Problem: Design DC. motor speed control circuit that is used to
control the speed of direct current.

Control the SPEED of direct current??? Other than using wire of
different velocity factor or doping the conductor, I cannot think of
many ways you can do this! You can certainly make the motor
speed change (what's new with that idea?? PWM has been around
for half a century or more...), but ya'll ain't gonna do much about
the speed of electrons in a wire to any meaningful degree. And why
would you want to?? Electrons seem to work just fine at the speeds
they achieve in wire - so why not just leave them alone?

Dave