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Power Control
A chopper converts fixed de input voltage to a controllable dc output voltage. It is the single stage dc to dc conversion device. It is a high speed on/ off semiconductor switch. The control of a dc series motor. When the chopper is ON ( this is ON period it means chopper switch is closed) for the period Ton output voltage Vo ( which is then applied to dc series motor) is equal to source voltages.
Vs in this period the inductance of armature winding will store the energy. When the chopper is OFF for period Toff ( it means chopper switch is Opened) output voltage will be zero but armature current will be flowing through freewheeling diode FD series fields and armature.
Figure voltage and current waveforms of a chopper controlled dc series motor
Therefore the output voltage can be controlled by varying duty cycle α hence the speed of dc series motor can be controlled.
Partial derivatives - Transistor hybrid model: The partial derivatives are taken by keeping the collector voltage or base current constant as pointed out by the subscript atta
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