Design, Modelling, and Control of Magnetic Ball Suspension System

Abstract

This paper presents the modeling, control design, and performance analysis of a Magnetic Ball Suspension System (MBSS), a nonlinear and inherently unstable electromechanical system used in various precision applications. The system's primary objective is to levitate a steel ball using electromagnetic force without physical contact, thereby eliminating frictional losses. A comprehensive state-space model was developed, capturing both the mechanical and electrical dynamics. The equilibrium points of the system were determined through feedback linearization using the Jacobian matrix. To ensure system stability, controllability and observability analyses were conducted, confirming that state feedback and observer-based control strategies could be effectively implemented. Three distinct control methods were explored: pole placement-based state feedback control, full-order observer design, and optimal state feedback control using the Linear Quadratic Regulator (LQR). Each control strategy was validated through Simulink simulations for both linearized and nonlinear models. Simulation results demonstrated that the linearized system consistently achieved desired performance with minimal oscillations, whereas the nonlinear system exhibited significant transient oscillations before stabilization. The full-order observer enhanced estimation accuracy, enabling effective control where direct state measurement was impractical. The LQR-based control offered improved robustness and minimized control effort, though its performance was comparable to standard state feedback in some cases.