In tuning a PID controller for a process in a feedback control system, a method is provided for bringing the system into symmetric self-excited oscillations for measuring the frequency and the amplitude of the oscillations, and tuning the controller in dependence on the measurements obtained. A control algorithm referred to as the modified relay feedback test is introduced into a system in series with a process to generate self-excited oscillations. Tuning includes the steps of selecting a desired gain margin or phase margin, generating oscillations with the algorithm parameter corresponding to a selected gain or phase margin, measurements of the amplitude and the frequency of these oscillations, and computing PID controller tuning parameters. Data and formulas are given for the computation of the specific parameter of the modified relay feedback test and for tuning the parameters of the PID controller. An apparatus for performing the method is disclosed.