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D-03 - current that opposes ia known as the back...

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Ea(s)    s(s+a m ) We will now proceed by deriving an expression for Km and a Let us consider schematic for an armature-controlled DC motor as shown below: Figure 1 : The Schematic for an armature-controlled DC motor The magnetic field imposes a total force on the armature circuit of F = 2Blia where B is the magnetic field strength, 2l is the total length of the  conductor that is perpendicular to the field, and ia is the current. Multiplying by  the rotor's radius r we obtain a torque, Tm = rF = r2Blia = Kt ia  ...................................................... 6 Where Kt = 2BLr is the motor torque constant. So, the current ia generates a torque. However, any conductor travelling through  a magnetic field will induce a voltage on the conductor. This voltage induces a 
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Unformatted text preview: current that opposes ia, known as the back electromotive force (emf) which is proportional to the motor speed. vb(t) = Kb d m(t) . 7 dt Where the constant Kb = Kt in a consistent set of units. In the frequency domain these two fundamental effects are expressed as follows: Tm(s) = Kt Ia(s) . . 8 Vb(s) = Kb s m(s) . . 9 Applying KVL we obtain,...
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