It is a non-trivial task to maintain the temperature in the reactor for various forcing functions (as defined by the rate at which the formaldehyde enters the reactor), much less to ensure the process proceeds efficiently (maximum hexamine production with minimal waste in ammonia and formaldehyde). The current industry standard for controlling a process like the production of hexamine is a proportional-integral-derivative (PID) controller. Although a PID controller can be used to maintain the reactor temperature, it cannot be used to “optimize the process.” The GA-driven FC, on the other hand, is capable of both maintaining control of a process and ensuring that it runs at a near-optimum level.

The architecture presented in the previous chapter is used here. The adaptive GA-FC simultaneously utilizes the process control capabilities of fuzzy logic and the search capabilities of GAs. While a FC is manipulating the hexamine system, a GA is searching for improved membership functions (to be used by the FC) to accommodate the changing process dynamics. Once a computer model of the hexamine system has been developed and a crude FC has been written, a GA is employed to produce an efficient, robust, adaptive controller.

14.3 An Adaptive Hexamine GA-FC

At this point, most of the groundwork is laid for the development of an adaptive hexamine GA-FC. The mechanics of a GA were introduced earlier in the book, and the basic coding scheme that will be used has been described and used in the preceding chapter. Before the adaptive capabilities supplied by the analysis and learning elements are discussed, the control element must be developed. Recall that the control element is a basic FC, and is constructed based on the fundamentals of FCs set forth in Part I of this book.

14.3.1 Control Element

The FC used rules of the form:

where the condition portion of the rules included information concerning the current status of the flow rates of ammonia, formaldehyde, and water (q_A, q_F, and q_w) and the temperature in the tank (T). The action portion of the rules contain instructions for adjusting q_A and q_w. Notice that q_A and q_F appear in both the condition and the action portions of the rule. This is not a typographical error; the values of these flow rates are the controls and thus appear in the action portion of the rule. However, since there are limitations on the amount these values can change, the current flow rates affect the decision that is ultimately made, and thus appear in the condition portion of the rules.

Five linguistic terms were used to characterize T, and q_A, while four were used for q_F, and three were used for q_w. The action variables, q_A and q_w, were characterized by seven linguistic terms each. As a consequence of the above decelerations, the FC was composed of 300 rules (5 * 5 * 4 * 3 = 300), a result of the inclusion of all possible combinations of the condition variables as described by the chosen linguistic variables. A standard center of area method was used for defuzzification.

Figure 14.2  The control element can be used independently of the analysis and learning elements to effectively control the hexamine system when the process dynamics are not changing.

The non-adaptive hexamine FC produced using the above guidelines can be used without adaptive capabilities to effectively control the hexamine system — until the system becomes dynamic, i.e., until the concentrations of the reactants are altered. Figure 14.2 shows the performance of the FC for a situation in which the hexamine system is not experiencing changing system dynamics. Certainly, the FC of the control element performs well when the process dynamics remain constant. However, when the system dynamics are altered (e.g., when the concentrations of the reactants are altered) the performance of the non-adaptive controller is not optimum, because the non-adaptive FC has no mechanism to accommodate the changes in system response caused by the changing concentrations.

14.3.2 Analysis Element

The changing system dynamics in the hexamine system can be accounted for by allowing the FC to alter its conception of the terms used in its rule set, or by changing the rules themselves. This is accomplished by altering the membership functions associated with the action and control variables in response to changes in the hexamine environment. Here, this task is accomplished with analysis and learning elements.

The analysis element is charged with the task of identifying when and to what extent the process dynamics change. As seen in the previous chapter on the pH system, this can be accomplished by employing a GA to tune the parameters of a computational model of the physical system. The parameters are adjusted so that the response of the simulated system matches the response of the actual system. In the current hexamine system, the coding scheme and the fitness function required by the GA to successfully complete the curve-fitting problem are the same as were set forth in the pH system of Chapter 14. The computational model that was presented in the previous section performed acceptably.