inverted pendulum
There should be some pendulum angle (no matter how small) which the cart can correct for. Hold the pentulum an some angle and put full voltage on the motor while releasing the pendulum to get an idea of what this angle is.
Then the question is how small an error angle can you detect and how fast can you compensate for it.
DC motors can be very nonlinear, especially at lower RPM, there is a non-zero voltage required to overcome friction and movement can be very rough at low speeds.
If the motor has a gear train, looseness in the gears can introduce a potentially unstablizing hysteresis, an appreciable time delay in reversing direction.