# lec16 - Nyquist Example 1 2K L(s) = (2s + 1)(s + 1)(s / 2 +...

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Nyquist Example 1 ) 1 2 / s )( 1 s )( 1 s 2 ( K 2 ) s ( L + + + = Im s Im L Slide 1 ME 475 Session 16: Nyquist Sketching Galen King Purdue University Re s Re L

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Nyquist Plot s = j ϖ : ) 2 / j 1 )( j 1 )( 2 j 1 ( 2 ) j ( L ϖ + ϖ + ϖ + = ϖ 2 ) j ( L = ϖ Slide 2 ME 475 Session 16: Nyquist Sketching Galen King Purdue University 2 2 2 ) 2 / ( 1 1 ) 2 ( 1 ϖ + ϖ + ϖ + 2 / tan tan 2 tan ) j ( L 1 1 1 ϖ - ϖ - ϖ - = ϖ - - -
Nyquist Plot s = Re j φ Slide 3 ME 475 Session 16: Nyquist Sketching Galen King Purdue University s =- j ϖ

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Nyquist Stability Criterion Slide 4 ME 475 Session 16: Nyquist Sketching Galen King Purdue University
Negative Real Axis Crossing 1 s 5 . 3 s 5 . 3 s 2 ) s ( L 2 3 + + + = 2 ) j ( L 3 2 = ϖ Slide 5 ME 475 Session 16: Nyquist Sketching Galen King Purdue University ) 5 . 3 ( j ) 5 . 3 1 ( ϖ - ϖ + ϖ -

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Nyquist Plot for Arbitrary K Im s Im L Slide 6 ME 475 Session 16: Nyquist Sketching Galen King Purdue University Re s Re L
) 1

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lec16 - Nyquist Example 1 2K L(s) = (2s + 1)(s + 1)(s / 2 +...

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