The process parameters for first-order-plus-dead-time (FOPDT) and second-order-plus-dead-time (SOPDT) stable processes are obtained using relay feedback test with the help of dual input describing function (DIDF). The limit cycle data is used to identify the unknown process parameters. This paper presents identification of stable FOPDT and SOPDT process for the cases with and without load disturbance. The relay settings are unchanged during load disturbance. The bias caused due to load is incorporated in the relay approximation using DIDF. This is used to obtain the parameters for both the cases. An on-line relay feedback test using a proportional integral and derivative (PID) controller is performed to obtain the unknown parameters. © 2016 IEEE.