{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture 17

# lecture 17 - z domain Analysis Mapping between the s plane...

This preview shows pages 1–7. Sign up to view the full content.

1 z domain Analysis Mapping between the s plane and the z plane ω σ jT T j T Ts e e e z j s e z = = + = = + ) (

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

View Full Document
2 Periodic strips in the s-plane are mapped into the unit circle in the z-plane. Signals in complementary strips will be folded into primary strip after sampling. To avoid the folding, the sampling frequency must be high enough. ω σ jT T j T e e e z = = + ) (
3 Constant-Damping Loci σ T j T e e z ω = which is a circle centered at the origin with a radius of T e Constant-Frequency Loci T j T e e z =

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

View Full Document
4 Constant-Damping Ratio Loci ζ The s -plane loci are described by d n n n j j s ω ζω + - = - + - = 2 1 The constant loci in the z -plane are described by ) 2 1 2 exp( ) exp( 2 s d s d d n Ts j T j T e z π πζ + - - = + - = = s d s d z z 2 ; ) 1 2 exp( 2 = - - =
5 Constant Natural-Undamped Frequency Loci n ω 2 2 1 2 2 ) 2 exp( ) 1 2 exp( ζ π πζω πζ - = = - = - - = s n s d s n s d z z

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

View Full Document
6 Stability ) ( 1 ) ( ) ( ) ( z GH z G z R z C + = The characteristic equation: 0 ) ( 1 ) ( = + = z GH z P Note: The roots must be inside the unit circle for a stable system The system is critical stable if the roots are on the unit circle. For a stable system, its zeros can be outside of the unit circle.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 7

lecture 17 - z domain Analysis Mapping between the s plane...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online