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243 Control Systems CEatStability1

243 Control Systems CEatStability1 - 29 29 29 2 2 2 However...

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1 Swansea University SCHOOL OF ENGINEERING EG 243: Control Systems Characteristic Equation The CE, 1+GH=0, determines the nature of the closed loop system response. To determine values related to the stability limits, then the 2 conditions, magnitude and phase are considered, ie |GH(jw)| =1 and arg(GH(jw)) = 180 (or (2n+1) π ). From this the stability limit frequency, ω s , and the stability limit gain, K s can be determined Consider the example ( 29
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Unformatted text preview: ( 29( 29( 29 2 2 2 ( )( ) However, arg( ( )) 180 ( since is wholly real), thus (- Strategy: let , and derive conditions for ( ) 1: ( ) ) or o ab j c GH j K j ab ab K GH s s a s b s c s j GH j K j a j b j c j a b ac bc ac bc ϖ + + = = + + + → = -= -+ + + = - -+ + + + = = + + Sketch the Nyquist, Bode and root locus diagrams for this condition. whence Note when 1 then 8. s s K a b c K = = = =...
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