What controller is this?
To earn the 'I' it has to have a bare \$s\$ in the denominator, i.e. \$\frac{k_i}{s}\$.  It's either a lag-lead or a lead-lag, depending on whether \$z\$ is bigger than \$p\$ (lag-lead) or the other way around.  If \$p\$ is very small compared to the process dynamics (i.e., if \$p\$ is 0.01 times or less the loop closing frequency) then some folks may call it a 'leaky integrator' -- I really don't like that term, though.