Math Is Fun Forum

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 164

Find a Function from Coordinates

The relation between the break time in seconds of an electrical breaker, y=brkTime, and the over-current ratio, x=I_real/I_nominal, is given by the following 6 points (x,y):
(1.03 , 3600)
(1.11 , 1000)
(1.35 , 100 )
(2.07 , 10)
(4.16 , 1)
(7.0 , 0.39)

Is it possible to find an analytical function, y=f(x), whose curve could be close to the one given above?
Thank you.

Last edited by KerimF (2023-11-15 09:46:47)

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 164

Re: Find a Function from Coordinates

I am 74. Lately, I write an MCU code (actually for ATmega8). And one of its algorithms is about emulating the response of a mechanical breaker (to cut a current when overload).

I thought I may gain time in asking for help. But I also understand that it may not be an easy exercise to most members.

For instance, I used to ask for technical help to also stimulate my brain's cells while some others may think with me about it (much like creating a virtual race... in which I may be the only racer).

So far, it is somehow obvious that f(x) here should have (x-1) in its denominator. And it should have two parameters, in the least, whose values let its graph be close to the breaker's response one.

I will be back when I will find a good f(x), unless someone will do it faster than me.

Good luck

Bob

Administrator

Registered: 2010-06-20

Posts: 10,190

Re: Find a Function from Coordinates

hi KerimF

I plotted x against LOG(y) in Excel and it looks like a negative power exponential. I've got to go out now so I'll come back later and, if needed, start trying an exact fit.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 164

Re: Find a Function from Coordinates

hi KerimF

I plotted x against LOG(y) in Excel and it looks like a negative power exponential. I've got to go out now so I'll come back later and, if needed, start trying an exact fit.

Bob

Hi Bob,

Thank you for replying.
My Excel is very old (2007) and its options of trendline are somehow restricted.
I try to figure out the possible general form of f(x) in order to calculate its parameters for this special graph.

Kerim

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 164

Re: Find a Function from Coordinates

So far, it seems there is no continuous function for f(x) whose curve could be made somehow close to the breaker's one.

I guess, a practical solution in this timing case could be the use of a piece-wise function.

Regards,
Kerim