I know there are multiple ways of discretizing a continuous system. In many occasion, I needed a discrete model for a simple first order system (RC circuit, inertial load, etc.) and most of the times I just went by intuition and converted it to something that ended up being an exponential averaging filter. I realized that I knew no formal method of passing from the continuous representation of the system to its discrete version that I just made by intuition.
Here's the approach I usually do. Consider a simple RC circuit with $$ i=\frac{V_R}{R} = \frac{V-V_c}{R} =C\frac{dV_c}{dt} $$ Rearrange and we get $$ dV_c = \frac{V-V_c}{RC}dt$$
Then I take that as is and make model like that
with $\tau=RC$, this would have the following discrete transfer function
$$ H(z) = \frac{T_s/\tau}{1 -(1-T_s/\tau)z^{-1}} $$
Which is, from what I know, an exponential averager with $\alpha = T_s/\tau$
Now. My problem is that I don't know what mathematical method can transform the continuous version of the RC circuit to what I modeled.
$$ \frac{1}{\tau s+1} \Rightarrow?\Rightarrow \frac{T_s/\tau}{1 -(1-T_s/\tau)z^{-1}}$$
I used Matlab to look at these methods : zoh, impulse invariance, foh, tustin, least-square. None gives exactly this result.
What's the name of the discretization method I used by intuition (if any)?