Stochastic optimization of levitation control system for maglev vehicles subjected to random guideway irregularity

Abstract

The dynamic performance of maglev vehicle-bridge coupled systems subjected to random guideway irregularity, especially the levitation stability of the running vehicle subsystem, is a critical issue affecting the safe operation and the comfort riding of maglev railways. This study is devoted to stochastic optimization of the levitation control system considering the coupled vibration of maglev vehicle and bridge under the random guideway irregularity. To alleviate the computational burden in the stochastic optimization process, the explicit expressions of the critical responses of the maglev vehicle-bridge coupled systems and the sensitivities of critical responses with respect to the feedback gains of the proportional-integral-derivative (PID) levitation controller are respectively constructed in terms of the guideway irregularity by virtue of the dimension-reduced formulation capability of the explicit time-domain method (ETDM), enabling stochastic dynamic analysis and stochastic sensitivity analysis to be executed at high efficiency. The stochastic optimization problem is formulated as the minimization of the standard deviation of the air gap variation with the constraint on the standard deviation of the current variation, and the optimal values of the PID gains are searched by the gradient-based method of moving asymptotes (MMA), in which the statistical moments and moment sensitivities of the critical responses required in the optimization process are obtained by ETDM. A numerical example with a 2-degree-of-freedom maglev vehicle moving on a multi-span simply-supported bridge is used to demonstrate the efficacy of ETDM for the stochastic analysis of maglev vehicle-bridge coupled systems under guideway irregularity. An engineering example involving a 3-car maglev train traversing a multi-span simply-supported bridge is further presented to show the effectiveness of the ETDM-based approach for the stochastic optimization of large-scale engineering problems. The levitation stability of the maglev train under the action of random guideway irregularity is considerably improved with the use of optimal feedback gains.