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Block Diagram and Transfer Function of DC Motor
Mechanical Engineering (Mee401)
Bells University of Technology
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Block Diagram and Transfer Function of DC Motor Armature Controlled DC Motor
Consider the armature controlled dc motor and assume that the demagnetizing effect of armature reaction is neglected, magnetic circuit is assumed linear and field voltage is constant i. if=constant Let Ra=Armture resistance La=Armatureself inductancecausedbyarmatureflux ia=armaturecurrent if=fieldcurrent E=Inducedemf∈armature V=Applied voltage T=Torquedeveloped bythemotor θ=Angulardisplacement of themotorshaft J=Equivalent momentof inertiaof motorshaft∧loadreferred¿themotor B=Equivalent coefficient of frictionof motor∧loadreferred¿themotor Apply KVL in armature circuit
v=Raia+Ldidta+E (i)
Since, field current if is constant, the flux ∅ will be constant when armature is rotating, an emf is induced
E∝∅w E=kbw E=kbdtdθ (ii)
where w=angular velocity kb=back emf constant
Now, the torque T delivered by the motor will be the product of armature current and flux T∝∅ia
T=kia (iii) where k=motortorqueconstant The dynamic equation with moment of inertia and coefficient of friction will be
T=J d 2 θ dt 2 +
Bdθ dt (iv) Take the Laplace transform V(s)−E(s)=Ia(s)(Ra+S La)
E(s)=kbSθ(s)
T(s)=k Ia(s)
T(s)=(S 2 J+SB)θ(s) T(s)=(sJ+B)Sθ(s) The block diagram for each equation
θ(s) V(s)=
k Ra( 1 +sLRaa)sB( 1 +sJB)+k kbs
where RLaa=τa, time constant of armature circuit
J B=τm, mechanical time constant θ(s) V(s)=
k sRaB( 1 +sτa)( 1 +sτn)+k kbs
From the block diagram the effect of back emf is represented by the feedback signal proportional to the speed of the motor. Field Control DC Motor
- A constant current ia is fed to the armature
- Flux is proportional to the field current ∅∝if ∅=kfIf (i)
- Apply KVL to the field circuit Vf=RfIf+Lfdtd If (ii)
- Torque developed by the motor is proportional to the flux and armature current T∝∅Ia From (i)
T=kIkfIaIf T=kkfIf (iii)
where k=kIIa
Dynamic equation of torque in terms of J & B
T=J d 2 θ dt 2 +
Bdθ dt (iv) Laplace transformation of (i), (ii), & (iv) Vf(s)=RfIf(s)+S LfIf(s)
¿If(s)[Rf+sLf]
If=RVf+f(sLs)f (v) T(s)=k kfIf(s) (vi) T(s)=θ(s)[s 2 J+sB] (vii) Sub. (v) in (vi)
T(s)=k .kf+f(sLs)f
θ(s) Vf(s)=
kkf S(SJ+B)(Rf+S Lf) (viii) (viii) can also be written as θ(s) Vf(s)=
k kf RfBs[ 1 +sJB][ 1 +sLRff] θ(s) Vf(s)=
kkf RfBs[ 1 +sτm][ 1 +τf]
where τm=BJ=mechanicaltimeconstant
Block Diagram and Transfer Function of DC Motor
Course: Mechanical Engineering (Mee401)
University: Bells University of Technology
