A current goal in microsystem research is to overcome small working ranges, typically resulting from mechanical connections and restoring forces such as for cantilevers. In the case of predefined resting positions and unidirectional motion, pseudo-levitation as in magnetic bearings is a promising solution.
In order to investigate concepts for energy efficient, cooperative microactuators, which allow free motion of small objects, we present a bistable levitation setup. The system consists of a magnetic proof mass within a glass tube, a piezoelectric staple actuator, two permanent magnets and a solenoid used as an electromagnet. The movable mass is mechanically unconstrained in its upper vertical motion and is intended to switch between two predefined equilibrium positions, namely on the staple actuator and levitating at a defined upper position. The transition is accomplished by an impulse-like kick force by the staple actuator, and subsequent feedback controlled following of a trajectory via electromagnetic actuation.
The goal of this work consists of both adapting the system parameters, guaranteeing stable and preferably robust equilibrium positions for the unactuated system, and finding optimal trajectories with a short settling time and minimum input effort for the controlled transition. These design and control objectives are combined within a co-design. In this approach, the system and controller optimizations are not performed consecutively, but within a single optimization, taking into account the coupling between the design and control. Here, we apply flatness-based control combined with feedback linearization, allowing for trajectories to be tracked without error in case of the undisturbed system. Thus, the controller is solely used for disturbance compensation and the problem can be simplified by optimizing only the trajectory without the controller parameters. We show that the combined optimization process is of advantage in comparison to the sequential approach and proficiently exploits the design parameters to improve the generated trajectories.