**Objective:**

To study the speed control of a DC shunt motor by the following methods:

- Armature voltage control: Variations of speed with armature voltage control at constant field current.
- Field Control: Variation of speed with variation of field current at constant voltage.

**Theory: **

** Fundamental Relationship:**

** **DC motor voltage equation is given by-

V=I_{a}R_{a}+E_{b} …………………(1)

Where V= supply DC voltage in volt, I_{a} = Armature current in amp, R_{a} =Armature resistance in ohm and E_{b} is the back e.m.f or counter e.m.f. in volt.

Now, E_{b} = KØ_{f}N …………….. (2)

where Ø_{f} is the field flux/pole in wb and K=PZ/60A is constant dependent on construction of the motor.

The field flux Ø_{f} is proportional to the field current if the magnetic path is not saturated and is represented as,

Ø_{f} α I_{f} [I_{f} = Field Current] ……………… (3)

combining equation (1), (2) and (3) we get

V α I_{a}R_{a}+ KI_{f}N

N α(V-I_{a}R_{a})/I_{f} ………… (4)

From the equation (4), it is seen that the rotor speed depends on V, I_{a}, R_{a} and I_{f}. If the supply is constant the the motor speed can be controlled by controlling I_{a}, R_{a} or I_{f}.

[A] Field Control:

In field control, the applied armature voltage is maintained constant. Then the speed is represented by

N α 1/I_{f} ………………….. (5)

It is evident from the above equation that motor speed is inversely proportional to the field current. Now, I_{f} is given by

I_{f} = where R_{f} = field resistance………….. (6)

In this type of control an external variable resistance (R_{ex}) is connected with the field circuit to vary the field current.

I_{f} = V/(Ra+Rex) ……………….(7)

By increasing the field resistance the I_{f} can be decreased which in turns increases the speed according to the equation (5). The upper speed is limited by the commutator and brushes structure. The speed control below the rated speed control is not possible using this type of control. Armature voltage control is used to control the motor speed below the rated speed.

[B] Armature Resistance Control:

In this method an external variable resistance (R_{x}) is connected in series with the armature. The supply voltage is kept constant to maintain the I_{f} or field flux constant. So the equation (4) can be written as

N α V-I_{a}(R_{a}+R_{x})………………(4)

It can be seen from the above equation that the motor speed will be decreased from the value rated to zero value by varying the R_{x} from zero to infinity. This type of control can only be used for speed control below the rated speed.

**Circuit Diagram:**

** Apparatus Required****:**

**DEVICE UNDER TEST:**

- DC motor

**Procedure:**

- The circuit is connected as shown in the circuit diagram.
- The DC supply is switched on with minimum resistance in the field circuit and maximum value of R
_{1}in the armature circuit. - The field current is adjusted to normal value corresponding to the normal speed.
- Keeping field current constant, the voltage across the armature is changed by changing R
_{1}in 5 steps. The armature voltage, speed and field currents are noted in Table-1 for each step. - The voltage across the armature is kept at rated value.
- Keeping armature voltage constant, the field current of the motor is decreased in 5 steps with the help of rheostat R
_{2}. The armature voltage, speed and field currents are noted in Table-II for each step.

**Experimental Data:**

**TABLE-1**

** ****TABLE-II**

** ****Precaution:**

- The current, voltage and speed are noted when values settle to a steady value.
- Voltage across armature should not be applied without applying voltage to the field winding of a D.C. motor.
- All connections are tightly connected.
- The speed of the machine should not exceed 125% of the rated value.
- The supply is switched off after experiment is over.

**Graphs:**

- The graph of Speed vs. Armature voltage with field current constant is plotted on a graph paper.
- The graph of Speed vs. Field current with armature voltage constant is plotted on a graph paper.
- The graph of Speed vs. Armature current with armature voltage constant is plotted on a graph paper.

**Conclusion:**