7. In the Cartesian coordinate system $x O y$, $P$ is a moving point on the ellipse $\frac{y^{2}}{4}+\frac{x^{2}}{3}=1$, and the coordinates of points $A, B$ are $(1,1),(0,-1)$, respectively. Then the maximum value of $|P A|+|P B|$ is $\qquad$.
Notice that $B$ is one of the foci of the ellipse $\frac{y^{2}}{4}+\frac{x^{2}}{3}=1$. Let the other focus of the ellipse be $C(0,1)$,
$$
\begin{array}{l}
\text { then }|P A|+|P B|=|P A|+2 a-|P C| \\
=4+|P A|-|P C| \leqslant 4+|A C|=5 .
\end{array}
$$

Equality holds when $P, A, C$ are collinear, as shown in the figure. Therefore, the maximum value of $|P A|+|P B|$ is 5.