Which transformation I can apply on $~f(\frac{1}{x})~$ to get linear output with respect to $~x~$ ?
Basically I want to control stepper motor. Stepper motor driver generally work based on number of steps. Speed is directly proportional to no of steps per second.
I can generate no of steps by changing PWM signal. But actually I will control time between no of turns(pulse). So delta time and frequency are inversely proportional to each other.
Please provide a solution which does simple mathematics so that I can execute it on small micro-controllers.
The speed of the robot would be $v = \frac{\Delta s}{\Delta t}$, where $\Delta s$ is the distance traveled during a time $\Delta t$. Since $\Delta s = N s_0$, where $N$ is the number of steps and $s_0$ is the distance of a single step, we have $v = s_0 \frac{N}{\Delta t}$. The number of steps is equal to the number of pulses, therefore $\Delta t = N t_0$, where $t_0$ is the time between two pulses. We end up with $v = \frac{s_0}{t_0} = s_0 f$, where $f$ is the frequency. Thus the time between pulses $t_0$ needed to achieve the velocity $v$ is given by $t_0 = \frac{s_0}{v}$.