A high-speed train is under development in Texas [21] with a design based on the French Train a Grande Vitesse (TGV). Train speeds of 186 miles per hour are foreseen. To achieve these speeds on tight curves, the train may use independent axles combined with the ability to tilt the train. Hydraulic cylinders connecting the passenger compartments to their wheeled bogies allow the train to lean into curves like a motorcycle. A pendulum like device on the leading bogie of each car senses when it is entering a curve and feeds this information to the hydraulic system. Tilting does not make the train safer, but it does make passengers more comfortable.
Consider the tilt control shown in Figure DP10.4. Design a compensator Gc(s) for a step input command so that the overshoot is less than 5% and the settling time (with a 2% criterion) less than
0.6 second. We also desire that the steady-state error for a velocity (ramp) input be less than 0.15A, where r(t) = At.t > 0. Verify the results for the design.