Co-Design and Control of a Magnetic Microactuator for Freely Moving Platforms

Abstract

A current goal for microactuators is to extend their usually small working ranges, which typically result from mechanical connections and restoring forces imposed by cantilevers. In order to overcome this, we present a bistable levitation setup to realise free vertical motion of a magnetic proof mass. By superimposing permanent magnetic fields, we imprint two equilibrium positions, namely on the ground plate and levitating at a predefined height. Energy-efficient switching between both resting positions is achieved by the cooperation of a piezoelectric stack actuator, initially accelerating the proof mass, and subsequent electromagnetic control. A trade-off between robust equilibrium positions and energy-efficient transitions is found by simultaneously optimising the controller and design parameters in a co-design. A flatness-based controller is then proposed for tracking the obtained trajectories. Simulation results demonstrate the effectiveness of the combined optimisation.

Design and Optimal Control of a Multistable, Cooperative Microactuator

“…That means that the transformation law (23) distributes the currents in such a way that the solenoid with the largest effect on the proof mass contributes the most to achieve the necessary force. This is a large improvement, compared to the previous solution with a single electromagnet, where a singularity occurs when the movable magnet coincides with the center of the solenoid [15]. It can be seen that the desired relation ( 16) between the electrical currents and the electromagnetic force results from Equations ( 23) and ( 24).…”

“…The microactuator setup investigated in this work consists of a movable, permanent magnetic proof mass guided by a glass tube, a piezoelectric stack actuator, two permanent ring magnets and two solenoids. In contrast to our previous work [15], the second magnet is used to imprint a second levitating equilibrium position, rather than weakening the field of the first magnet. The additional solenoid allows a less restrictive motion range of the proof mass, which was an issue of the initial setup.…”

“…Provided that the maximum magnetic force is larger than the gravitational force, there exists at least a single stable equilibrium position. In our previous work [15], a second stable position was generated due to the contact with the stack actuator. Here, we take advantage of the nonlinearity of the magnetic force to generate a larger number of equilibria at predefined positions by superimposing magnetic fields of multiple ring magnets.…”

“…The overall system can be described by the dynamics of each individual component and the respective couplings between them. The model is adapted from [15] and generalized for an arbitrary number of magnets and solenoids. Let us assume that the setup comprises m ring magnets and n electromagnets.…”

“…In order to allow a flexible application in both the horizontal and vertical directions, we previously presented a magnetic actuator moving a cylindrical permanent magnet with one DoF [15]. To this end, finite element models (FEM) were used to calculate the magnetic forces, and their complexity was reduced by different approaches, i.e., a lookuptable, a semi-analytical compact model, and a parametric reduced order model [16,17].…”