Train travel between cities will increase as trains are developed that travel at high speeds, making the travel time from city center to city center equivalent to airline travel time. The Japanese National Railway has a train called the Bullet Express that travels between Tokyo and Osaka on the Tokaido line. This train travels the 320 miles in 3 hours and 10 minutes, an average speed of 101 mph [17]. This speed will be increased as new systems are used, such as magnetically levitated systems to float vehicles above an aluminum guide way. To maintain a desired speed, a speed control system is proposed that yields a zero steady-state error to a ramp input. A third-order system is sufficient. Determine the optimum system transfer function T(s) for an ITAE performance criterion. Estimate the settling time (with a 2% criterion) and overshoot for a step input when ωn = 10.