In this paper critically damped system is identified using online relay feedback test. Relay test comprises of a PID controller connected in parallel with the relay. Limit cycle information ultimate gain and frequency are used for the identification process. The objective of the proposed method is to identify an nth order critically damped system with the same order. Simple expressions for the process parameters are derived which can be used for higher order critically damped systems. The proposed identification method is tested with different examples. Identification is also done under load disturbance using DIDF (Dual input describing function). © 2016 IEEE.