Servo Control of a Current-Controlled Attractive-Force-Type Magnetic Levitation System Using Fractional-Order LQR Control

Abstract

Recent research on fractional-order control laws has introduced the fractional calculus concept into the field of control engineering. As described herein, we apply fractional-order linear quadratic regulator (LQR) control to a current-controlled attractive-force-type magnetic levitation system, which is a strongly nonlinear and unstable system, to investigate its control performance through experimentation. First, to design the controller, a current-controlled attractive-force-type magnetic levitation system expressed as an integer-order system is extended to a fractional-order system expressed using fractional-order derivatives. Then, target value tracking control of a levitated object is achieved by adding states, described by the integrals of the deviation between the output and the target value, to the extended system. Next, a fractional-order LQR controller is designed for the extended system. For state-feedback control, such as fractional-order servo LQR control, which requires the information of all states, a fractional-order state observer is configured to estimate fractional-order states. Simulation results demonstrate that fractional-order servo LQR control can achieve equilibrium point stabilization and enable target value tracking. Finally, to verify the fractional-order servo LQR control effectiveness, experiments using the designed fractional-order servo LQR control law are conducted with comparison to a conventional integer-order servo LQR control.