Integrating processes with inverse response and time delay are frequently encountered in the level control of a boiler steam drum and are difficult to identify and control. In this paper, a systematic approach for autotuning of a proportional-integral (PI) or proportional-integral-derivative (PID) controller is proposed for this type of process. A single run of a biased relay feedback test is carried out to obtain four parameters of the model without any prior information about the time delay or the steady-state gain. Since the exact limit cycle expressions are derived, accurate parameter estimations are achieved. Then, according to the estimated model, an analytical procedure for PI/PID controller design is developed based on H-infinity optimization and internal model control (IMC) theory. The internal stability of the closed-loop feedback system is guaranteed. Moreover, robust stability analysis for the proposed control scheme is provided in the presence of model mismatches. Hence, the best tradeoff between robust stability and nominal performance of the closed-loop system can be achieved by adjusting the controller parameter lambda conveniently. For illustration, simulation examples are given to compare the proposed method with those previously used.