System identification for second order overdamped systemsSecond Order Overdamped ResponseSecond Order Overdamped Response SolutionCalculation of %IncompleteProcedure for %incomplete responseSlide 62/1/05 BAE 5413 1System identification for second order overdamped systemsMethod of % Incomplete Response2/1/05 BAE 5413 2Second Order Overdamped Response 11)()(21ssKsInputsOutpu tConsider a second order overdamped system where:For a unit step input: 1111)(2121scsbsasssKsOutputAnd we can readily find a,b,c to be: 2122112121111111)(sssKssssOutput2/1/05 BAE 5413 3Second Order Overdamped Response SolutionAnd inverting:211221211)(tteeKsOutput211221211)(tteeKAsOutputFor a step of A2/1/05 BAE 5413 4Calculation of %IncompleteThis may be written as:1121303.2log1)(logtKAsOutpu tAssuming one time constant is much larger than the other, that is 1>> 2 , for large time:11211)(teKAsOutputThis is in the form of:mtby A classic linear form.The slope m=-1/1 can be determined by plotting on simi-log paper and using the slope for large time.2/1/05 BAE 5413 5Procedure for %incomplete responseAKtOutpu tPIR)(1100Use a step of magnitude A to excite the system.Plot PIR on a log scale vs. time on a linear scale. Use large times to plot a linear curve of constant slope. This curve is the response for the 1 term.2/1/05 BAE 5413 6Procedure for %incomplete responsePlot the difference between the first linear curve and the actual response. This difference is the response for the 2 term. Plot a linear curve for this difference.For both linear curves, take each intercept at t=0 as 100% response. Determine the time at 100% -0.368*100% response (this is the 63.2% response point). These times will be 1, and
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