New passenger rail systems that could profitably compete with air travel are under development. Two of these systems, the French TGV and the Japanese Shinkansen, reach speeds of 160 mph [17]. The Transrapid, a magnetic levitation train, is shown in Figure E5.3(a).
The use of magnetic levitation and electromagnetic propulsion to provide contactless vehicle movement makes the Transrapid technology radically different. The underside of the carriage (where the wheel trucks would be on a conventional car) wraps around a guideway. Magnets on the bottom of the guide way attract electromagnets on the "wraparound," pulling it up toward the guide way. This suspends the vehicles about one centimeter above the guide way.
The levitation control is represented by Figure E5.3(b).
(a) Using Table 5.6 for a step input, select K so that the system provides an optimum ITAE response.
(b) Using Figure 5.8, determine the expected overshoot to a step input of I(s).

Table 5.6
The Optimum Coefficients of T(s) Based on the ITAE Criterion for a Step Input

Transcribed Image Text:

Gap dynamics (s) Coil cuTent s 34) spacing FIGURE E5.3 Levitated train control. s* + 2.1 ans. 3.400,2 + 2.7ωί;s + cut