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We want to introduce a new and effective method to find the maximum value and minimum value of a function in this paper. The proposed method is very short in calculation and easy compared with existing methods. The proposed method is illustrated by t
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EXP-5. TRANSFER FUNCTION OF A PMDC MOTOR Date Batch
Aim To find the transfer function of a Permanent Magnet DC Motor.
Apparatus
Student name Signature
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Diagram
+ e b
e b = K b ω
Te= K b ia V = Applied voltage across the motor terminals. Ia = Current through through the motor. R a = Armature resistance. La = Armature inductance.
e b
= Back emf developed.
Te = Electromagnetic torque developed.
(1)
(2) (3) (4)
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Tl = load torque. K b = back emf constant.
Procedure Finding armature resistance (Ra) •
• •
When the rotor is blocked from rotation (at zero rpm) as per (2) back emf b ecomes zero. Apply very less amount of DC voltage to the motor under blocked rotor condition, When the current reaches steady state the effect of inductance becomes zero. Under this condition (1) becomes V = ia R a
•
Measure ia and find resistance.
Finding armature inductance (La) •
•
•
Apply a small AC voltage to the motor under blocked rotor condition. Measure current passing through the motor. The ratio of the applied voltage to this current gives impedance of the armature (Za). Za= R a + jXL From the above equation we find the value of XL. XL = 2 Π f La Where ‘f’ is the frequency of applied voltage From above equation find the the value of XL .
Finding back emf constant (Kb) •
•
•
Apply a DC voltage to the motor and motor starts to rotate. Allow the motor to reach a steady state. At the steady state inductance effect is zero. Measure current through the motor and speed of the motor. By solving (1) & (2) find the value of K b.
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Finding viscous friction coefficient (B) •
Under no-load condition apply a DC voltage to the motor and allow the motor to reach a steady state or constant speed. At this condition (3) becomes Te = B ω.
•
Measure speed and current through the motor. Calculate Te using (4) . From above equation calculate the value ‘B’.
Finding the rotor moment of inertia(J) • •
•
•
Connect the speed sensor to DSO. Apply a DC voltage to the motor. After a few seconds motor reaches the steady state speed. Observe the waveform of speed and find the time constant. Time constant = J/B From the above equation calculate ‘J’.
Tabulation Armature Resistance (Ra) Voltage(v)
Current(ia)
Ra = v/ia
Average
Armature inductance (La) Impedance (Z)
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Back emf constant(Kb) and viscous friction coefficient(B) Applied voltage
Ia
w
K b
Te
B
Average value
Rotor Moment of Inertia (J) Time constant Moment of Inertia
Finding transfer function After finding all the machine constants using (1),(2),(3),(4), find the ratio of
ω(s)/V(s).
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