PLCs and Fuzzy Logic (5)

Fuzzy Processing

During fuzzy processing, the controller analyzes the input data, as defined by the membership functions, to arrive at a control output. During this stage, the processor performs two actions:

• rule evaluation
• fuzzy outcome calculation

Rule Evaluation. Fuzzy logic is based on the concept that most complicated problems are formed by a collection of simple problems and can, therefore, be easily solved. Fuzzy logic uses a reasoning, or inferencing, process composed of IF…THEN rules, each providing a response or outcome.
Basically, a rule is activated, or triggered, if an input condition satisfies the IF part of the rule statement. The triggering of the IF part of the rule results in a control output based on the THEN part of the rule statement. In a fuzzy logic system, many rules may exist, corresponding to one or more IF conditions. A rule may also have several input conditions, which are logically linked in either an AND or an OR relationship to trigger the rule’s outcome. Different fuzzy logic controllers have different rule evaluation capabilities. Some can process more rules, inputs, and outputs than others.
Sometimes, more than one rule is triggered at a time in a fuzzy control process. In this case, the controller evaluates all the rules to arrive at a single outcome value and then proceeds to the defuzzification process. For instance, if two inputs are logically ANDed or ORed in several rules, then they will produce several outcomes, of which only one will be logically added to determine the final outcome. Figure 7a illustrates an example of two fuzzy inputs, X1 and X2, and one fuzzy output, Y1. The rules shown in Figure 7b represent four of nine possible rules that cover the two inputs. The four shown, however, cover the four possible triggering points for the two input value readings, X1 and X2. Given the input values in Figure 7a, the inputs will trigger rule 1 because X1 = ZR AND X2 = NL. This will generate two outputs for Y1 = NL. One output will be at a grade of 0.6 (due to the ZR input value of X1), and the other will be at a grade of 0.75 (due to the NL input value of X2). In a fuzzy logic situation where a two-input rule with an AND relationship produces two outcome values, the controller will choose the outcome with the smallest grade, in this case 0.6NL.
If the rule utilizes OR logic, the chosen outcome will be the one with the largest grade. If rule 1 had used an OR function instead of an AND function, then the controller would have selected the Y1 = 0.75NL outcome, the largest of the two outcomes. Fuzzy Outcome Calculations. Once a rule is triggered, meaning that the input data belongs to a membership function that satisfies the rule’s IF statement, the rule will generate an output outcome.
This fuzzy output is composed of one or more output membership functions (with labels) that have grades associated with them. The outcome’s membership function grade is affected by the grade level of the input data in its input membership function. However, which output membership function grade the fuzzy controller selects for the final output value depends on the user’s programming of the IF…THEN rules.
For example, in Figure 8, the 60% input value (fuzzy input FI) triggers rules 3 and 4 because that value of FI belongs to both membership functions ZR and PS. Rules 3 and 4 indicate that both fuzzy output action ZR and action PL must be applied to the process. These output actions will be applied at a value that corresponds to the grades generated in the input membership functions (i.e., output 0.6ZR and 0.4PL). Note that the 0.6 grade is applied to output ZR and the 0.4 grade is applied to output PL because the user programmed the rules that way. Figure 8c shows these two output grades for fuzzy output FO. To arrive at a final outcome value, the fuzzy logic controller logically adds both fuzzy outcomes to produce an aggregate outcome curve, which is illustrated in Figure 8e. The controller then generates an output signal (during defuzzification) that controls the process’s field device (e.g., valve, motor, etc.) according to the input data (see Figure 8f).  A fuzzy logic controller may represent its output membership functions as noncontinuous functions that resemble spikes rather than as continuous geometrical shapes. Each spike has a specific output value associated with it. Figure 9 shows the three output membership functions from Figure 8 represented as noncontinuous spikes. Each membership function corresponds to a particular output count value (i.e., 0 counts, 2048 counts, and 4095 counts). The shaded bars represent the outcome grade levels of 0.6ZR and 0.4PM, which were determined by the rule evaluation. to be continued…………