Linearization Decoupling Method and Control Stability Analysis of Maglev Train in Two-Dimensional Wide Domain Spaces

The electromagnetic forces exerted by a maglev train are highly nonlinear with respect to the varying currents and gaps in a two-dimensional wide domain space. As the speed of the vehicle increases, the difficulty of achieving stability in controlling the levitation gap will progressively increase to the point of impossibility. The Taylor series method is employed to decouple the electromagnetic force into the product of two separated variables, with current and gap serving as independent variables. Second, the optimal first-order approximation polynomials and Chebyshev orthogonal polynomials are employed to linearize the electromagnetic force based on the error distribution, respectively. Third, a dual-loop proportional integral derivative (PID) control model with voltage feedback for high-speed magnetic levitation vehicles is constructed based on this linearized decoupled model. The derivation of each control parameter is provided without loss of generality. In conclusion, a hybrid simulation model of a linear control system and a nonlinear magnetic field is constructed, and the control stability of the vehicle is analyzed using the German low interference track, which was used in the Shanghai Maglev commercial demonstration line. It is demonstrated that the two-dimensional spatial linearization method offers significant performance advantages over alternative control system methodologies. Furthermore, the absolute vibration value of the solenoid exhibits an order of magnitude advantage over conventional methods at specific speed conditions. Additionally, the reduction in current variation and current variability can significantly diminish the hardware resource requirements necessary for the control system. It is noteworthy that the control system based on this linear approach exhibits reduced sensitivity to vehicle speed. Over the speed range of the Maglev train, which varies from 300[Formula: see text]km/h to 600[Formula: see text]km/h, the control system demonstrates remarkable robustness.