1, the basic principle of fuzzy control
Fuzzy Control is an intelligent control fuzzy set theory, fuzzy linguistic variables and fuzzy logic-based, it is an imitation of an intelligent control fuzzy reasoning and decision-making process from the person's behavior. Firstly, the operator or expert experiences knitted fuzzy rules, then the real-time signal from the sensor blurring, blurring of the signal input as fuzzy rules, the fuzzy inference is completed, the output of the inference execution obtained was added on the device.
2, fuzzy controller
Fuzzy controller (the Controller of Fuzzy-the FC) : also known as fuzzy logic controller (Fuzzy Logic Controller-FLC), because the fuzzy control rules used by the fuzzy conditional statement to describe fuzzy theory, and therefore is a fuzzy controller controller languages, it is also known fuzzy language controller (Fuzzy language controller-FLC).
(1) Fuzzy interfaces (Fuzzy interface)
Input fuzzy controller must be used to solve by the fuzzy control output to, so it is actually the fuzzy controller inputs. Its main role is to determine the amount of real input into a fuzzy vector.
(2) Knowledge (Knowledge Base-KB)
Knowledge database and rule base consists of two parts.
① database (Data Base-DB) database is stored in the membership vector values of all the fuzzy sets all the input and output variables (i.e., through the domain of level discrete set of corresponding values later), if the domain of continuous domains is for the membership function. Fuzzy reasoning rules in relation equation solving process, provide data to the inference engine.
② the rules of the rule base (Rule Base-RB) fuzzy controller based on expert knowledge or experience of the operator to manually accumulated, it is a language expressed by human intuition reasoning form. Fuzzy rules usually have a series of relationships connected to each word, as if-then, else, also, end, or so on, the relationship between the word must be "translated" to the value of fuzzy rules. The most commonly used word for the relationship if-then, also, for multivariable fuzzy control system, as well as and so on.
(3) reasoning and defuzzification interfaces (Inference and Defuzzy-interface)
Reasoning is fuzzy controller, the blur amount according to the input, the fuzzy control rules is done by solving the fuzzy inference of fuzzy relational equation, and obtaining a functional part of the fuzzy control amount. In the fuzzy control in consideration of the inference time, usually a relatively simple calculation method of reasoning. There are basic Zadeh approximate reasoning, it contains two types of forward reasoning and backward reasoning. Forward reasoning is often used fuzzy control, while the reverse reasoning is generally used for expert systems in the field of knowledge engineering. The results obtained reasoning, expressed fuzzy control rules of inference has been completed. However, the results obtained so far is still a fuzzy vector, can not be directly used as the controlled variable, a conversion must be made, to obtain a clear control output, i.e. defuzzification. The output terminal portion typically having a conversion function called defuzzification interfaces .
3, the working principle of Fuzzy Control System (Example)
Fuzzy control the water level, for example, shown in Figure 4-4. A water tank is provided, inwardly through the regulating valve and pumping water out. Design of a fuzzy controller, the water level will be stabilized by adjusting the valve in the vicinity of the fixed point. According to the daily experience, you can get basic control rules:
"If the water level is higher than the point O, the outward drainage, greater the difference, the faster the drainage";
"If the water level is below the point O, the water inwardly, the greater the difference, the faster the water."
According to the experience, the fuzzy controller designed according to the following steps:
1) and a control amount determining observables
O level is defined over the level of the point H 0 , the measured actual water level is h, selecting level difference:
The current water level for the point O as measured deviation e View.
2) input and output fuzzification
The deviation e is divided into five fuzzy sets: Negative Big (NB), Negative Small (NS), Zero (O), positive small (PS), CP (PB). The variation range is divided into seven levels of the deviation e: -3, -2, -1, 0, +1, +2, +3. Get water level changes fuzzy Table 4-1.
U is the control amount adjusting valve opening degree changes. It will be divided into five fuzzy sets: negative big (NB), negative small (NS), zero (ZO), positive small (PS), Chia Tai (PB). U and the variation range is divided into nine levels: -4, -3, -2, -1, 0, + 1, + 2, + 3, + 4. Fuzzy control amount obtained allocation tables 4-2.
Description 3) of fuzzy rules
According to the daily experience, the following design fuzzy rules:
(1) "If e is negative large, negative big u"
(2) "If e is negative small, u is negative small"
(3) "If e is 0, u is 0"
(4) "If e is positive small, u is positive small."
(5) "If e CP, the CP u"
Wherein, when the drainage, u is negative, when the water, u is positive.
Using the above rule "IF A THEN B" described in the form:
（1） if e=NB then u=NB
（2） if e=NS then u=NS
（3） if e=0 then u=0
（4） if e=PS then u=PS
（5） if e=PB then u=PB
According to the above rule of thumb, the fuzzy control available Table 4-3.
4) Fuzzy Relation
Fuzzy control rules a multiple statements, it can be expressed as a fuzzy set on U × V, i.e., the fuzzy relation R:
Fuzzy set in the regular expression on the intersection, between fuzzy sets and set to take the regular expression.
5) Fuzzy Decision
Fuzzy controller output is the error vector and the synthesis of fuzzy relation:
When the error e is NB, e = [1,0.5,0,0,0,0,0] controller output is:
6, the control amount of the anti-blur
Seen from fuzzy decision, when a negative error is large, much higher than the actual level over the level, e = NB, the fuzzy controller output is a vector, it can be expressed as:
If the anti-blur in accordance with "the principle of maximum degree of membership", the selection control amount u = -4, i.e. the valve opening clearance should be larger, to reduce the amount of water.