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RH Stability Webpage - Chapter 6 Algebraic Criterion for...

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Chapter 6 Algebraic Criterion for stability
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Stability of a system: bounded input produces bounded output In the absence of input output tends to zero
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C R G GH = + 1 1+GH = 0 is called the characteristic equation of the system. Its roots are the closed loop poles. If the real part of closed loop poles are in L H P, stable response
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unstable stable
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Second order : as 2 + bs + c = 0 product of roots = c a sum of roots = - b a Both the roots will have negative real part only when a, b, c are of the same sign. first order : s + α = 0 s = - α , If α is positive, stable condition
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Therefore necessary and sufficient conditions for negative ness of real part is all coefficients must be non zero and of the same sign. First & Second order: If the order of the system is more than two…. The condition is necessary but not sufficient.
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s 3 s 2 s 1 s 0 a 0 a 2 a a a a a 1 2 0 3 1 - 0 a 1 a 3 a 0 s 3 + a 1 s 2 + a 2 s 1 + a 3 = 0 b a a b 1 3 1 1 0 - . = =b 1
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After completing the table, look for sign change in FIRST COLUMN.
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