The procedures for determining the complete sets of stabilising proportional integral derivative (PID) controllers are presented for three classes of second-order integrating processes with time delay. The necessary condition for the PID controllers to stabilise second-order integrating processes with time delay is first derived in the case where frequency, ω, equals zero or infinity. On the basis of the extended Hermite–Biehler theorem, analytical formulas are provided to determine the admissible ranges of the proportional gain (kp), integral gain (ki) and the derivative gain (kd), respectively, and the complete set of stabilising PID controllers is found by sweeping over the entire range of allowable kp values. The stability analysis on the basis of the extended Hermite–Biehler theorem shows that the stability boundary in the controller parameter space depends only on the frequencies in the defined small range. In view of this, the sets of stabilising PID controllers are also determined by sweeping over the admissible ranges of kd and ki, respectively. As a result, for a given second-order integrating process with time delay, the complete set of stabilising PID controllers can be determined by sweeping any one of the PID parameters over the corresponding admissible range.