Question

stability of a closed loop control system whose characteristic equation is s5+s4+2s3+2s2+11s+10=0
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Answer 1

By Routh array s =0 and s =+j. It is having a pair of conjugate root lying on imaginary axis. System is marginally stable.

Solving by Ruth Array,

• $S^{5}$     1      2     11
• $S^{4}$     1      2      10
• S³    ∈      1      
• S²    $\frac{1 -2\epsilon}{\epsilon}$  
• S

As ∈ ⇒ 0 , 1 -2∈ ⇒ 1 > 0

Therefore the system has no sign changes in the first coloumn .

Hence by Routh Array Method the control system is stable.