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Control ENG HW_Part_65

# Control ENG HW_Part_65 - of instability 14.11 for the...

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For verge of instability 8 ) 3 1 3 =  + = Kc Kc Characteristics equation 0 3 ) 1 ( ) 1 ( 10 1 = + + + s kcs 0 11 ) 10 3 ( 3 2 3 = + + + + Kcs s s s Routh Array 30 / 2 2 30 11 ) 10 3 ( 3 11 3 10 3 1 2 3 > > > + + D S s D vege for s s s τ τ τ τ 14.10 (a) Write the characteristics equation for the central system shown (b) Use the routh criteria to determine if the system is stable for Kc=4 © Determine the ultimate value of Kc for which the system is unstable (a) characteristics equation

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0 2 ) 1 ( 3 2 0 ) 2 ( ) 1 2 )( ( 0 ) 1 ( 1 1 2 1 3 2 1 2 3 2 = + + + + = + + + + = + =  + + kc s kc s s s kc s s s s s s kc 0 ) 1 ( 3 3 2 3 = + + + + kc s s s Kc=4Routh array 3 ; 0 3 0 3 4 ) 1 ( 3 3 / 1 8 3 5 2 2 3 = = - = - + - Kc Kc kc kc stable not s
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Unformatted text preview: of instability 14.11 for the control shown, the characteristics equation is ) 1 ( 4 6 4 2 3 4 = + + + + + k s s s s (a) determine value of k above which the system is unstable. (b) Determine the value of k for which the two of the roots are on the imaginary axis, and determine the values of these imaginary roots and remaining roots are real. ) 1 ( 4 6 4 2 3 4 = + + + + + k s s s s...
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Control ENG HW_Part_65 - of instability 14.11 for the...

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