The ultimate sensitivity method ( Figure 300-24) is also a closed loop test. Adjust the integral time and/or the derivative time to their minimum values. Then narrow the proportional band (increase gain) in small steps, each time changing the setpoint as described in Section 351, until the controller measurement just begins to cycle continuously. This proportional band setting is called the ultimate proportional band, denoted “PBu.” The period of oscillation at the ultimate proportional band is called the ultimate period, measured in minutes and denoted “Pu.” The amplitude of the oscillations in Figure 300-24 has been exaggerated for clarity.

The ultimate proportional band, PBu, and the ultimate period, Pu, are then used to calculate tuning constants as shown in Figure 300-25. These constants give the quarter damping response already discussed.

Note that Figures 300-25 and 300-26 show two sets of equations for a proportional plus-integral-plus-derivative controller. The set identified as “Commercial” should be used for controllers encountered in industry. The set identified as “Ideal” is based on an ideal control algorithm equation commonly used in universities. They are included here for completeness.