The PID controllers of single loop systems are, in general, designed according to FOPDT or SOPDT models which represent the dynamics of open-loop processes. An identification system, which aims to identify such low order models for monitoring and autotuning of PID controllers, is presented. The identification is conducted by compensating the output of the relay feedback loop with a simple compensator laying outside the loop. The objective is to make the compensated output behave like the one from a process consisting of an integrator plus dead time. An on-line mechanism to adjust the compensator is presented, which will lead to the final apparent model. Meanwhile, the optimal performances of PID control associated with low order dynamics are tabulated. Based on the identified model, the performance of the system can thus be assessed. As the identification is implemented in parallel to a relay feedback loop, it is thus feasible for on-line use to monitor the performance of a PID controller in the system. From the control assessment, the control performance can be improved by an autotuning procedure.