Question

1. Consider a schematic diagram of the permanent magnet brushed DC motor used in Quanser system with two inertia loads (Jh and J4) and no viscous damping as shown in Fig. 2-1.. Since there is no gear system, motor shaft angular position and velocity, 0m, and wm, respectively, are equal to disc load angular position and velocity 0, and w, respectively. Derive electrical and mechanical differential equations describing this DC motor dynamics, as well as the relationship between motor torque T,m and motor current Im (5 Marks) Lm Rm 000 WWo Тm Ө, Ф Өт, От Ja Im Jh т V — Кьот Vm +

Answer 1

Fom the given data Arply KVL fy AYmatune 0p ofgiven mr Nb gy dt K iv cohere elechica diffeuniaeqpmatabrg Jer Om= Jey KmTm TorqMe,T Jegws TmJeqaS whene mechawi cal differantiol eg atio m Jeys Tm Km whene Je dation butween Tme Tm Apphy nplae tranrm (Rmt 52m) Vm5K wa) = Jey a) K t JeySRm+ slm) Km Ky KntTea/ SR Jeq S2m Km

Km Jey Lm Jeq S Rm + Kb Km Kym Je, L + Jeg, Rm S + Kb Km trque Constamt where to bal nrkia Cu(S) Km SJe L Teq Rm S+ Km Kb) Applied Itage) Anmatue Cumut (A) Motor torq r Contant (11- in] Km mtr windang Bnductamce (H mat resvafam ca ) Ln Ra o tor valocity rad (se c) A darotrma (pec) (Agular peuihian) rad