# A#18-1 - (h(7 Now use to bring down the overshoot i.e...

This preview shows pages 1–2. Sign up to view the full content.

Assignment #18 ECSE-2410 Signals & Systems - Spring 2007 Fri 04/13/07 1(75). Given the system, D ( s ) Assign#18. p.1 X ( s ) H 1 ( s ) H 2 ( s ) Y ( s ) H 3 ( s ) - + + + where , s K K s H 1 1 ) ( + = ) 2 )( 1 ( 1 ) ( 2 + + = s s s H , and 1 ) ( 3 = s H . The purpose of K is to provide proportional feedback and the purpose of is to provide derivative feedback. In practice, K is used to minimize steady-state errors and is used to keep down overshoot, i.e., add damping. 1 K 1 K (a)(7). Find ) ( ) ( s X s Y when . 0 ) ( = s D (b)(6). Find , when and ) ( lim t e t ) ( ) ( ) ( t y t x t e = ) ( ) ( t u t x = . What is this steady-state error when K =34? (c)(7). Find ) ( ) ( s D s Y when . 0 ) ( = s X (d)(6). In (c) above, find when is a unit step. What is the steady-state output due to the disturbance, D ( s ), when K = 34? ) ( lim t y t ) ( s D (e)(5). Find the characteristic equation of the closed-loop system in terms of K and . 1 K (f)(7). For 4 and =0, find the closed loop poles, and the corresponding values of 3 = K 1 K ζ and n ω . Note that the choice of K =34 helps the steady-state errors, but contributes greatly to overshoot.

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: (h)(7). Now use to bring down the overshoot, i.e., increase 1 K . With the proportional gain K= 34, find so that 1 K =0.8. (i)(15). Set =0, and draw the root locus as K varies from 1 K ∞ → . (Note. Root locus refers to a plot of the roots of the closed-loop characteristic equation as a constant, say K, varies. Choosing several values of K should give you a good idea of the basic shape of this root locus plot.) (j)(15). Set K =34, and draw the root locus as varies from 1 K ∞ → . 2(25). For the block diagram shown, +-+-s 1 s 1 20 ) ( s W 10 ) ( s Y +-) ( s X (a)(10). Find the transfer function ) ( ) ( ) ( s W s Y s Z = . Express the numerator and the denominator in descending powers of s . (b)(15). Find the transfer function ) ( ) ( s X s Y . Express as the ratio of two polynomials in descending powers of s . Assign#18. p.2...
View Full Document

## This homework help was uploaded on 04/10/2008 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

### Page1 / 2

A#18-1 - (h(7 Now use to bring down the overshoot i.e...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online