Robust observer-based adaptive backstepping levitation control for maglev trains with stochastic time delay and disturbance

Electromagnetic levitation system (EMLS) plays a crucial role in ensuring the safety and riding comfort of maglev trains. As operating speeds increase and systems undergo long-term service, EMLS is required to exhibit robust performance subject to external disturbances and input delay, and a composite levitation control strategy for the vehicle-magnetic coupled system is proposed in this paper. The mathematical model of EMLS is analyzed at first. To eliminate the impact of time delay on dynamic response, the Padé approximation is utilized to convert the original time-delay system into an equivalent delay-free formulation. An adaptive disturbance observer is then designed to estimate stochastic disturbances and provide feedforward compensation. In this way, the robust adaptive controller via backstepping technique is formulated to regulate the levitation gap between the carriage and the track. The asymptotic stability of the closed-loop system is rigorously proved by constructing appropriate Lyapunov functions. A parameter tuning guideline based on the Multiple Population Genetic Algorithm is integrated to enhance control accuracy and minimize steady-state tracking errors. Numerical simulations and experiments are conducted to validate the effectiveness and feasibility of the proposed control approach.