pump_model_1 - MULTI-DOMAIN MODELING WHAT'S THE ISSUE Why...

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MULTI-DOMAIN MODELING W HAT ' S THE ISSUE ? Why not just “write down the equations”? — standard formulations in different domains are often incompatible usually due to incompatible boundary conditions (choice of “inputs”) E XAMPLE : SIMPLE FLUID SYSTEM Scenario
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Modeling goal The simplest model competent to portray resonance in this system. Assumptions rigid-body motion (e.g., lever & pivot do not bend) mass concentrated at c.g. of magnet electro-magnet applies an oscillating force • small motion mechanical elasticity only in the flexible bellows no power dissipation except in the check valves (this assumption highlights any resonant behavior) linear model of mechanical-to-fluid transduction • incompressible fluid • ideal check valves “Write down” the equations First define quantities: l 1 l 2 y 1 y 2 m P lef t P chamber P right A k Modeling and Simulation of Dynamic Systems Air pump model page 2
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Mechanical Domain m ÿ 2 := F magnet – F spring – F dissipation (symbol := denotes an assignment operator; right side is computed to evaluate left side.) F spring := k l 1 l 2 y 2 F dissipation is due to fluid forces. Substituting: m ÿ 2 := F magnet l 1 l 2 k l 1 l 2 y 2 l 1 l 2 F dissipation This implies state equations: d dt y 2 := ˙
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