Duty cycle calculation
When you go from 15V to 5V, you get \${5 \over 15} = {1 \over 3}\$ of the original speed.
What you actually want \${400 \over 2000} = {1 \over 5}\$ of the original speed, so you will somehow have to reduce the speed further by &quot;PWM-ing your way&quot; from \$1 \over 3\$ to \$1 \over 5\$ of the original speed. So:
\${1 \over 3} \times dutycycle = {1 \over 5} \implies dutycycle = {3 \over 5} = 60\%\$
Going from 15V to 5V has reduced the speed to \${2000 \over 3} \mathrm{\, rad/s}\$, reducing the speed further to 60% of that gives \$60\% \times {2000 \over 3} = 400 \mathrm{\, rad/s}.\$