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EE291E Hybrid Modeling of Microelectromechanical Systems

EE291E Hybrid Modeling of Microelectromechanical Systems. Jason Clark BSAC UC Berkeley. What’s the Motivation. Boundary Element Analysis. Currently, there has been great success modeling the electrostatic and structural dynamics of MEMS. Finite Element Analysis.

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EE291E Hybrid Modeling of Microelectromechanical Systems

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  1. EE291EHybrid Modeling of Microelectromechanical Systems Jason Clark BSAC UC Berkeley

  2. What’s the Motivation Boundary Element Analysis • Currently, there has been great success modeling the electrostatic and structural dynamics of MEMS Finite Element Analysis REF: MEMCAD, Automm Automatic Generation of Dynamic Macromodels

  3. Motivation, cont. Modified Nodal Analysis Mirror Comb-drive array Torsional hinge MEMS modeling is complex due to multi-scales and multi-energy domains such as electro-magnetic, mechanical, thermal, digital/analog electrical, etc.

  4. Motivation, cont. • But a particular class of MEMS, such as actuators involving contact, has remained more of a challenge. Abe Lee : UC Berkeley, PhD dissertation (1992) Roger Hipwell : UC Berkeley, MS thesis (1998) Norman Tien : Cornell, thermal impact actuator (2000) *Richard Yeh : UC Berkeley, PhD dissertation (2001) Easier to make than to simulate in current FEA & MNA frameworks * test case

  5. Progression in MEMS simulation • CT : ODEs • E.g. MEMCAD, SUGAR • CT+DE : Mixed signal systems • E.g. SUGAR • CT+DE+FSM : Hybrid systems • E.g. Ptolemy Next step

  6. Why has CT modeling of impact been impractical for MEMS simulation?

  7. First test case: the Inchworm Motor Operation principles

  8. Impacted State

  9. Non-Impacted State

  10. Non-impacted state K1 K2 K1 K1 K1 M1 M1 Holder Mover F2 F1 M2 F1 = f(v1,v2) FSM - A F2 = f(v3)

  11. Impacted State K2 K2 K1 K1 K1 M1 M1 Holder Mover F2 F1 M2 FSM - B

  12. Hold State K2 K2 K1 K1 K1 M1 M1 Mover Holder F1 F2 M2 FSM - C

  13. Hybrid System CT+DT+FSM v1 v2 v3 ti ti+1 ti+2 ti DT: engage pull hold A B/C CT integration for FSM - A CT integration for FSM – B/C

  14. Q - Switching Gap(X1) < 0.1mm Free Pull Gap(X2) < 0.1mm F2RXN < 1mN & F1RXN < 1mN F2RXN < 1mN Hold Inchworm Loop Gap vs FRXN guards are used to tame Zeno behavior. They widen the marginal thresholds for switching.

  15. Sugar to Ptolemy where G=conductance ce=constitutional eqs C=capacitance c=C contribution V=voltage Q=charge M=mass D=damping K=stiffness F=force q=displacement Electrical & Mechanical = Coupled MNA solution vector MNA matrix Excitation vector Multi-domain state vector Input coupling matrix System matrix 1st order ODE

  16. Hybrid execution • Time propagates to all components • t is global • System is CT at each integration time point • Within DT and a FS • FSM cannot make transitions during t+dt • Time stands still during transitions • After dt FSM examines switching thresholds • At t = t + dt • FSM makes transitions according to guards • Switching control • FSM performs actions on the transition • Initial conditions are set for new state Zeno execution: An execution is Zeno is it contains an infinite number of transitions in a finte amount of time. An automaton is Zeno if it accepts a Zeno execution.

  17. Ptolemy Abstraction

  18. E.g. Sticky Mass K2 K1 M2 M1 FSM-A F1 FSM-B/C

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