will take on. Using this, we choose the gain so that normally encountered values of c(kn) will not result in saturation of the outermost input membership functions We can choose gu so that the range of outputs that are possible is the maximum one possible yet still so that the input to the plant will not saturate(for practical problems the inputs to the plant will always saturate at some value) Clearly, this is a very heuristic choice for the gains and hence may not always work. Sometimes, tuning of these gains will need to be performed when we tune the overall fmrlc Rule-Base The rule-base for the fuzzy controller has rules of the form If e is e and c is c then i isU where e and c denote the linguistic variables associated with controller inputs e(kn) and c(kn), respectively i denotes the linguistic variable associated with the controller output u, E and C denote the jth(hth) linguistic value associated with e(c), respectively, U denotes the consequent linguistic value associated with i Hence, as an example, one fuzzy control rule could be If error is positive-large and change-in-error is negative-small Then plant-input is positive-big (in this case e="error positive-large", etc. ) We use a standard choice for all the membership functions on all the input universes of discourse, such as the ones shown in Figure 3. 4. Hence, we would simply use some membership functions similar to those in Figure 3. 4, but with a scaled horizontal axis, for the c(kn) input E E E -1-0.8-0.6-04-0.2 04060.81e(kT) Figure 3. 4 Membership functions for input universe of discourse We will use all possible combinations of rules for the rule-base. For example, we could choose to have 1l membership functions on each of the two input universes of discourse, in which case we would have 112=121 rules in the rule-base. At first glance it would appear that the complexity of the controller could make implementation prohibitive for applications where it is necessary to have many inputs to the fuzzy controller. However, we must remind the reader of the results in Section 2.6 where we explain how implementation tricks can be used to significantly reduce computation time when there are input membership functions of the form shown in Figure 3.4 Rule- Base initialization PDF文件使用" pdffactory Pro"试用版本创建ww. fineprint,com,cnwill take on. Using this, we choose the gain so that normally encountered values of c(kT) will not result in saturation of the outermost input membership functions. We can choose gu so that the range of outputs that are possible is the maximum one possible yet still so that the input to the plant will not saturate (for practical problems the inputs to the plant will always saturate at some value). Clearly, this is a very heuristic choice for the gains and hence may not always work. Sometimes, tuning of these gains will need to be performed when we tune the overall FMRLC. Rule-Base The rule-base for the fuzzy controller has rules of the form j l m If e is E  and c is C then u is U where e and c denote the linguistic variables associated with controller inputs e(kT) and c(kT), respectively, u denotes the linguistic variable associated with the controller output u, j E and l C denote the jth (lth) linguistic value associated with e c  ( ) , respectively, m U denotes the consequent linguistic value associated with u . Hence, as an example, one fuzzy control rule could be If error is positive-large and change-in-error is negative-small Then plant-input is positive-big (in this case e = "error", 4 E = "positive-large", etc.). We use a standard choice for all the membership functions on all the input universes of discourse, such as the ones shown in Figure 3.4. Hence, we would simply use some membership functions similar to those in Figure 3.4, but with a scaled horizontal axis, for the c(kT) input. e( ) kT E E E -2 -1 0 1 2 E E -0.6 -0.4 -0.2 0.2 0.4 0.6 1 -1 -0.8 0.8 1 E E E E -5 -4 5 -3 3 4 E E Figure 3.4 Membership functions for input universe of discourse We will use all possible combinations of rules for the rule-base. For example, we could choose to have 11 membership functions on each of the two input universes of discourse, in which case we would have 112 = 121 rules in the rule-base. At first glance it would appear that the complexity of the controller could make implementation prohibitive for applications where it is necessary to have many inputs to the fuzzy controller. However, we must remind the reader of the results in Section 2.6 where we explain how implementation tricks can be used to significantly reduce computation time when there are input membership functions of the form shown in Figure 3.4. Rule-Base Initialization PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn