PI compensator question
First: $$Q = 1/s$$ is only an integral, not a PI. You want $$1 + \frac{1}{T_is}$$ so that your compensator is given by

$$
PI(s) = K + \frac{K}{T_is}
$$

and you actually have some way to tune both terms independently. The CLTF is then 

$$H_{CL}(s) = \frac{PI(s)P(s)}{1+PI(s)P(s)}.$$

Since the overshoot will be determined by the damping of the complex poles, you need to find the root locus of $$1+PI(s)P(s)$$ and choose some value for K which minimizes the damping; the root locus can be overlayed with lines of constant damping ratio to make it easy to see which roots are within your allowable range. SISOtool in Matlab makes this pretty easy to do.