Plant model does not have an integrator in it, so you need an integral term to achieve zero steady-state error. In other words, if the controller is simply Kp, closed loop transfer function in Kp*K/(1+Kp*K). For Kp=1/K, closed loop transfer function is 1/K*K/(1+1/K*K)=1/2=0.5.
To get zero steady state error you need to add an intergral control. Integral control is all you really need in this case. Hope this helps.
