EEL5173 Fall 2009 Lecture _9

EEL5173 Fall 2009 Lecture _9 - (a Mapping Contours •...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: (a) Mapping Contours • Nyquist Path (b) Nyquist Diagram • Frequency Response (c) Nyquist Criterion (2) Nyquist Criterion ) ( ) )( ( ) ( ) )( ( ) ( ) ( 1 ) ( 2 1 2 1 n m p s p s p s z s z s z s k s H s G s F − − − − − − = + = L L Poles of the system, i.e. of T ( s ), come from the zeros of F ( s ). Figure 10.20 Closed-loop control system by N. S. Nise ) ( ) ( ) ( ) ( 1 ) ( ) ( ) ( ) ( s F s G s H s G s G s R s C s T = + = =- a proper rational function with real coefficients . Where (a) Mapping Contours Figure 10.21 Mapping Contour A through function F ( s ) to Contour B by N. S. Nise A contour is a closed path, with a direction, in a complex plane. ) ( Q F Q = ′ Figure 10.22 Examples of contour mapping by N. S. Nise ɵ ∆ɵ = 0 = Δ = ∠ Δ = ∠ θ θ F F ɵ ϕ- ϕ ∆ϕ = 0 = Δ − = ∠ Δ − = ∠ φ φ F F ɵ ɵ π θ θ 2 − = Δ = ∠ Δ = ∠ F F ∆ɵ = -2 π ∆ϕ = -2 π ϕ- ϕ π φ φ 2 = Δ − = ∠ Δ − = ∠ F F ) 2 ( ) 2 ( = − − − = Δ − Δ = ∠ Δ − = ∠ π π φ θ φ θ F F ɵ ϕ Figure 10.23 Figure 10....
View Full Document

{[ snackBarMessage ]}

Page1 / 20

EEL5173 Fall 2009 Lecture _9 - (a Mapping Contours •...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online