**Chopper Control of Separately Excited DC Motor:**

**Motoring Control :** A transistor Chopper Control of Separately Excited DC Motor drive is shown in Fig. 5.41(a). Transistor T_{r} is operated periodically with period T and remains on for a duration t_{on}. Present day choppers operate at a frequency which is high enough to ensure continuous conduction. Waveforms of motor terminal voltage v_{a} and armature current i_{a} for continuous conduction are shown in Fig. 5.41(b). During on-period of the transistor, 0 ≤ t ≤ t_{on}, the motor terminal voltage is V.

The operation is described by

In this interval, armature current increases from i_{al} to i_{a2}. Since motor is connected to the source during this interval, it is called **D****uty Interval**.

At t = t_{on}, T_{r} is turned-off. Motor current freewheels through diode D_{F} and motor terminal voltage is zero during interval t_{on} ≤ t ≤ T. Motor operation during this interval, known as freewheeling interval, is described by

Motor current decreases from i_{a2} to i_{a1 }during this interval.

Ratio of duty interval t_{on} to chopper period T is called **duty ratio or duty cycle** (δ). Thus

From Fig. 5.41(b)

Equation (5.2) and (5.7) are also applicable here

From Eqs. (5.7), (5.8). and (5.114)

The nature of speed torque characteristic is shown in Fig. 5.43.

**Regenerative Braking:**

Chopper Control of Separately Excited DC Motor for regenerative braking operation is shown in Fig. 5.42(a). Transistor T_{r} is operated periodically with a period T and on-period of t_{on}. Waveforms of motor terminal voltage v_{a} and armature current i_{a} for continuous conduction are shown in Fig. 5.42(b). Usually an external inductance is added to increase the value of L_{a}. When T_{r} is on, i_{a} increase from i_{a1} to i_{a2}.

The mechanical energy converted into electrical by the motor, now working as a generator, partly increases the stored magnetic energy in armature circuit inductance and remainder is dissipated in armature resistance and transistor. When T_{r} is turned off, armature current flows through diode D and source V, and reduces from i_{a2} to i_{a1}. The stored electromagnetic energy and energy supplied by machine is fed to the source. The interval 0 ≤ t ≤ t_{on} is now called **energy storage interval** and interval t_{on} ≤ t ≤ T **the duty interval**. If δ is again defined as the ratio of duty interval to period T, then

From Fig. 5.42(b)

and from Fig. 5.42(a)

Since l_{a} has reversed

From Eqs. (5.8), (5.118) and (5.119)

The nature of speed torque characteristic is shown in Fig. 5.43.

**Motoring and Regenerative Braking:**

Chopper circuits of Figs. 5.41 and 5.42 can be combined to get a two quadrant chopper of Fig. 5.44, which can provide motoring and regenerative braking operations in the forward direction. Transistor T_{rl} with diode D_{1} form a chopper circuit similar to that of Fig. 5.41, and therefore, provide control for forward motoring operation. Transistor T_{r2} with diode D_{2} form a chopper circuit similar to that of Fig. 5.42, and therefore, provide control for forward regenerative braking operation. Thus, for motoring operation transistor T_{rl} is controlled and for braking operation transistor T_{r2} is controlled. Shifting of control from T_{rl} to T_{r2} shifts operation from motoring to braking and vice versa.

In servo drives where fast transition from motoring to braking and vice versa is required, both T_{rl} and T_{r2} are controlled simultaneously. In a period T,T_{rl} is given gate drive from 0 to δT and T_{r2} is given gate drive from δT to T, where δ is the duty ratio for T_{rl}. Therefore, from 0 to δT motor is connected to source either through T_{rl} or D_{2} depending on whether the motor current i_{a} is positive or negative. Since V > E, during this period the rate of change of current is always positive. Similarly from δT to T, motor armature is shorted either through D_{1} or T_{r2} depending on whether i_{a} is positive or negative and during this period rate of change of current is always negative. Motor terminal voltage and current waveforms are shown in Fig. 5.44 (b).

From Fig. 5.44(b)

Above equation suggests that motoring operation (+ve I_{a}) takes place when δ > (E/V) and regenerative braking operation takes place when δ < (E/V) and transition from motoring to braking and vice versa occurs when δ = (E/V). The above equations are similar to those obtained for chopper of Fig. (5.41), and therefore, given the same numbers

**Dynamic Braking:**

Dynamic braking circuit and its waveforms are shown in Fig. 5.45. During the interval 0 ≤ t ≤ t_{on}, i_{a} increases from i_{a1} to i_{a2}. A part of generated energy is stored in inductance and rest is dissipated in R_{a} and T_{r}. During interval t_{on} ≤ t ≤ T, i_{a} decreases from i_{a2} to i_{a2}. The energies generated and stored in inductance are dissipated in braking resistance R_{B}, R_{a} and diode D. Transistor T_{r} controls the magnitude of energy dissipated in R_{B}, and therefore, controls its effective value.

If i_{a} is assumed to be rippleless dc, then energy consumed E_{N} by R_{B} during a cycle of chopper operation is

Average power consumed by R_{B}

Effective value of R_{B}

where

Equation (5.122) shows that the effective value of braking resistor can be changed steplessly from 0 to R_{B} as δ is controlled from 1 to 0. As the speed falls, δ can be increased steplessly to brake the motor at a constant maximum torque as shown in Fig. 5.8 by chain-dotted line.