Design of feedback control of levitation system excited by track irregularity for targeting a pre-specified stationary probability density

Abstract

Stochastic control of levitation systems is paramount for enhancing system stability, optimizing performance, and ensuring operational safety. The present paper investigates the control of stochastic levitation systems to achieve a pre-specified stationary probability density function (PDF). Firstly, the method for predicting the stationary PDFs of the stochastic responses of the levitation system is introduced, leveraging stationary solution theory. Building on this foundation, a feedback control strategy is developed to target the pre-specified stationary PDFs in two practical scenarios through the stochastic linearized levitation system. In the first scenario, the objective is to regulate the vibration amplitude of the stochastic levitation system. The second scenario extends the design framework to include tracking piecewise constant reference signals associated with the stochastic levitation system. Furthermore, the Lyapunov function method is employed to rigorously prove that the proposed feedback control ensures the asymptotic convergence of the PDF of the system response to the desired stationary PDFs over time. The efficacy of the proposed control forces, derived from linearized systems, is validated in both linearized and nonlinear systems. Numerical results demonstrate that the control strategy designed through the linearized system performs effectively even in nonlinear systems. This study presents a novel approach for precise probabilistic control, offering significant advancements in the stability and performance of practical stochastic levitation systems.