Dual Nonlinear Saturation Control of Electromagnetic Suspension (EMS) System in Maglev Trains

This paper presents a nonlinear vertical dynamic model of an electromagnetic suspension (EMS) system in maglev trains regulated by a dual nonlinear saturation controller (DNSC) under simultaneous resonance ($\Omega \cong {\omega }_s,{\omega }_s\cong 2{\omega }_c$). The governing nonlinear differential equations of the system are addressed analytically utilizing the multiple time-scale technique (MTST), concentrating on resonance situations obtained from first-order approximations. The suggested controller incorporates two nonlinear saturation functions in the feedback and feedforward paths to improve system stability, decrease vibration levels, and enhance passenger comfort amidst external disturbances and parameter changes. The dynamic bifurcations caused by DNSC parameters are examined through phase portraits and time history diagrams. The goal of control is to minimize vibration amplitude through the implementation of a dual nonlinear saturation control law based on displacement and velocity feedback signals. A comparative analysis is performed on different controllers such as integral resonance control (IRC), positive position feedback (PPF), nonlinear integrated PPF (NIPPF), proportional integral derivative (PID), and DNSC to determine the best approach for vibration reduction in maglev trains. DNSC serves as an effective control approach designed to minimize vibrations and enhance the stability of suspension systems in maglev trains. Stability evaluation under concurrent resonance is conducted utilizing the Routh–Hurwitz criterion. MATLAB 18.2 numerical simulations (fourth-order Runge–Kutta) are employed to analyze time-history responses, the effects of system parameters, and the performance of controllers. The evaluation of all the derived solutions was conducted to verify the findings. Additionally, quadratic velocity feedback leads to intricate bifurcation dynamics. In the time domain, higher displacement and quadratic velocity feedback may destabilize the system, leading to shifts between periodic and chaotic movements. These results emphasize the substantial impact of DNSC on the dynamic performance of electromagnetic suspension systems. Frequency response, bifurcation, and time-domain evaluations demonstrate that the DNSC successfully reduces nonlinear oscillations and chaotic dynamics in the EMS system while attaining enhanced transient performance and resilience.