**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, TI The back emf developed by the motor is E

_{m}= K_{m }Φ_{a}.

_{b}= K_{b}Φ ω_{m.. }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) / V

_{a}(s) = K_{m }/ [s (1+sτ_{a})(1+sτ_{m}) + (K_{b}K_{t}/R_{a}B)]where

Motor gain constant, K

_{m }= (K_{t}/R_{a}B) Motor torque constant, K

_{t }= T / I_{a}_{ }Torque, T in Nm = 9.55 E

_{b}I

_{a}

Back emf, E

_{b}in volts = V_{a}– I_{a}R_{a} V

_{a}= Excitation voltage in volts Back emf constant, K

_{b}= V_{a}/ ω Angular velocity w in rad/ sec = 2πN / 60

Armature time constant, τ

_{a }= L_{a }/ R_{a}_{ }Armature Inductance, L

_{a}in H= X

_{La}/ 2pf

X

_{La}in W =Ö(Z_{a}^{2}– Ra^{2})**Z**

_{a}in W = V

_{a2}/ I

_{a2}

Armature resistance,R

_{a}in W = V_{a1}/ I_{a1} Mechanical time constant, τ

_{m }= J / BMoment of inertia, J in Kg m

^{2}/ rad =__W x (60 / 2____p )__^{2}x dt/dN N

Stray loss, W in Watts = W’ x [ t2 / (t1-t2) ]

Power absorbed, W’ in watts = V

_{a}I_{a} 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 ( I

_{a}+ I_{f }) Copper loss = I

_{a}^{2 }R_{a}_{ }N is rated speed in rpm

**PROCEDURE:**

**1. To determine the motor torque constant K**

_{t }and Back emf constant K_{b}:- 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 I
_{a}, armature voltage V_{a}, and speed N. - Find the motor torque constant K
_{t }and Back emf constant K_{b}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,V_{a}(V) | Armature Current,I_{a}(A) | Speed,N(rpm) |

| | | |

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