Time-delay control of magnetic levitated linear positioning system

In this paper, a high accuracy linear positioning system with linear force actuator and magnetic levitation is proposed. By locating a permanently magnetized rod inside a current-carrying solenoid, the axial force is achieved by boundary effect of magnet poles and utilized to power the linear motion. While the force for levitation is governed by Ampere\´s law supplied with the same solenoid. With the levitation in radial direction, there is hardly any friction between the rod and the solenoid. The high speed motion can hence be achieved. Besides, the axial force act on the rod is a smooth function of rod position, so the system can provide nanometer resolution linear positioning to the molecule size. Since the force-position relation is highly nonlinear, and mathematical model is derived according to some assumptions, such as equivalent solenoid of the permanently magnetized rod, so there exists unknown dynamics in practical application. Thus "robustness" is an important issue in controller design. Meanwhile the load effect reacts directly on the servo system without transmission elements, so the capability of "disturbance rejection" is also required. With above consideration, a time-delay control scheme is chosen and applied. By comparing the input-output relation and the mathematical model, the time-delay controller calculates an estimation of unmodelled dynamics and disturbance then composes the desired compensation into the system. Effectiveness of the linear positioning system and control scheme are illustrated with simulation results.