P5.12 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 Shinkansen train that travels an average speed of 320 km/hr [17]. 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 trans

fer function T s( ) for an ITAE performance criterion.

Estimate the settling time (with a 2% criterion) and percent overshoot for a step input when ωn = 10.