543f682b-eb11-4de1-8975-e2e2ca8c51bc 13 3 5 decimal

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

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

Lead_Lag . . .

Is typical of the most efficient PID for

controlling heat exhangers, associated

with Quick Opening control valve.

Try other fake demo 'u'.

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Lead time
Lag time > Ts
Sampling interval Td 0.5 : Ti 1.375 : Ts 0.5 : 31 sys

j 120 range :

β 0.75 :

u j β^vectorize :

data j 120 range j 1 ≡ Y 1 el 0 : j 2 ≡ Y 2 el 1 : Y j el Y j 1 - el Ts Ti / u j 1 - el Y j 1 - el - (* + Td Ti / u j el Y j 2 - el - (* + : if if for u Y augment 21 line :

Lead_Lag data o 5 black plot :

Lead_Lag x β ^ 2 1 sys

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

Avance [Lead]
Delay [Lag]
Sampling interval
SP setpoint Td 1 : Tg 0.5 : Ts 0.25 : Cs 1.5 : 41 mat

M Cs Cs Cs 2.625 2.5 2.375 2.25 2.125 2 1.875 1.75 1.625 0.5 0.625 0.75 0.875 1 1.125 1.2 1.3 Cs 121 mat transpose :

LEAD n 125 range n 1 ≡ Q 1 el Cs : n M rows ≥ Q n el Cs : Q n el Q n 1 - el Ts Tg / M n 1 - el Q n 1 - el - (* + Td Tg / M n el M n 1 - el - (* + : if if for Q 21 line :

n 1 LEAD rows range : Response n LEAD augment : 21 sys

j 1 M rows range : model j M augment : 21 sys

Model model o 5 red plot : response Response o 5 black plot : 21 sys

LEAD ... observe the blue

Response response Cs Model 4 1 sys

Lead time
Lag time > Ts
Sampling interval Td 0.5 : Ti 1.375 : Ts 0.5 : user 10 : 41 sys

u M :

LAG j 1 u rows range j 1 ≡ Y 1 el u 1 el : j 2 ≡ Y 2 el u 2 el : Y j el Y j 1 - el Ts Ti / u j 1 - el Y j 1 - el - (* + Td Ti / u j el Y j 2 - el - (* + : if if for Y 21 line :

n 1 LAG rows range : Response n LAG augment : 21 sys

j 1 M rows range : model j M augment : 21 sys

Model model o 5 red plot : response Response o 5 black plot : 21 sys

LAG ... observe blue

Response response Cs Model 4 1 sys