{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

l8 - (b In each case high-order poles are about ten times...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
16.06 Lecture 8 Dominant Modes Karen Willcox September 18, 2003 Today’s Topics 1. Dominant mode concept 2. ”Invasion” of a first-order system 3. Examples of high-order systems Reading : 1.8, 4.4, ln 1
Background image of page 1

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

View Full Document Right Arrow Icon
1 Dominant mode concept Example 4.5.1 from text: Step response of a DC motor position servo. 0 . 5 (a) G ( s ) = s (0 . 25 s +1) is the transfer function from field voltage to shaft po- sition of the motor. Draw the closed-loop system using a proportional controller: C ( s ) = R ( s ) = Draw the pole-zero diagram for C ( s ) with K = 1: 2
Background image of page 2
(b) The PFE is: (c) Graphical residues: 3
Background image of page 3

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

View Full Document Right Arrow Icon
(d) Step response: (e) Plot each piece of the step response: (f) What happens if we increase K ? Type 1 system: Velocity error constant = . There is a conflict between 4
Background image of page 4
2 First-order system ”invaded” by a single pole Consider the following example, where T 2 varies. See Fig. 2.18 on the next page for response plots. Observations: at t = 0 slope of c ( t ) is zero for two-pole system and finite for one-pole system in case 2, the magnitude of the residue at -10 is 0.1 times the magnitude of the residue at -1 in case 3, the magnitudes of the residues at -1 and -2 are not widely different, so case 1 is not as good an approximation 5
Background image of page 5

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

View Full Document Right Arrow Icon
insert fig 2.18 here 6
Background image of page 6
3 Examples of high-order systems (a) Consider the following systems:
Background image of page 7

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

View Full Document Right Arrow Icon
Background image of page 8
Background image of page 9

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

View Full Document Right Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (b) In each case, high-order poles are about ten times removed from the dominant pole. Question: Are they important in each case? 7 (c) Consider G 1 ( s ): c 1 ( t ) = The residue of the complex pair contribution is small. (d) Consider G 2 ( s ): c 2 ( t ) = The residues of the faraway poles are comparable in magnitude to the residue of the pole at-1. But the residues of the two faraway poles have nearly equal and opposite magnitudes, therefore they cancel each other and the pole at-1 is dominant. In particular, the pole at-1 is a good approximation for t > 4 (2% from the final value). (e) See Figure E2.2 on the next page. 8 Insert Fig. E2.2 here. 9 4 What is important? 5 F-8 example As part of your reading for this week, review the attached example on longi-tudinal response modes for the F-8 aircraft. 10...
View Full Document

{[ snackBarMessage ]}