This article classifies the process dynamics involving one or two unstable poles into three types, which are of paramount importance in controller design. Necessary and sufficient conditions are addressed for gain and relay stabilizability of such dynamics. Two nonlinear elements, one being a relay, are employed to excite rich input-output data for identification. A procedure is then developed to identify an unstable delayed model of appropriate order(second or third order), followed by the optimal PID controller design established based on the weighted ISE index. The resultant controller can cope with both loaddisturbances and set-point changes simultaneously and provide good robustness by satisfying the maximum gain margin criterion. The method is tested with good results on a nonlinear CSTR process.