lec15 - Galen King Purdue University Stability Condition A...

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Principle of the Argument (Cauchy) Let F(s) be a single-valued function that has a finite number of poles in the s-plane. Choose a closed path Γ s in the s-plane such that it avoids Slide 1 ME 475 Session 15: Nyquist Stability Galen King Purdue University any poles or zeros of F(s). Then the corresponding contour Γ F mapped in the F(s)- plane will encircle the origin N CW times in a clockwise direction.
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Contour in s Slide 2 ME 475 Session 15: Nyquist Stability Galen King Purdue University
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Application of P of A to Stability Recall: Controller Plant R(s) Y(s) + - G c G p H G G ) s ( L p c = Slide 3 ME 475 Session 15: Nyquist Stability Galen King Purdue University zeros of F(s) poles of F(s) H ) s ( P ) s ( Z = 0 ) s ( P ) s ( Z ) s ( P ) s ( P ) s ( Z 1 ) s ( F let = + = + =
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Relate to Loop Transfer Function ) s ( L 1 ) s ( F + = Slide 4 ME 475 Session 15: Nyquist Stability Galen King Purdue University
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Nyquist Stability Criterion p z CW N N N - = Slide 5 ME 475 Session 15: Nyquist Stability
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Unformatted text preview: Galen King Purdue University Stability Condition A feedback system having open-loop poles in the RHP is stable if and only if the Nyquist plot of L(s) encircles-1 times in a counter-clockwise Slide 6 ME 475 Session 15: Nyquist Stability Galen King Purdue University direction. Steps in Sketching a Nyquist Plot Plot open-loop poles in the s-plane. Draw the Nyquist contour s , indenting to the right of any open-loop poles on the imaginary Slide 7 ME 475 Session 15: Nyquist Stability Galen King Purdue University axis. Map contour s to L(s)-plane. Apply encirclement condition. Example 10 s 2 s K 10 ) s ( L 2 + + = Im s Im L Slide 8 ME 475 Session 15: Nyquist Stability Galen King Purdue University Re s Re L...
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lec15 - Galen King Purdue University Stability Condition A...

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