Counting slow to fast in a microcontroller.(Ramp)

Question

I want to make an increment(++) to a variable initially slowly then speed up linearly. For example, using a timer interrupt(every 1 sec) in increase the variable x by 1.so at first variable get incremented by 1 in 1 sec. Then it should get incremented by 1 in 0.9 sec, then it should get incremented by 1 in 0.8 sec and so on linearly. who to do it?

Fact is that I have a switch case loop function for bldc motor.

    switch(step)
        {
            case 0:
            {
                commutation 1
            }
            break;
            case 1:
            {
                commutation 2
            }
            break;
            case 2:
                {
                commutation 3
                }
            break;
            case 3:
                {
                commutation 4
                }
            break;
            case 4:
                {
                commutation 5
                }
            break;
            case 5:
            {
                commutation 6
            }
            break;
        }
}

I want so run commutation steps one by one inside a timer interrupt.

void Handle_T13()// every 10000ms
{
    step++;
    if(step==6)
     {step=0;}      
}

It works fine. But now I want to increase the speed gradually. so I need to increase the increment of steps gradually. !!!

Answer 1

In your example, you only seem to need 10 ms resolution. In that case, just count 10 ms ticks until the next time to increment the variable. That count decreases by 1 each increment.

Another way is to realize what you are really asking for is a variable that is a quadratic function of time. Increment it much more often than you need, like every 1 ms maybe. The increment is itself incremented a little each time. Put another way, this holds the second derivative constant, so the first derivative is linear, and the value itself is quadratic. Of course this requires carrying extra fraction bits you don't ultimately use when grabbing the final integer.