Currently, I'm working on a battery analysis system. For now, I have this transfer function:
$$\frac{V_L(z)}{I_L(z)} = \frac{\left(\frac{V_{oc}}{I_L(z)}\right) +b_0 - b_1z^{-1}}{a_0 - a_1z^{-1}}$$
Where:
- $V_L$ is terminal voltage
- $I_L$ is load current
- $V_{oc}$ is estimation of battery voltage while open-circuit
- $a_0$, $a_1$, $b_0$, and $b_1$ are constants
We are not talking about physics property of the battery, but we're focusing on transfer function mathematically. The problem is how do I get rid of $\left(\frac{V_{oc}}{I_L(z)}\right)$ and make a valid transfer function?