<p> OUT </p>

b4105c18-b814-47fa-bb32-2db7d373e2fe 9 3 5 decimal

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

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

P 0.875 :

I 0.5 :

D 0 :

[D,± 0.5] demo values

Example: 1

m 30 :

<= 'm' duration SetPoint initial

sp 30 :

<= 'sp' length SetPoint final

xx j 1 m range xx j el 1 : for xx 21 line :

uu j 1 sp range uu j el 0.5 : for uu 21 line :

XY u xx uu stack : j 1 u rows range v j el j : for v u augment 31 line :

u xx uu stack :

XY XY :

P 0.75 :

I 0.25 :

Too much 'I'[>1.75] goes haywild, crashes Smath !

D 0.25 :

[D,± 0.5] demo values

step 0.5 :

OUT Y 0 : CPV recursive PID Y 1 el 0 : Y 2 el step u 1 el * : i 3 u rows range Y i el Y i 1 - el P u i el u i 1 - el - (* + I u i 1 - el Y i 1 - el - (* + D u i el 2 u i 1 - el (* - u i 2 - el + (* + : for i 1 Y rows range x i el i : for x Y augment 71 line :

a b c spec . 10 black 13 mat : sp XY a b c spec pts : 21 sys

a b c spec . 8 blue 13 mat : algo OUT a b c spec pts : 21 sys

Title 16 1.375 The balistic CPV PID 11 black 15 mat :

algo sp Title m 1 + 250 red 1 5 mat 60 0.5 + 50 red 1 5 mat 5 1 sys

This much simpler CPV needs less 'Z' accumulated initial values, recovers faster, NO overshoot. Most industrial controllers are of this CPV type. In this example, derivative mode 'D = 0'. Y1, Y2 = 0 ... the system at rest is stable, the last two accumulated 'Y's' are '0' [no output]. For faster response, take 0.5 the step change.

XY rows OUT rows 21 mat 606021 mat

The classical exponential smoothing

'α' smoothing factor α 0.25 :

XY 171270369468564665772878975107511751270122 mat :

X XY 1 col : Y XY 2 col : 21 line 11 mat

x c 10 x ≤ (x 13 ≤ (& cases :

Exponential smoothing [input] S S 1 el Y 1 el : j 2 XY rows range S j el α Y j el * 1 α - (S j 1 - el * + : for X S augment 31 line :

vx S 1 col : vy S 2 col : 21 line

n Predict vx vy n cinterp :

a b c spec o 5 black 13 mat : input XY spec pts : smooth S spec pts : 31 sys

If you need 'D' in the PID mode, a window of 3 smoothed inputs is required.

plot XY S input smooth 41 sys :

Exponential smoothing of input data

plot 1 1 sys smooth x Predict x c * 2 1 sys