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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 2.004 Dynamics and Control II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . s- p l a n e j M x a s i n g l e r e a l p o l e 1 J- I Massachusetts Institute of Technology Department of Mechanical Engineering 2.004 Dynamics and Control II Spring Term 2008 Lecture 20 1 Reading: Nise: Secs. 4.1 4.6 (pp. 153- 177) 1 Standard Forms for First- and Second-Order Systems These are (a) all pole system (with no zeros), and (b) have unity gain (lim t y step ( t ) = 1). 1.1 First-Order System: We define the first-order standard form as 1 G ( s ) = , s + 1 where the single parameter is the time constant. As a differential equation dy + y = u ( t ) . dt and the system has a single real pole at s = 1 / . 1 copyright c D.Rowell 2008 201 T 4 t 1 t y ( t ) s t e p 0 . 9 8 t 1 t 0 . 1 0 . 9 R T s i n i t i a l s l o p e i s The step response is y step = L 1 1 1 / = 1 e t/ s s + 1 / 1.1.1 Common Step Response Descriptors: (a) Settling Time: The time taken for the response to reach 98% of its final value. Since y step ( t ) = 1 e t/ and e 4 = 0 . 0183 . 02, we take T s = 4 as the definition...
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lecture_20 - MIT OpenCourseWare http://ocw.mit.edu 2.004...

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