electical Engineeing & Telecommunication ELEC463 Electic Dive Sytem Tutoial 5 Dive dynamic & contol. The ollowing paamete ae known o two high peomance DC moto: Moto Moto 0.75 kw, 500 /min, 40V 75kW, 750 /min, 40V R a = 7.56 Ω R a = 0.04 Ω L a =0.055 H L a = 0.00H K E = 4.3V/ad/ K E =.7V/ad/ J m = 0.068kgm J m =.8kgm Aume that the DC upply line have eitance and inductance which ae equal to thoe o the moto. Alo aume that the load inetia eeed to the moto hat i equal to the moto inetia. The toque-peed chaacteitic o the load i a taight line though the oigin and the ated load point. Neglect the ational loe in the moto. Compae the un-damped natual equencie ω n, the damping atio ξ and the time contant T a (o τ a ) and T m (o τ m ) o the two moto. [An: Moto : ω n = 38. ad/, ξ =.8, τ a = , τ m = 0.5 ; Moto : ω n = 4.6 ad/, ξ = 0.396, τ a = , τ m = 0.065]. Fo a DC moto with negligible ictional and othe load toque, expe the peed-amatue () / KE voltage tane unction G(), in the ollowing om: G() V() a ( ) (i) Calculate ξ and ω n o the moto with the ollowing paamete: T ated = 0Nm, ω ated = 3700/min, K T = 0.5Nm/A, K E = 53V/k/min, R a = 0.37 Ω and τ a = 4.05m, τ m =.7m. (ii) Plot the magnitude and phae o G () in Bode plot. [An: ω n = 45. ad/, ξ = 0.85] n n Tutoial 5 Contolle deign o dive

2 Electic Dive Sytem 3. A poition contol ytem i indicated in Fig.. A techo-geneato i ued to povide o damping though an inne peed loop. The moto toque i aumed to be popotional to the moto cuent i a. The eo ampliie gain K c i 0 and the powe convete gain (G) i 5. The moto toque i Nm/A. The moto and load paamete ae: J T =.0 kg-m eeed to the moto D = 0.09 Nm/ad/ eeed to the moto T L = 3 Nm at the load The gea atio N = 0. Fig. (i) Calculate the equied techo-geneato voltage contant (K g ) in ode to have a citically damped poition epone. [Hint o citically damped ytem ξ=]. (ii) Calculate the poition ollowing eo when the taget poition eeence move at 70 ad/ eeed to the moto hat. [An : K g = V/ad/ at moto hat eo = 8.8 ad] 4. Conide the cuent contolled ytem o igue, in which the convete output i 00 V at maximum (the ated voltage o the machine). The maximum cuent allowed in the machine i 0A which i twice the continuou cuent ating o the machine. The DC moto paamete ae: R a =, L a = 30mH, and K E = 0. V/ev/min. Calculate the maximum poible cuent contol bandwidth o the dive. Aume that at maximum bandwidth, the cuent i jut able to each the peak value o 0A in the talled condition. Comment on the maximum bandwidth i the convete output voltage i highe o lowe than 00V. * i a i a Figue Tutoial 5 Contolle deign o dive

3 5. A DC moto dive ha the ollowing paamete: Electic Dive Sytem R a = 0.5; L a = 5mH; V aated = 60V. The witching equency o the convete i 600Hz. The convete output voltage i 60V o contol input o 0V. Deign a PI cuent contolle (i.e., toque contolle) with a bandwidth o 50Hz. 6. The DC moto o Quetion 4 ha total inetia J T (eeed to moto hat) = 9.55 m. The total vicou iction i negligible. The dive include a cuent contolle o 50 Hz bandwidth. Deign a PI peed contolle o the dive to achieve peed contol bandwidth o Hz. 7. The geneal tanomation matix o thee-phae voltage, cuent and luxe in the otating dq-axe i given by co co co d a q in in in b 3 o c i the intantaneou angula diplacement o the otating d-axi o the ictitiou dq winding om the axi o phae MMF o a. (a) Given that the upply voltage to the tato ae an bn cn v 30 in t v 30 in t 0 v 30 in t 40 V whee 50 i the equency o the tato upply voltage. Calculate v d and v q o 0 and t 0. Plot thee on a phao diagam. (b) Given that cuent to the tato winding ae an bn cn i 0 in t 0 i 0 in t 00 i 0 in t 040 A Calculate i d and i q o 0 and t 0. Plot thee on a phao diagam. Tutoial 5 Contolle deign o dive 3

4 Electic Dive Sytem 8. A 4-pole, 45V, 50Hz, Y-connected NSP ynchonou moto develop back em o 00V (pe-phae, RMS), when opeating at ynchonou peed. (a) Calculate the tato lux linkage due to oto excitation. The developed toque and tato lux linkage o uch a moto unde oto lux oiented contol, in which the dq vaiable ae expeed in the oto eeence ame, ae given by T 3p iq Nm and d Li d d epectively. (b) (c) (d) Calculate the tato cuent eeence i d in the otato eeence ame, o that the tato lux linkage d along the oto d-axi emain contant at. Calculate the tato cuent eeence o i q in the otating eeence ame i the moto i to develop 0 Nm o toque. Sketch the toque and lux-linkage contol cheme in which the tato lux-linkage mut be maintained at. 9. The paamete o a 45V, 50Hz, 4-pole, Y-connected quiel-cage IM ae: R = 3.57 ; R 3.39 ; L = L = mh; L m = mh; Stato I ated = 5.08 A (RMS); The maximum allowed tato cuent = I ated. The lip, developed toque and oto lux linkage o uch a moto unde indiect oto lux oiented contol (without ield weakening), in which the dq vaiable ae expeed in the oto eeence ame, ae given by m l e e q d L L R i T dev 3P Lm i L d q L R d dt d d Li m d (a) Calculate the ated oto lux linkage and tato cuent eeence o i d. (b) Calculate the tato cuent eeence o i q i the moto i to develop 0 Nm o toque. (c) Calculate the maximum developed toque unde ated oto lux linkage. (d) Complete the ollowing block diagam o RFOC IM dive o the condition o (b). Tutoial 5 Contolle deign o dive 4

5 Electic Dive Sytem Tutoial 5 Contolle deign o dive 5

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