db379bd3-1517-427a-a0e6-a0ffb1e0f03d 14 4 5 decimal

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The classical 2nd order system

α 1.25 :

β 0.5 :

K.p 1 :

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

start 0 : end 10 : 12 mat

UnitXFR t start end start 0.05 + (range : i 1 t rows range X i el t i el : Y i el t i el XFR eval : 21 line for X Y augment 31 line :

Δ 0.25 :

N end start (- Δ / : 40

UnitXFR t 0 N range x t 1 + el t x : y t 1 + el t y : 21 line for x y augment 21 line :

t x Δ t * :

t y Δ t * XFR eval :

τ 0 N range :

xfr t x t y + 100 red 15 mat :

The classical XFR of a 2nd order "open loop" under UnitStep. XFR is the response in time 't' of an open loop under UnitStep [0/1] w/o [without] oscillation, i.e: solution of the Laplace Algebra.

UnitXFR xfr 2 1 sys