O-K-State BAE 5413 - Series systems with lumped parameters - D2348653

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O-K-State BAE 5413 - Series systems with lumped parameters

School name Oklahoma State University

Course Bae 5413- Instruments Biol Sys

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Second order Overdamped thermal systemPhysical modelAlgebraic manipulationCombining equationsFurther combining equationsFinal model1/1/05 BAE 5413 1 of 6Second order Overdamped thermal systemSeries systems with lumped parameters1/1/05 BAE 5413 2 of 6Physical modelT1T2q2q1m2m1TmdtdTCmqdtdTCmqqpp1111222120   222212111TTAUqTTAUqm1/1/05 BAE 5413 3 of 6Algebraic manipulation    dtdTCmTTAUdtdTCmTTAUTTAUppm111121122212112220     d tdTAUCmTTdtdTAUCmTTAUAUTTppm11111122222212221120 1/1/05 BAE 5413 4 of 6Combining equations 1111112212221122222TdtdTAUCmTTTTAUAUdtdTAUCmTppm111111111111122111111112222TdtdTAUCmTTdtdTAUCmAUAUdtTdtdTAUCmdAUCmTppppm1/1/05 BAE 5413 5 of 6Further combining equations111111122111112TdtdTTTdtdTAUAUdtTdtdTdTm1111122111221212TdtdTdtdTAUAUdtdTdtTdTm11122112212121 TdtdTAUAUdtTdTm1/1/05 BAE 5413 6 of 6Final model•Note, if U1A1/U2A2 is very small, then we have:•Writing in terms of deviation variables and Transforming, we have:•Or:   sssmsss12212 111221212TdtdTdtTdTm 1112212ssms 

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O-K-State BAE 5413 - Series systems with lumped parameters

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