ff582084-c1d2-47ac-857f-79a58edb05e3 7 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 :

Recursive behaviour of a 2nd order homogeneous system

a 0.894839 - :

b 1.790648 :

c 0.104191 :

ε 1 :

a b + c + 1

Title 2 0.375 - response 2nd order under unit forcing [ε] 11 black 15 mat :

system s 1 el 0 : s 2 el 0 : n 3100 range s n el a s n 2 - el * b s n 1 - el * + c ε * + : for i 1 s rows range x i el i : for x s augment 51 line :

CWD C:\SmathFile CurrentDirectory :

system CWD 2ndorder wfile 1

system CWD 2ndorder rfile :

a b c spec o 5 blue 13 mat : sys2nd system a b c spec pts : 21 sys

The a+b+c = 1 is a particular property of a 2nd order correctly modeled for recursive. Observe that the system recovers more quickly with smaller [ε]

In the control room, operators have long learned how to minimise overshoot from changing SetPoint brutally. Instead, they ramp or move SetPoint slowly. Here is the 'ramping' response, scaled wrt the 'm = 40' & 'sp =60' of this typical demo. Observe the ramped SetPoint settles a bit faster than the UnitStepPoint.

m 40 :

<= 'm' ramp length

sp 60 :

<= SetPoint final

X j 1 m range X j el j 3 / : for X 21 line :

U j 1 sp range U j el X X rows el : for U 21 line :

Exact track a 0.894839 - : b 1.790649 : c 0.104191 : 31 sys

User track a 0.8 - : b 1.7 : c 0.1 : 31 sys

vx X U stack :

ramp s 1 el 0 : s 2 el 1 : n 3 vx rows range s n el a s n 2 - el * b s n 1 - el * + c vx n 2 - el * + : for i 1 s rows range x i el i : for x s augment 51 line :

scale 1 vx max / :

scale 0.075 :

X ramp 1 col :

Y ramp 2 col scale * :

rampOUT X Y augment : a b c spec . 10 black 13 mat : OUT rampOUT a b c spec pts : 31 sys

Line ramp 1 col vx scale * augment : a b c spec o 4 red 13 mat : ramp Line a b c spec pts : 31 sys

Title 16 0.2 damped 2nd order under ramped forcing 11 black 15 mat :

UnitStep & ramp SetPoint 2nd order response Under no control, the free 2nd order oscillates violantly. Such violent oscillations may be detrimental/dangerous to the plant. So, if production requires some different operating point, Control Room operators must cope with some sort on cotrol algorithm to bring the plant operation back to stability under minimal perturbation. The ramped setpoint SP is a valid control scheme, easy to implement.

sys2nd ramp Title OUT 1 m 1 + 100 green 1 5 mat 6 1 sys

Explain experiment . . .

oooooooooo is a 2nd order system reaching stability by itself .

oooooooooo is a ramped setpoint assigned by the Control Room Operators .

............... is the balistic stability under UserTrack [a, b, c] .

..................................................................................................

As presented, the demo project is fixed. It can be modeled otherwise.

At each loop scan, the ramp values are passed to the controlling element.

The response is the black balistic. This sytem is a NON-feedback loop.

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