EE2257 DETERMINATION OF TRANSFER FUNCTION OF ARMATURE CONTROLLED DC SERVO MOTOR - Computer Programming

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Monday, March 28, 2011

Determination Of Transfer Function Of
ARMATURE CONTROLLED DC Servo Motor

AIM:   To determine the transfer function of armature controlled DC servo motor.

APPARATUS / INSTRUMENTS REQUIRED:

 S. No Description Range Type Quantity 1. DC servo motor trainer kit - 1 2. DC servo motor 1 3. Rheostat 500Ω/1A 1 4. Ammeter (0-1)A MC 1 (0-100) mA MI 1 5. Voltmeter (0–300) V MC 1 (0–75) V MI 1 6. Stopwatch - 1 7. Patch cords - As  required

THEORY:
In servo applications a DC motor is required to produce rapid accelerations from standstill. Therefore the physical requirements of such a motor are low inertia and high starting torque.  Low inertia is attained with reduced armature diameter with a consequent increase in the armature length such that the desired power output is achieved.  Thus, except for minor differences in constructional features a DC servomotor is essentially an ordinary DC motor. A DC servomotor is a torque transducer which converts electrical energy into mechanical energy. It is basically a separately excited type DC motor. The torque developed on the motor shaft is directly proportional to the field flux and armature current, Tm = Km Φ Ia.  The back emf developed by the motor is Eb = Kb Φ ωm..  In an armature controlled DC Servo motor, the field winding is supplied with constant current hence the flux remains constant. Therefore these motors are also called as constant magnetic flux motors.  Armature control scheme is suitable for large size motors.

ARMATURE CONTROLLED DC SERVOMOTOR:

FORMULAE USED:

Transfer function of the armature controlled DC servomotor is given as
θ(s) / Va(s) = Km /  [s (1+sτa)(1+sτm ) + (Kb Kt /RaB)]
where

Motor gain constant, Km = (Kt/RaB)

Motor torque constant, Kt  = T / Ia
Torque, T in Nm = 9.55 Eb Ia
Back emf, Eb in volts = Va – Ia Ra
Va = Excitation voltage in volts

Back emf constant, Kb  = Va / ω

Angular velocity w in rad/ sec = 2πN / 60

Armature time constant, τa =  La / Ra

Armature Inductance, La  in H= XLa / 2pf
XLa in W =Ö(Za2 – Ra2)
Za in W = Va2 / Ia2
Armature resistance,Ra in W = Va1 / Ia1
Mechanical time constant, τm = J / B

Moment of inertia, J in Kg m2 / rad = W x (60 / 2p )2 x dt/dN
N
Stray loss, W in Watts = W’ x [ t2 / (t1-t2) ]
Power absorbed, W’ in watts = Va Ia
t2 is time taken on load in secs
t1 is time taken on no load in secs
dt is change in time on no load in secs
dN is change in speed on no load is rpm
N is rated speed in rpm

Frictional co-efficient, B in N-m / (rad / sec ) = W’’ / (2pN / 60 )2
W’’ = 30 % of Constant loss
Constant loss = No load i/p – Copper loss
No load I/P = V ( Ia + If )
Copper loss =  Ia2 Ra
N is rated speed in rpm

PROCEDURE:

1.  To determine the motor torque constant Kt and Back emf constant Kb:

• Check whether the MCB is in OFF position in the DC servomotor trainer kit
• Press the reset button to reset the over speed.
• Patch the circuit as per the patching diagram.
• Put the selection button of the trainer kit in the armature control mode.
• Check the position of the potentiometer; let it initially be in minimum position.
• Switch ON the MCB.
• Vary the pot and apply rated voltage of 220 V to the armature of the servomotor.
• Note the values of the armature current Ia, armature voltage Va, and speed N.
• Find the motor torque constant Kt and Back emf constant Kb using the above values.

Note:
If  the voltmeter and ammeter in the trainer kit is found not working external meters
of suitable range can be used.

OBSERVATIONS:

 S. No. Armature Voltage,Va(V) Armature Current,Ia(A) Speed,N(rpm)