7. Modeling_upload

7. Modeling_upload - Electromech Systems JIN KANG...

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Electromech Systems JIN KANG
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Background Last few lectures have been on mathematical model representations Block diagrams Transfer functions State space representations Entering argument has been diff eqs Next few lectures on forming diff eqs for physical systems
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Modeling Methods Systems Mechanical / electrical Methods Physics, FBD, and Kirchoff volt/current Mechanical network diagrams Loops analysis (electrical) Bond graphs (powerful)
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Mechanical Network Diagrams One modeling methodology for creating ‘compliance’ transfer functions for mechanical system Compliance: output = position X(s), input = force F(s) Physics of method Based on newton eq: But consider externally applied forces balanced by reaction forces x m dt mv d F = = ) ( k b m reaction external F F F F F + + = =
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Mechanical Network Diagrams Node A point in system that undergoes unique motion w.r.t. ground Area we are interested in describing motion Objects in system that are kinematically constrained (rigidly connected), and move together w.r.t. ground (reference) MND process Identify nodes, assign displacement to each Draw a node/ground diagram Create component node links Applied and inertial forces always to ground Shows interaction of forces Determine equation of motion for each node Force applied = force reaction Component forces are determined by node you are analyzing minus other mode it is attached to Mass forces always to ground
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MND Example Define nodes ads Point that undergoes unique motion Region whose motion is of concern 1. At mass 2. At interface MND Equations ) ( 0 : ) ( ) ( : 1 2 1 2 2 2 1 1 1 2 1 1 z z k z b z z z k z k z m t f z + = + + =
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State Space Equations # of vars = 2 nd order + 1 st order = 3 Input f(t) Output = z 1 = position of mass State vars = = + = = + + 2 1 1 2 1 2 1 2 1 1 1 1 2 1 0 ) ( z z k z k z b z t f z k z k z k z m 2 3 1 1 2 1 1 z x x z x z x = = = =
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Output equations Transfer function bm k k s m k k s b k s m b k s s Y bm k k s m k k s b k s A Det DET ADJ A sI c s c b s a
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7. Modeling_upload - Electromech Systems JIN KANG...

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