The equations of a permanent magnet DC machine read as follows (Laplace operator s denotes differentiation with respect to time):

Armature voltage loop    : VA - Vi = RA(1 + s TA)IA
Armature time constant   : TA = LA / RA
Induced voltage          : Vi = kΦ ω
Flux constant            : kΦ = (VA,Nom - RAIA,Nom) / ωNom
Torque                   : τ = kΦ IA
Equation of motion       : s Jtot ω = τ - τLoad
Moment of inertia        : Jtot = Jr + JLoad
Mechanical time constant : Tm = Jtotal ωNom / τNom
Position                 : s φ = ω

The inverter applies the reference voltage to the machine, but normally we have to take a dead time into account. The inverter's dead time is approximated by a first order block with time constant = dead time Td.

The example VoltageSupplied applies a step voltage to the machine at stand still, the load torque is linearly dependent on speed.

Speed will rise up to that point of operation, where the difference between armature voltage and induced voltage drives an armature current which causes a torque that is in balance with the load torque at that speed.

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