In reset feedback, the selector output is connected to the input of unity-gain first order lags in each controller. The time constants are the reset times of the controllers. (Click the figure to view an enlarged .pdf.)
ASSUME THAT the left-hand controllers output is selected. Since its output is connected (through the selector) to the reset feedback, it is acting as a normal PI controller. The output of the right-hand controller is the product of its gain-times-error plus the output of the first-order-lag. At steady state, the output of the first-order lag is equal to its input; at other times the first-order-lag output will lag its input. Note that the non-selected controller in Figure 4 below does not wind up.Except for set point changes, the output of both controllers will only change gradually. Therefore, there will never be a bump in the output of the selector device. If the PV of the non-selected controller begins to approach its set point, its output will approach that of the selected controller. At equality, the crossover point is reached. Any further encroachment on the limit will cause a graceful reversal of the roles of the selected and non-selected controller.Similarly, in forced initialization, the output of the selected controller is connected to the reset feedback port of the both controllers. Logic in the selection device detects which is the non-selected controller. For the non-selected controller, this reset feedback immediately passes through (or bypasses) the first order lag (See Figure 4 below). Hence, the output of the non-selected controller is always the output of the selected controller, plus its own gain-times-error.FIGURE 4: FORCED INITIALIZATION OVERRIDE