Closed Loop Transfer Function - PD Control
To find the \$K_p\$ value that leads to less than a 15% Overshoot for the system. we can use the root locus plot, by looking at the position of the dominant poles (the two closer to the imaginary line). I have also added the sgrid lines showing the \$\zeta\$ and \$\omega\$ positions. Using the formula that
$$ \zeta \geq \frac{-\ln(PO/100)}{\sqrt{ \pi^2 + \ln^2(PO/100) }},$$
we have that 
$$ \zeta \geq \frac{-\ln(15/100)}{\sqrt{ \pi^2 + \ln^2(15/100) }}= 0.517.$$
So, by positioning the poles below that 0.55 damping line should get you the overshoot to meet your requirement. Therefore, for a gain in \$K_p \in [-1,2]\$ you would meet that requirement. (the image looks horrible, but if you click on it it gets slightly better)