math - matlab PID controller, SISO tools gives a "pid" with s^2 in the denominator -

when try use sisotool in matlab, gives me equation pid controller

0.056301 * (1+1000s)            s(1+4.2s) 

this means equation comes out s^2 in denominator. not equation pid.

i don't understand that. mean pid not exist system?

does mean pid not exist system?

no, doesn't.

textbooks introduce transfer function of pid controller using expressions like

c(s) = kp + ki/s + kd*s

for simplicity , emphasise conceptual aspects. however, pure differentiation useful term. can see both in time , frequency domain. s increases, last term above increases without bound. in time domain, last term differentiate not useful signals, noise in input of pid controller. recall happens when differentiate sin or cos: frequency @ front coefficient. anyway, these 2 aspects of same phenomenon. so, next step start designing more practical pid replace term kd*s filter of form

kd*a*s/(s+a)

if sum terms in c(s) filter substituted kd*s s^2 in denominator.

the control toolbox in matlab quite developed (at least linear systems). wouldn't dismiss results gives. on other hand, scrutinise them.