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MEM355W07-08.Exam1.soln_stud - MEM 355 Performance...

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MEM 355: Performance Enhancement of Dynamic Systems MidTerm Exam I Fall 07-08 (Relevance to a-k outcomes: a, c, e, k) Allotted time: 1hr. 30 min. Write your name on each sheet Plagiarists will be penalized ======================================================================== ============
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I. Problem I (20%) A temperature control system (negative, unity feedback) is found to have zero error to a constant input and an error of 0.5 o C to a tracking input that is linear in time, rising at the rate of 50 o C/minute. What is the type of this control system and what is the relevant error constant [K p or K v or etc.]? Solution: Zero error to step input at least type-1 system. Finite non-zero error to ramp (“velocity”) input type-1 system. Since this is type-1 system, the acceleration (“parabolic input”) error would be . Hence the relevant error constant would be for ramp input. K p would of course would be . The steady state error e(t ) for a unit ramp input is . Hence from the given data, one gets K v = 50/0.5 = 100.
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MEM355W07-08.Exam1.soln_stud - MEM 355 Performance...

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