A method for obtaining a linear spring for a permanent magnet levitation system using electromagnetic control

Since the electromagnetic force is a function of the gap between magnets, the spring constant has large nonlinearities with respect to the displacement. Hence the spring constant varies significantly with the initial load. This implies that the linear control theory is limited to a range of very small displacement. To treat the system with variable initial loads and large displacements, this paper presents a procedure for obtaining a linear spring with variable spring constants by using a repulsive type actuator with permanent magnets and electromagnets. The analytical expression for obtaining a linear spring is presented. Experimental tests were carried out, and are compared with theoretical results. As an example, the results are applied to the problem of dynamic absorbers. In this actuator, the feedback loop for obtaining the linear spring constant has no dependence on the damping force generated by a velocity feedback loop. Hence the velocity feedback coefficient can be decided without consideration of its effect on the spring constant