To minimize the construction cost of track beam and enhance the dynamic performance of the magnetic suspension system, a simplified coupled vibration model of the electromagnet-track beam-vehicle body was established. Initially, by defining a Lyapunov function to represent the quadratic performance index of the maglev system under parameter perturbation, the controller design problem for the closed-loop system was transformed into an existence problem of linear matrix inequality (LMI) solutions. Consequently, a state-feedback cost-preserving robust controller for a flexible track beam was designed. Subsequently, the impact of the suspension controller on the dynamic characteristics of the flexible track beam, both with and without considering parameter perturbation, was compared and analyzed. Furthermore, the robustness, high-frequency suppression, and low-frequency following characteristics of the LMI-based controller were evaluated. Finally, the influence of two distinct state feedback controllers on the dynamic characteristics of the flexible track beam across different frequency bands was analyzed. Correlation analysis revealed that accounting for parameter perturbation can improve the suspension and dynamic characteristics of the suspension controller. When the system experiences parameter perturbation, the LMI-based suspension controller can achieve stable suspension on the flexible track beam while demonstrating strong robustness, high-frequency suppression, and low-frequency following capabilities. On the flexible beam, controllers with different state feedback exhibit varying dynamic characteristics in different vibration frequency segments of the track beam. Specifically, reducing the feedback state variables in the low-frequency band and increasing them in the high-frequency band can appropriately improve the system’s dynamic characteristics.
Wang et al. (2026) studied this question.