Two closed-loop autotuning methods are developed to provide superior alternatives to tune a proportional-integral-derivative (PID) controller for single-input-single-output systems. The first method is a closed-loop extension of the Astrom-Hagglund autotuner. A relay is connected in the feedback loop to the PID control system to produce a stable limit cycle. On the basis of the resulting oscillations, the process is identified as a first- or second-order plus time-delay model. The second method is a time domain approach, which identifies the process as a second-order plus time-delay model via an underdamped transient. The identification scheme permits the use of any control mode (P, PI, or PID) and any test input signal (step, pulse, or impulse) applied in setpoint. Simple-to-use correlation formulas based on the identified model are derived to provide optimum PID settings which yield the desired decay ratio, robustness, and minimum integral of the absolute error. With an initial stabilizing controller, the two methods allow the control parameters to be adjusted iteratively to the correct values. The proposed methods are demonstrated to be valid for a wide range of process dynamics and insensitive to measurement noise and disturbances.