1abb1b5a-2818-4300-9520-dab6b9dbdf55 3 3 5 decimal

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

System response 2nd order NON-homogeneous

a1 y t 2 diff * b1 y t diff (* + y + a2 x t 2 diff * b2 x t diff * + x + ≡

a1 4 :

b1 1 :

a2 2 :

b2 0.5 :

Δt 0.5 :

c1 c2 c3 c4 c5 51 mat 2 a1 * b1 Δt * - 2 a1 * b1 Δt * + / (- 4 a1 * 2 Δt 2^* - 2 a1 * b1 Δt * + / 2 a2 * b2 Δt * - 2 a1 * b1 Δt * + / 4 a2 * 2 Δt 2^* - 2 a1 * b1 Δt * + / (- 2 a2 * b2 Δt * + 2 a1 * b1 Δt * + / 15 mat transpose : 0.882 - 1.824 0.441 0.882 - 0.5 51 mat

c1 c2 c3 c4 c5 51 mat sum 1

n 100 :

i 0 n range :

Set Point SP 1 :

initials y 1 el 0 : y 2 el 1 : 12 mat

Null 0 c4 2 c5 * + (* 0 c5 * + :

1. recursive simulation algorithm ... shrink/expand from Δt.
2. a1 sets the amplitude ... increasing Δt increases overshoot. j 0 n range f j 1 + el 0 j y 1 el ≡ 0 j y 2 el ≡ c1 f j 1 - el * c2 f j el * + c3 c4 + c5 + (SP * + Null + cases : for

simul i f augment :

'SP' set point

shrink/expand from Δt

simul SP 2 1 sys

a1 b1 a2 b2 14 mat real a1 0 ≠ (& (≡

simul 2 col Max 1.446

y i el c1 y i 2 - el * c2 y i 1 - el * + c3 x i 2 - el * + c4 x i 1 - el * + c5 x i el * + ≡

y i el c1 y i 2 - el * c2 y i 1 - el * + c3 c4 + c5 + (x i 2 - el * + c4 2 c5 * + (Δx i 1 - el * + c5 ΔΔx i el * + ≡