Feedback controls are important to the improvement of dynamic performance of high-speed trains. However, designing an active control for these vehicles is a very challenging task because the control system is usually under-actuated and has to meet multiple conflicting objectives. Examples of conflicting objectives include designing a highly relative stable system while minimizing the control efforts or maximizing the capability of the system to reject external disturbances. In addition, the mathematical models of these systems are not completely controllable and observable. This paper studies multi-objective optimal design of feedback controls for a sub-system of high-speed trains, i.e. the bogie system.
The bogie system can be decomposed such that the observable and controllable components of the model are used to stabilize the internal states and therefore the overall system. A linear mathematical model of the system is used in the design. The controllable and the observable states of the model are separated to form a state-feedback control to drive the internal modes and the whole system to stability. A multi-objective genetic algorithm is used to search for the feedback control gains to optimize three objectives: the Frobenius norm of the control law, relative stability and the disturbance rejection. The solutions of the multi-objective optimization provide various trade-offs among the objectives. Numerical simulations show that the proposed control designs can stabilize the system even at a high critical speed of 500 km/h.