# 9 - Lecture 9: Time-Response Characteristics (II) Time...

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

1 Lecture 9: Time-Response Characteristics (II) • Time Specifications of Continuous-Time Systems • Mapping the s -Plane to the z -Plane • Time Specifications of Sampled-Data System • Reading: Chapter 6.4 Sampled-Data Systems C ( s ) H ( s ) G ( s ) R ( s ) + ¡ T Transfer function from R ( z ) to C ( z ): C ( z ) R ( z ) = G ( z ) 1+ GH ( z ) Characteristic equation: 1 + GH ( z ) = 0 whose roots are the closed-loop poles: p 1 , p 2 ,..., p n Stable systems: all closed-loop poles within the unit circle Dominant closed-loop poles: the closed-loop pole(s) furthest away from 0 Transient response largely determined by the dominant closed-loop pole(s) Problem : quantify the response characteristics based on dominant pole locations

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

View Full Document
2 Continuous-Time Feedback Systems 1 + G ( s ) H ( s ) = 0 C ( s ) H ( s ) G ( s ) R ( s ) + ¡ Transfer function from R ( s ) to C ( s ): C ( s ) R ( s ) = G ( s ) 1+ G ( s ) H ( s ) Characteristic equation: q 1 , q 2 ,..., q n Stable systems: all closed-loop poles strictly on the left half of the complex plane Dominant closed-loop poles: the closed-loop pole(s) furthest to the right Transient response largely determined by the dominant closed-loop pole(s) whose roots are the closed-loop poles: Step Response Time (sec) Amplitude 0 5 10 15 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time Specifications of Continuous-Time Systems t d : delay time , time for s ( t ) to reach half of s ( 1 ) t r : rise time , time for s ( t ) to reach s ( 1 ) t p : peak time , time for s ( t ) to reach first peak M p : maximum overshoot t s : settling time , time for s ( t ) to settle within a range (2% or 5%) of s ( 1 ) Step response s ( t ) t d t r t p M p = s ( tp ) ¡ s ( 1 ) s ( 1 ) s ( 1 ) 0 : 5 s ( 1 ) t s
3 Time Specifications for a Real Dominant Pole £ q 2 q 3 £ £ q 1 1 ¿ Time constant: ¿ = 1 j q 1 j Dominant closed-loop pole: q 1 < 0 Time Specifications:

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.

## This note was uploaded on 04/15/2011 for the course ECE 483 taught by Professor Evens during the Spring '08 term at Purdue.

### Page1 / 12

9 - Lecture 9: Time-Response Characteristics (II) Time...

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

View Full Document
Ask a homework question - tutors are online