Question

Using pid controler closed-loop transfer function c(s)/r(s)=kp/s(s+1)(s+5)+kp b) the characteristic equation for the closed-loop system is

Answer 1

The characteristic equation is :
`s^(3) + 6s^(2) +5s +k_(p)  = 0`

Explanation:

The transfer function is c(s)/r(s)=kp/s(s+1)(s+5)+kp

The denominator of the transfer function is known as characteristic equation,

so the characteristic equation is : s(s+1)(s+5)+kp = 0

Multiplying the terms and adding respective terms, we get the characteristic equation as :

`s^(3) + 6s^(2) +5s +k_(p) = 0`