How to get inverse function of x-sin(ax)

Asked Mar 02 '24 at 14:50

Active Mar 02 '24 at 14:50

Viewed 27 times

$f(x)=\frac{x}{2}-\frac{sin(200πx)}{400π}$

I'm not a mathematician. I'm making a heater which uses this formula to calculate the watt of given x. The problem is I need inverse of this function between (0 and 0.01) to use in PID algorithm. I couldn't get inverse of it so I asked Wolfram Alpha which told me that it doesn't have a closed mathematical form. I know that functions can be represented as Taylor Series so is it possible to get inverse of this in terms of Taylor Series?

asked Mar 02 '24 at 14:50

Taner Caslaman

1

See Kepler equation – Тyma Gaidash Mar 02 '24 at 14:53
The most practical way would be to implement a straightforward numerical scheme to compute the inverse function. Computationally it certainly is much simpler and efficient than any closed form formula, which probably does not exist. – uniquesolution Mar 02 '24 at 14:53
Sorry that I didn't mention but I cant use computation since this function actually takes milliseconds as parameter so I cant use time consuming methods. – Taner Caslaman Mar 02 '24 at 14:58

How to get inverse function of x-sin(ax)

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