lecture_20

lecture_20 - MIT OpenCourseWare http/ocw.mit.edu 2.004...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ) = , τs + 1 where the single parameter τ is the time constant. As a differential equation dy τ + y = u ( t ) . dt and the system has a single real pole at s = − 1 /τ . 1 copyright c D.Rowell 2008 20–1 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 /τ = 1 − e − t/τ s s + 1 /τ 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/τ and e − 4 = 0 . 0183 ≈ . 02, we take T s = 4 τ as the definition...
View Full Document

{[ snackBarMessage ]}

Page1 / 8

lecture_20 - MIT OpenCourseWare http/ocw.mit.edu 2.004...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online