Efficient Multi-Physics Transient Analysis Incorporating Feedback-Dependent Boundary Conditions

This paper describes the ANSYS simulation of an electrostatically-actuated MEMS device, in which the drive voltages are computed using feedback control laws. The device consists of a movable electrode suspended on flexible, elastic structures, and one or more fixed drive electrodes. The feedback control laws are used to determine the level of a variable voltage supply in a drive circuit for each drive electrode, and take inputs such as the total charge on the drive electrode, and the position of various points on the movable electrode. The simulation requires the solution of coupled structural and electrostatic field equations, and presents two challenges for a standard ANSYS multifield analysis. The first is that the boundary conditions for each load step are not known beforehand, but are generated by the controller logic based on the output of the previous simulation step results. The second is that the elements used to model the drive electrode control circuitry are incompatible with the electrostatic elements. We present several extensions that enable this analysis. We eliminate the circuit elements from the model, and instead propagate the associated states in an APDL macro. To allow efficient solution of the closed-loop model we incorporate an adaptive step size Runge-Kutta integration routine within this macro. Implementation of the adaptive step size routine speeds some transient simulations by a factor of more than 100. We present results for representative MEMS devices including a one-DOF piston microactuator and a two-DOF rotating/translating microactuator.