**1.2 Components of the fuzzy control system**

There is not much difference between a fuzzy control system and a computer digital control system. As shown in **Figure 1**, a fuzzy control system can be divided into four components: fuzzy controller, A/D and D/A interface to U, generalized objects (actuators and controlled objects) and sensors [2].

In the microcomputer fuzzy control system, the sensor replaces the human eye, the fuzzy controller replaces the human brain to control decisions, and the executive mechanism replaces the functions of the human arm and hand.

#### *1.2.1 The basic form of fuzzy control*

The decision-making process of fuzzy control is the three basic forms of human fuzzy thinking include fuzzy concept, fuzzy judgment and fuzzy reasoning. In the fuzzy controller, the fuzzy concept is a fuzzy linguistic variable represented by a fuzzy set. For example, the exact amount of error (continuous domain) is converted to the fuzzy quantity on the discrete domain (discourse domain). This process is called fuzzy quantization processing.

**Figure 1.** *Block diagram of fuzzy control system.*

*Overview of Some Intelligent Control Structures and Dedicated Algorithms DOI: http://dx.doi.org/10.5772/intechopen.91966*

Human operating experience can be summarized into several fuzzy control rules in language. These rules can be described by a fuzzy relation matrix. It is actually a general principle of the operating process. These fuzzy control rules are also called the language model of the controlled object.

According to the syllogistic fuzzy reasoning synthesis rule, the fuzzy relationship determined by the fuzzy control rule is taken as the major premise of fuzzy reasoning, and the input fuzzy variable is used as the small premise. The known small premise and fuzzy relationship can be concluded by fuzzy inference synthesis.

According to the syllogism fuzzy inference synthesis rule, the fuzzy relationship *R* determined by the fuzzy control rule is taken as the major premise of fuzzy reasoning, the input fuzzy variable is *A* is taken as the small premise, and the known small premise *A* and fuzzy relationship *R* are synthesized by fuzzy relation inference Conclusion *B* ¼ *A* ∘ *R*.

As shown in **Figure 2**, the schematic diagram of the fuzzy control system is given. For the sake of comparison, the fuzzy logic thinking form of the person is placed above the figure. The three forms of fuzzy logical thinking correspond. Among them, the fuzzy quantization process is to obtain the fuzzy amount of the control variable [3].

For the sake of simplicity, only the error signal is selected as the input variable of the fuzzy controller and abbreviated as *e* (*t*) to illustrate the working principle of the fuzzy controller. The microcomputer obtains the precise value of the controlled quantity y by interrupting the sampling, and then compares this quantity with the given quantity to obtain the precise value of the error signal *e* (*e = r-y*, here the unit feedback is taken) as the input quantity of the fuzzy controller. The exact amount of the error e becomes the fuzzy amount of the error through the fuzzy quantization process, which can be represented by a subset *e* of the corresponding fuzzy language set. Then the fuzzy relationship between the fuzzy amount of the error *e* and the fuzzy control rule *R* is used to make a fuzzy inference decision. The fuzzy amount of the control amount is shown in Eq. (1).

$$
\underline{\mu} = \underline{\varepsilon} \circ \underline{R} \tag{1}
$$

The fuzzy amount of the control amount cannot be directly sent to the actuator to control the controlled object, the fuzzy amount of *u* of the control amount must

**Figure 2.** *System principle of fuzzy control.*

also be converted into an accurate amount *u* through non-fuzzy (clarification, deblurring, and defuzzification) processing. After the digital-to-analog conversion into an accurate analog quantity, it is sent to the executive body, which controls the controlled object by one step. Then, it waits for the second sampling and performs the second step control. Continuously controlling in this way will make the actual output of the controlled object approach the expected value with certain accuracy, thereby achieving fuzzy control of the controlled object.

It is not difficult to see that the input quantity *e* of the fuzzy controller is an accurate quantity, and its output control quantity *u* is also an accurate quantity. Therefore, the control of the fuzzy controller is not fuzzy, and it can achieve precise control of the controlled object. Only the fuzzy logic reasoning is used in the inference part of the fuzzy controller. The advantages are: first, this reasoning decision does not require an accurate mathematical model of the controlled object; second, this reasoning decision simulates the thinking process of a person, and has intelligent and efficiency.

In the following, a single input single output temperature fuzzy control system is used to specifically explain the working principle of the fuzzy control system. An electric heating furnace is used for the heat treatment of metal parts. According to the requirements of the heat treatment process, the furnace temperature must be kept constant at 600°C. The experience of manual operation to adjust the voltage to control the furnace temperature can be summarized in language as the following control rules: If the furnace temperature is lower than 600°C, the voltage will be increased. When the temperature is lower, the voltage will be higher. If the furnace temperature is equal to 600°C, the voltage will be kept unchanged, as the voltage increases, the voltage will decrease.

According to the above control rules, the application of a microcomputer to achieve fuzzy control of the furnace temperature needs to be designed according to the following steps.

1.Determine the input and output variables of the fuzzy controller.

Select the difference between the actual value of the furnace temperature and the set value as *e* (*n*) *= t0-t* (*n*) as the error input variable, and select the voltage *u* to adjust the furnace temperature as the output variable of the fuzzy controller.

2.Determine fuzzy language variables of input and output variables.

First, select a fuzzy subset of the input and output variables as:

{Negative large, negative small, zero, positive small, positive large} = {*NB, NS, O, PS, PB*}.

Among them, *NB, NS, O, PS, PB* are English abbreviations of negative large, negative small, zero, positive small, and positive large respectively.

Second, the domain *X* of the selection error e and the domain Y of the control quantity u are both *X=Y=* {3, 2, 1, 0, 1, 2, 3}.

Third, determine the membership functions of the input and output language variables as shown in **Figure 3**. From this, the assignment of fuzzy variables *e* and *u* can be obtained from this, see **Table 1** [4].

Establish fuzzy control rules using the above-mentioned rules for manually adjusting the voltage to control the furnace temperature, using the error as an input variable, and the voltage as an output variable, five rules can be written as follows:

*Overview of Some Intelligent Control Structures and Dedicated Algorithms DOI: http://dx.doi.org/10.5772/intechopen.91966*

1. If the error is negative, the voltage is positive; If *e* ¼ *NB* then *u* ¼ *PB*.

2. If the error is small, the voltage is small; If *e* ¼ *NS* then *u* ¼ *PS*.

3. If the error is zero, then the voltage is zero; If *e* ¼ *O* then *u* ¼ *O*.

4. If the error is small, then the voltage is small; If *e* ¼ *PS* then *u* ¼ *NS*.

5. If the error is positive, the voltage is negative; If *e* ¼ *PB* then *u* ¼ *NB*.

In the above rules, the left side is expressed in Chinese, and the right side is written in English if-then fuzzy conditional statements.

#### *1.2.2 Fuzzy matrix representation of fuzzy control rules*

A fuzzy control rule is actually a set of multiple fuzzy conditional statements, which can be expressed as a fuzzy relationship from the error domain *X* to the control quantity domain *Y*. Because when the universe is limited, fuzzy relations can be represented by fuzzy matrices. In the furnace temperature fuzzy control, the universe of discussion *X* and *Y* are limited to 7 levels, so the fuzzy relation matrix can be used to represent the above fuzzy control rules.

The above fuzzy conditional statement can be expressed as a fuzzy relationship as show in Eq. (2).

$$\underline{R} = \text{NB}\_{\varepsilon} \times \text{PB}\_{\mathfrak{u}} + \text{NS}\_{\varepsilon} \times \text{PS}\_{\mathfrak{u}} + \text{O}\_{\varepsilon} \times \text{O}\_{\mathfrak{u}} + \text{PS}\_{\varepsilon} \times \text{NS}\_{\mathfrak{u}} + \text{PB}\_{\mathfrak{u}} \times \text{NB}\_{\mathfrak{u}} \tag{2}$$

**Figure 3.** *Membership functions of language variables.*


#### **Table 1.**

*Assignment table of fuzzy variables (*e, u*).*

Among them, the subscripts *e* and *u* of language variables *NBe*, *PBu*, etc. indicate that they are language variables of error and control amount, respectively. **Figure 4** shows the fuzzy rule base.
