603a0f96-36fa-43bf-921f-e3ab97d097a9 10 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

An 'n' stages system

The classical 2nd order system

n 9 :

T 1 :

α 1.25 :

β 0.5 :

K.p 1 :

==================== XFR [Transfer Function] =======================

XFR of 'n' multistage system of
=  Unit Time Constant [1] t nth 1 t - T / exp 1 k! / t T / (k^* (k 0 n sum * - :

XFR of the 2nd order classical system:
Kp [Process gain], α,β [Dynamics] t XFR K.p 1 α β α - (/ t - α / exp * + β β α - (/ t - β / exp * - (* :

==================== Reaction Rate =======================

Reaction rate of the nth system t Laplace t n 1 - (^n 1 - (! / t - T / exp T n^/ * :

Reaction rate 2nd order x XFR x diff K.p x β / - exp x α / - exp - (* β α - / ≡

x nth x Laplace 2 1 sys x XFR x XFR x diff 2 1 sys

Source: Inst_PID Discrete Schema