With flight dynamic equations, how do I return to positive alpha if alpha is always negative with negative w?
I think your problem is in part, that you assume that $w$ is positive if your aircraft is ascending. The opposite is the case. The aircraft coordinate system is defined as a right-handed system with the z-axis pointing downward.

This means a positive $w$ indicates that your aircraft is descending.
Therefore, if your plane keeps a constant velocity $u$, the body-fixed downward velocity $w$ will get positive because of the gravity pulling you down. This in turn results in a positive $\alpha$ providing lift. Eventually if you have implemented your simulation correctly, the $\alpha$-angle (and $w$) will oscillate for a bit at the beginning of your simulation, but after finding the steady-state, it will steadily descend with a positive angle-of-attack and a positive value of $w$.
P.S.: For the calculation of $\alpha$ it is very helpful to use the atan2() function, as it correctly discerns the various sign cases.