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Inverse Response (IR) processes are difficult to be identified and controlled due to the presence of right half plane (RHP) zeros. In this paper, relay feedback test is conducted on IR process (a second order system with RHP zero and time delay) resulting from two opposing first - order systems with time delay. On the basis of the shape of the response from relay feedback test, it is found that IR process with time delay initially exhibits relay response in opposite direction with respect to ultimate steady state value. This shape information is very unique for IR process and is used to identify the model structure. The analytical expressions are derived using the relay output response. The model parameters are estimated by solving the analytical expressions using boundary conditions. A single run of relay feedback test is carried out to estimate all the parameters of the model without any prior information. Internal Model Control (IMC) structure based PID controller is designed to carry out the closed loop study. The stability analysis is done using dual-locus diagram. The closed loop performance and the robustness of the proposed scheme for model structure mismatch are also discussed. At last, the effectiveness of the proposed scheme is tested in the presence of measurement noise.