__Speed Control of DC motor by varying__

__Armature and Field resistance.__

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**Introduction**

We know that the speed of shunt motor is given by.

Where, *Va *is the voltage applied across the armature and φ is the flux per pole and is proportional to the field current *If.*. As explained earlier, armature current *Ia *is decided by the mechanical load present on the shaft. Therefore, by varying *Va *and *If *we can vary *n*. For fixed supply voltage and the motor connected as shunt we can vary *Va *by controlling an external resistance connected in series with the armature. *If *of course can be varied by controlling external field resistance *Rf *connected with the field circuit. Thus for .shunt motor we have essentially two methods for controlling speed, namely by:

1. Varying armature resistance.

2. Varying field resistance.

__Speed control by varying armature resistance__

In this method a variable series resistor is put in the armature circuit. In this case the field is directly connected across the supply and therefore the flux ɸ is not affected by variation of in this case the current and hence the flux are affected by the variation of the armature circuit resistance. The voltage drop in reduces the voltage applied to the armature and therefore the speed is reduces.

The slope of the *n *vs. *I**a *or *n *vs. *T**e *characteristic can be modified by deliberately connecting external resistance *r**ext *in the armature circuit. One can get a family of speed vs. armature curves for various values of *r**ext*. From these characteristic it can be explained how speed control is achieved. Let us assume that the load torque *T**L *is constant and field current is also kept constant. Therefore, since steady state operation demands *T**e *= *T**L*, *T**e *= *k*φ too will remain constant; which means *I**a *will not change. Suppose *r**ext *= 0, then at rated load torque, operating point will be at C and motor speed will be *n*. If additional resistance *r**ext*1 is introduced in the armature circuit, new steady state operating speed will be *n*1 corresponding to the operating point D.

In this way one can get a speed of *n*2 corresponding to the operating point E, when *r**ext*2 is introduced in the armature circuit. This same load torque is supplied at various speed. Variation of the speed is smooth and speed will decrease smoothly if *r**ext *is increased. Obviously, this method is suitable for controlling speed below the *base *speed and for supplying constant rated load torque which ensures rated armature current always. Although, this method provides smooth wide range speed control (from base speed down to zero speed), has a serious draw back since energy loss takes place in the external resistance *r**ext *reducing the efficiency of the motor.

__Speed control by varying field current__

In this method field circuit resistance is varied to control the speed of a d.c shunt motor. Let us rewrite .the basic equation to understand the method.

If we vary *I**f*, flux φ will change, hence speed will vary. To change *I**f *an external resistance is connected in series with the field windings. The resistance is called the shunt field regulator .the field coil produces rated flux when no external resistance is connected and rated voltage is applied across field coil. It should be understood that we can only decrease flux from its rated value by adding external resistance. Thus the speed of the motor will rise as we decrease the field current and speed control above the *base *speed will be achieved. Speed versus armature current characteristic is shown.