**Introduction**

Direct-current motors are extensively used in variable-speed drives and position-control systems where good dynamic response and steady-state performance are required.

For example in application of robotic drives, printers, machine tools, process rolling mills, paper and textile industries, and many others. Control of a dc motor, especially of the separately excited type, is very straightforward, mainly because of the incorporation of the commutator within the motor.

The commutator brush allows the motor-developed torque to be proportional to the armature current if the field current is held constant. Classical control theories are then easily applied to the design of the torque and other control loops of a drive system.

**Advantage of D.C. Drive**

• Wide speed range

• High starting torque

• Very precise speed control

• Reliability and simple control

• Lower cost

**Characteristic of D.C. Motor **

.................... (5.1)

**Separately Excited or Shunt D.C. Motor**

**(a) Separately excited** **(b) Series**

** Fig 5.1 Speed-Torque characteristics of dc motor with resistance control**

**Series D.C. Motor**

**D.C. Motor Starting**

A separately excited DC motor started by an armature rheostat is shown in the figure. The field current is kept at rated value of 1.6 Amp in this case. The rated armature current is 10 A.

Normally the armature current Ia = (Vdc-Eb) / (Ra+Rext)

Where Eb is the back emf and Vdc is the applied armature voltage. When initially the motor is started, the back emf is zero because the speed is zero and hence the armature current,

Ia = Vdc/ (Ra +Rext)

Where, Ra is the armature resistance.

Torque developed by the motor Te = KфIa

Where, K = Back emf constant of the motor

Ф = main flux of the motor

Ia = Armature current

The back emf developed by the motor at any speed of ω rad/sec is

Eb = Kфω

The power output is the product of Eb and Ia.

Initially the current will be very large if no external resistance is included due to the back emf being zero. So, the motor starter generally consists of a large resistance in series with the armature circuit which is cut down slowly as the motor picks up speed. This is being emulated in this experiment with the help of a series rheostat Rext.

**Circuit diagram**

**Fig.5.2 Starting Arrangement for a DC Motor**

The initial current drawn Ia allows a finite value of electromagnetic torque to be developed depending upon the field current supplied. This torque allows the acceleration of the motor from zero speed provided this Te is greater than the load torque TL. The acceleration (dω/dt) follows the equation

J(dω/dt) =Te-TL

Where, J = moment of inertia of the motor.

The transients in the current, the build-up of back emf and speed can be observed in this experiment at varying values of Rext and load torque as well as Vdc.

As the load torque is increased the steady state speed at which the motor works will get reduced according to the equation

Eb = Kфω = Vdc- IaRa

ω = (Vdc/Kф) – TeRa/(Kф)2

Thus speed decreases as Torque demand is increased at constant applied voltage and flux.

The following are typical plots of the armature current, electromagnetic torque and speed of the motor at the rheostat position of 0.5 (only 50% voltage applied).

**Speed Control**

According to Eq. (5.1), speed can be controlled by any of the following methods:

i. Armature voltage control

ii. Field flux control

iii. Armature resistance control

For speed control below base speed the armature voltage control is employed and for above base speed field flux control is used.

In armature resistance control, speed is varied by adding an external resistance (Rext) in series with the armature. Since the energy was wasted in resistor, it is an inefficient method of speed control and used only in intermittent load applications where the duration of low speed operation forms only a small proportion of total running time (Eg. traction application).

Fig 5.1 shows the speed – torque characteristics of a dc separately and series motor with external resistance control.

**Electric Braking**

Electric Braking of DC motor can be done by three methods

i. Regenerative braking if the speed exceeds no-load value or when TL=0

ii. Dynamic braking or rheostatic braking by including an external resistance across the armature in place of DC supply

iii. Plugging or reverse current braking by connecting the power supply Vdc in reversed mode.

The first method allows the mechanical energy stored in the rotor to be fed back to the battery by converting the kinetic energy into electrical energy. The second method, though, makes the machine work as a generator but it dissipates the power in the external resistance connected. The third method draws extra power from the external power supply and wastes both- energy drawn from the power supply as well as the kinetic energy stored in the rotor. The last two methods can be used for stopping the motor whereas the first one can bring it up to no-load speed which is (Vdc/Kф).

The circuit for simulation of the latter two methods is shown below:

**Dynamic Braking (Rheostatic Braking)**

In this braking method armature terminal disconnect from supply & connect to high value of resistance. When it is disconnected from the supply with field supply is remains on, the dc machine will acts as a generator and converts kinetic energy stored in its moving parts to electrical energy, which is dissipated as heat in the dynamic brake resistance RD and armature resistance Ra. For good rate of retardation the RD should be variable. This method of braking is called rheostatic braking.

since V=0,

Ia=-Eb/ (Ra+Rb)

& torque (T) = -KØ Ia

Negative sign shows that the armature current is reversed.

**Fig. 5.3 Dynamic braking in separately excited DC motor.**

**Fig 5.4. Speed-Torque characteristics of separately excited DC motor.**

**Fig 5.5 Dynamic Braking Speed-Torque characteristics of **

separately excited DC motor with variable RD

The first one is for dynamic braking. Initially the motor is allowed to accelerate normally. The supply is connected to the motor with the help of a MOSFET that is kept ON for the initial 1.25 sec. After this duration, the power supply Vdc is disconnected and in its place, a resistance of 10 ohms is connected with the help of another MOSFET. When the motor speed and current are observed, both can be seen to increase in the positive direction initially; After 1.25 sec, speed starts falling and current flows in the reverse direction, indicating braking operation.

**Fig. 5.6. Dynamic Braking of DC Motor**

A typical response for the dynamic braking of DC motors in terms of its armature current, speed, electromagnetic torque and terminal voltage are shown below:

**Reverse current braking or plugging**

Reverse the motor terminal. Speed torque is negative direction means reverse motoring operation.

**Fig. 5.7. Plugging of Separately excited DC motor.**

**Fig 5.8. Plugging speed –torque curves DC separately excited motor**

**Fig. 5.9 Plugging of DC motor.**

The method of plugging is implemented as follows: Initially the motor is accelerated for 1.25 sec. The rate at which the machine accelerates depends upon V_{dc}, R_{ext}, and load torque on the motor. After this, the source is connected with its polarity reversed so that the current starts flowing in the opposite direction and braking torque is developed.

A typical response for plugging is shown below in terms of I_{a}, Speed, T_{em} and V_{a}.