Question

A second order process with the transfer function KpGp(s) = 1/S²+2S+3 is controlled with a proportional integral controller. If all the other lags in the control loop are negligible and their steady state gains are equal to unity, find the relation between the parameters of the controller that should be satisfied for the control system to be stable.

Answer 1

$K_pG_p(s) = \dfrac1{S²+2S+3}$

$\dfrac1{S²+2S+3} = 1$

${S²+2S+3}= 1\\ S²+2S+3-1=0\\ S² + 2S+2= 0$

$S =-1-i\\ S = -1+i$