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The speed of a separately excited DC motor can be controlled from below and up to rated speed using DC chopper as a converter. The DC chopper firing circuit receives signals from speed controller and then DC chopper gives variable output voltage to the armature of the separately excited DC motor for achieving desired speed. There are two control loops, one for controlling armature current and second for controlling speed. The controllers are used Proportion-Integral (PI) type which removes the delay and provide fast speed response. The mathematical modeling of separately excited DC motor is done. The mathematical model of closed loop speed control of separately excited DC motor using dc chopper is obtained. The optimization of speed controller transfer function is done using modulus hugging approach, in order to get stable and fast response of the closed loop system. By this approach gain of the closed loop system becomes unity. The stability of overall transfer function of closed loop system is checked by Routh-Hurwitz criteria and Bode plot, before and after designing of speed controller using modulus hugging approach.