Consider the furnace shown in Fig. P12-7, which consists of two sections with one common stack. In each section the cracking reaction of hydrocarbons, C,‘s and C,‘s, with steam takes place. The temperature of the products in each section is controlled by manipulating the fuel to the particular section. The pressure in the stack is controlled by manipulating the speed of a fan installed in the stack. This fan induces the flow of flue gases out of the stack. As the pressure in the stack increases, the pressure controller speeds up the fan to lower the pressure. (a) Design a control scheme to ratio the steam flow to the hydrocarbon flow in each section. The operating personnel set the hydrocarbon flow. (b) During the last few weeks, the production personnel have noticed that the pressure controller’s output is consistently reaching 100%. This indicates that the controller is doing the most possible to maintain pressure control. However, this is not desirable because it means that the pressure is really out of control-not a safe condition. A control strategy must be designed
such that when the speed of the fan is greater than 90%, the flow of hydrocarbons starts to decrease to maintain the fan speed at 90%. As the flow of hydrocarbons decreases, less fuel is required to maintain exit temperature. This in turn reduces the pressure in the stack, and the pressure controller slows down the fan. Whenever the speed is less than 90%, the feed of hydrocarbons can be whatever the operating personnel require. It is known that the left section of the furnace is less efficient than the right section. Therefore, the correct control strategy to reduce the flow of hydrocarbons calls for reducing the flow to the left section first, up to 35% of the flow set by the operating personnel. If further reduction is necessary, the flow of hydrocarbons to the right section is reduced, also up to 35% of the flow set by the operating personnel. (If even further reduction is necessary, an interlock system would then drop off line the furnace.) Design the control strategy to maintain the fan speed below 90%.
(c) If the flow of hydrocarbons changes, the outlet temperature will deviate from set point, and the feedback controller will have to react to bring the temperature back to set point. This situation seems a natural for feedforward control. Design this strategy for each section