Mixed H₂/H_∞ cruise controller design for high speed train

A cruise controller for two typical traction types of high speed train (HST), the push-pull driving (PPD) type and the distributed driving (DD) type, are designed using a mixed H₂/H_∞ approach in this paper. The dynamics of a high speed train are modelled by a cascade of cars which are connected with flexible couplers and are subject to rolling mechanical resistance, aerodynamic drag and wind gust. A mixed H₂/H_∞ controller is synthesized via linear matrix inequalities to satisfy a mixed design objective of speed command tracking (measured by H₂ norm) and gust attenuation (measured by H_∞ norm). Performance of the proposed cruise controller is verified by non-linear simulation wherein two types of HST under three different control approaches, namely H₂, H_∞ and H₂/H_∞, are compared in the aspects of gust attenuation, command tracking, control effort and oscillation of flexible connection. The simulation results show that the H₂ controller has the best command tracking performance and the H_∞ controller has the best gust attenuation performance, while the mixed H₂/H_∞ controller has excellent flexibility in trade-off between the other two conflicting objectives.