First Order Response CharacteristicsHeat BalanceHeat TransferDeviation VariablesPartial FractionsInverse TransformationSolutionFirst order systems1/12/06 BAE 5413First Order Response CharacteristicsModeling Thermistor Response1/12/06 BAE 5413Heat Balance1/12/06 BAE 5413Heat Transfer1/12/06 BAE 5413Deviation Variables1/12/06 BAE 5413Partial Fractions1/12/06 BAE 5413Inverse Transformation1/12/06 BAE 5413SolutionThermistor Response0246810120 2 4 6 8 10 12t / t ( )Temperature deviation (C)1/12/06 BAE 5413First order systems)()(1)(sInputsOutputsKsG tA standard form for the transfer function of a first order system is:Where: K is the “Steady State Gain” or “sensitivity” of the system and it describes the output per unit of input when the system comes to steady state. t is known as the “time constant” and it describes the time required for a first order system to complete 63.2% of its eventual response to a step input.1sKtI n p u t ( s ) O u t p u t ( s )This relationship may also be expressed as a block diagram as
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