Aim
The purpose of this loop is to maintain the pressure in the combustion chamber within a narrow band around the set point to ensure satisfactory combustion as well as safe operation.
Philosophy of control
In boilers with forced and induced draft fans, a balanced draft must be maintained so that the pressure in the combustion chamber remains around 0. This is achieved by adjusting the control element in the induced draft fan to increase or decrease the suction. The simplest control method is shown in Figure 3-71, where the combustion chamber pressure is used as the process variable, with the setpoint being the desired pressure value.
This type of control is usually inadequate in most cases. The combustion airflow is managed by the greater or lesser contribution of the forced-draft fan. Every time the airflow changes, a change in the combustion chamber pressure occurs. Furthermore, combustion chamber pressure is a variable subject to a significant amount of process noise, which in principle should be adjusted with low gain and integral to minimize the effect of this noise. This creates further problems in the response to load changes, as these entail modifications in the airflow.

Figure 3-71. Shot Control
To solve this last problem, a regulator with variable gain is usually used, so that the gain is small when the error remains within certain limits and increases substantially when the error exceeds them.
Additionally, to solve for the correct response to changes in airflow, the demand on the control element is used as an index of the position of the induced draft fan and corrected for the pressure error (Figure 3-72).

Figure 3-72. Shot control with variable gain and feedforward
This design allows the controller to be considerably slow without reducing the effectiveness of the loop and reducing the effect of noise, which generates greater stability.
Since both fans work in parallel, the interaction between them is significantly reduced.
As we have seen in other sections, if there are two induced draft fans, the control output must be split according to the weight of each fan. Furthermore, the loop must be prepared for situations where one of the fans fails in terms of gain (Figure 3-73).

Figure 3-73. Automatic compensation of the number of fans
Although the behavior of this design may be sufficient to maintain the home pressure at the desired value, since malfunction of this loop can lead to serious safety risks to the integrity of the boiler and people, the NFPA standard for boilers with more than one burner requires an even more complex design (Figure 3-74).
According to this standard, the system must include the following features and functions:
– Three pressure transmitters to minimize the possibility of working with an erroneous pressure measurement.
– An anticipatory signal representing the air demand. This signal could be the air demand, flow rate, or boiler load, but in no case the air flow rate (since this would create interaction and positive feedback problems).
– A corrective action that minimizes pressure excursions after auto/manual station.
– An anticipatory action in the event of a boiler trip that minimizes pressure excursions after the auto/manual station.
– When axial fans are used, they must be operated in such a way as to avoid stall conditions.

Figure 3-74. NFPA 8502 Requirements
One possible design incorporating these needs is shown in Figure 3-75. The system receives signals from three different transmitters and performs a two-out-of-three vote on their measurements. This vote can be a choice of the mean (Figure 3-76), in which case the signals are compared two by two, the smaller value is selected, and the output of these three comparisons is compared again, selecting the larger value this time. Another possible voting method is to average the signals two by two and then select either the larger or the average (Figure 3-77). In this case, the two-out-of-two average will only be valid for comparison when there is no excessive deviation between the transmitters. In both cases, deviation alarms must be triggered to meet the variable monitoring requirement.
The signal from the transmitters is sent as a process variable to the variable gain controller, whose output is corrected for the two required factors. In the first case, when an MFT boiler trip occurs, the furnace cools and a negative pressure develops. To minimize its effects, a ramp will be implemented from the current airflow to zero, which will correct the controller's output in the direction necessary to reduce the draft.
The second correction must be made when the error exceeds certain limits. This correction can be made either by adjusting the position, as shown, or by limiting the opening or closing of the control element. In this case, using a function generator and based on the error, the system generates a corrective signal that acts in the opposite direction to the error.

Figure 3-75. Shot control including implosion protection
Interlocks
In addition to the interlocks inherent to the fan start-up sequence in relation to its dampers, when the furnace control is switched to manual, the air, oxygen, and fuel flow controls must also be switched to manual.

Figure 3-76. Selection of the medium transmitter

Figure 3-77. Two out of three voting in transmitters
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Hello
Could you share the mathematical modeling for the boiler pressure control loop with the fan?