Question

Determine the stability of closed loop control system whose characteristic equation is 

s5+3s4+5s3+4s2+s+3=0​

Answer 1

Answer:

46815*6+6-6*54556/6-+5+5-6---*%/6-66--66-*3*3*-jjjJJ6644545445455445454757544545445454545344346434344

Explanation:

sjsjhshdhdhdhdhdhdhchdhddhdhddhdhdydhedhdhdhehehdueudhdhdudfhdudufighdhhdhggggghhhghhhggtjfjfjjhggg55986644233333363864464644646464644664646465566464644646464644646464464646446464646446464644658858581161616113435626265646165616134611614464623162431262663232

djddjdjjjjjnv56663668597946466464646644313131313119282282826656567676464609066464646867686886868646865646446464646446464646446464644666jjj6464646jjdjsjssjsidjddkdjdjdjfjddjdjdjddjdjdhdjdjrjrfjururhrrurhdudhdhwjdjejrdjdurjdurjdejejdDddddddttt

Answer 2

Given:

• Characteristic equation = $s^5 +3s^4 +5s^3 +4s^2 +s+3 =0$

To find:

• Stability of closed loop control system

Answer:

• This is determined by Routh - Hurwitz Test. To have a stable closed loop control system, all the elements of the first column of the Routh array should have the same sign .
• Routh Array

         $s^5$     1                                5                              1

         $s^4$    3                                4                              3

         $s^3$    $\frac{5*3 - 1*4}{3} = \frac{11}{3}$         $\frac{3*1 - 1*3}{3} = 0$             $\frac{0*3 - 0*1}{3} =0$  

         $s^2$    $\frac{4 *\frac{11}{3} - 3 *0}{\frac{11}{3}} = 4$        $\frac{\frac{11}{3}* 3 - 3*0}{\frac{11}{3}} = 3$            $\frac{\frac{11}{3}*0-3*0}{\frac{11}{3}} = 0$

         $s^1$   $\frac{4*0 - \frac{11}{3}*3}{4} =\frac{-11}{4}$            0                             0

         $s^0$   $\frac{\frac{-11}{4}*3 - 4*0}{\frac{-11}{4}} =3$              0                             0

• As in the first column, all the numbers don't have the same sign. So, the closed loop control system whose characteristic equation is  $s^5 +3s^4 +5s^3 +4s^2 +s+3 =0$  , is unstable.