Question

Determine the stability of closed loop control system whose characteristic equation is s5+3s4+5s3+4s2+s+3=0

Answer 1

Answer:

The system of equation is always stable.

Step-by-step explanation:

CE=$S^{5} +3S^{4} +5S^{3} +4S^{2} +S+3$

Apply Routh Array method:

$S^{n}$ $a_{0} a_{2} a_{4}$ .........

$S^{n-1}$$a_{1} a_{3}a_{5}$.........

$S^{n-2}$$b_{1} b_{2} b_{3}$.............

here $b_{1} =a_{1} a_{2} -a_{0} a_{ 3}$  /$a_{1}$

       $b_{2}$  =$a_{1} a_{4}-a_{0}a_{5}$  /$a_{1}$

$S^{5}$ 1 5 1..................

$S^{4}$ 3 4 3...............

Here in the first column,the sigh is always positive.Therefore The system is always stable.