Introduction to Fuzzy Control

Introduction to Fuzzy Control

Www.7613.com 2004-6-19

 

[Keywords] Fuzzy Control

I. Overview of Fuzzy Control

Fuzzy Logic Control (Fuzzy Control) is a Computer Digital Control Technology Based on Fuzzy Set Theory, fuzzy language variables, and fuzzy logic reasoning. In 1965, L. A. Zadeh of the United States created a fuzzy set theory. In 1973, he gave the definition and related theorem of Fuzzy Logical Control. In 1974, E. H. Mamdani in the UK first formed a fuzzy controller using a fuzzy control statement and applied it to the control of boilers and steam engines. This pioneering work marks the birth of fuzzy control theory.

Fuzzy control is essentially a kind of non-linear control, from the scope of intelligent control. A major characteristic of fuzzy control is its systematic theory and extensive practical application background. The development of fuzzy control initially encountered great resistance in the west; however, in the east, especially in Japan, it was quickly and widely applied. Over the past 20 years, fuzzy control has made great strides both theoretically and technically, and has become a very active and fruitful branch in the field of automatic control. Examples of typical applications involve many aspects of production and life, such as fuzzy washing machines, air conditioners, microwave ovens, vacuum cleaners, cameras, and recorders in household appliances; in the field of industrial control, there is a fuzzy control of water purification, fermentation process, chemical reaction kettle, cement kiln, etc; in special systems and other aspects, there are subway station parking, car driving, elevators, escalators, steam engines, and fuzzy control of robots.

Ii. Foundation of Fuzzy Control

The basic idea of fuzzy control is to use computers to implement human control experience. Many of these experiences are vague control rules expressed in languages. The main reason for the success of a fuzzy controller (FC) is that it has the following outstanding features:

Fuzzy control is a rule-based control. It directly uses language-based control rules. The starting point is the control experience of field operators or the knowledge of relevant experts. In the design, precise mathematical models of controlled objects are not required, therefore, the control mechanism and policies are easy to accept and understand, and the design is simple and easy to use.

Starting from the qualitative understanding of the industrial process, it is easier to establish language control rules. Therefore, fuzzy control is very suitable for objects that are difficult to obtain mathematical models, difficult to grasp dynamic characteristics, or have significant changes.

Model-Based ControlAlgorithmAnd system design methods, because of the different starting point and performance indicators, it is easy to cause a large difference. However, the language control rules of a system are relatively independent, using the fuzzy connection between these control rules, it is easy to find the option of compromise, so that the control effect is better than that of the conventional controller.

Fuzzy control algorithms are designed based on enlightening knowledge and language decision-making rules. This helps to simulate the process and method of manual control, enhance the adaptability of the control system, and make it intelligent.

The fuzzy control system has strong robustness, and the impact of interference and parameter changes on the control effect is greatly reduced. It is especially suitable for the control of non-linear, time-varying and pure lagging systems.

The basic structure of the fuzzy control system is as follows:

Figure 1 fuzzy control system diagram

S is the set value of the system, Y is the system output, and E and C are the differential signals of system deviation and deviation, that is, the input of the fuzzy controller, U is the control signal output by the Controller, and E, C, and u are the corresponding fuzzy values. The figure shows that the fuzzy controller consists of three functional links: the fuzzy quantization and fuzzy links used for input signal processing, the functional units of the fuzzy control algorithm, and the fuzzy decision links used for output decoding.

The basic methods and steps for fuzzy controller design are as follows:

1. Select the input and output variables of the fuzzy controller and perform range conversion. The selection method is generally 1, that is, take E, C, and U respectively.

2. determine the value of the fuzzy language of each variable and the corresponding membership function, that is, blur it. Fuzzy Language values are usually set to 3, 5, or 7. For example, {negative, zero, positive}, {negative, small, zero, small, and large }, or {negative large, negative medium, negative small, zero, positive small, median, zhengda} and so on. Then, define the membership function for the selected fuzzy set. You can use the triangle membership function (as shown in Figure 2) or trapezoid, and take the same interval or unevenly based on different problems; you can also use the single-point Fuzzy Set Method to blur the image.

Figure 2 Description of membership function acquisition

3. Establish fuzzy control rules or control algorithms. This refers to rule induction and rule repository establishment. It is the central link from actual control experience to fuzzy controller. The control law is usually composed of a set of fuzzy condition statements with the if-then structure. For example, if E = N and C = N, then u = Pb ...... Or summarized as a fuzzy control rule table, as shown in table 1, you can directly query the corresponding control U by E and C.

Table 1 example of a fuzzy control rule table

U	C: N	C: z	C: P
E: n	Pb	PM	Z
E: z	ps	Z	NS
E: P	Z	nm	Nb

4. Determine Fuzzy Inference and deblur methods. There are two common fuzzy inference methods: maximum and minimum reasoning and maximum product reasoning. You can choose one of them based on your actual situation. The fuzzy solution includes the maximum membership method, median method, weighted average method, and center of gravity method, the summation or estimation method selects appropriate methods based on different system requirements or operating conditions, and converts the fuzzy quantity to the precise quantity to implement the final control strategy.

Iii. Current Situation of Fuzzy Control Application

The key to the good control effect of fuzzy control is to have a complete control rule. However, fuzzy rules are used to generalize the process or object fuzzy information, and to control complex processes with high order, non-linearity, large latency, time-varying parameters, and serious random interference, people's understanding is often relatively poor or difficult to sum up the complete experience, which makes simple fuzzy control in some cases very rough, difficult to adapt to different running states, affecting the control effect.

The two main problems of conventional fuzzy control are: improving the accuracy of steady-state control and improving the intelligence level and adaptability. In practical application, the idea of fuzzy control or fuzzy reasoning is often combined with other mature control theories or methods to give full play to their respective strengths and achieve the desired control effect. Fuzzy Rules and languages are easily accepted by people. In addition, the fuzzy technology can be easily implemented in the microprocessor and computer, so this combination shows great vitality and good results. The methods for improving fuzzy control include Fuzzy Composite Control, adaptive and Self-learning fuzzy control, and the combination of fuzzy control and intelligent methods.

1. Fuzzy Composite Control:

Fuzzy-PID compound control: fuzzy PID control is usually used when the error is large, while PID control is used when the error is small, so as to ensure the dynamic response effect, it can also improve the accuracy of steady-state control. A simple and effective method is that the fuzzy controller and I regulator work together to control the synthesis.

Fuzzy-linear Compound Control: for example, fuzzy-feed-forward compensation control. In practice, fuzzy control is a variable-Gain PI controller, which achieves better results in actual system control.

Smith-Fuzzy Controller: designed for the system's pure lagging characteristic, replacing the PID with a fuzzy controller can solve the defect that the conventional Smith-PID controller has weak adaptability to parameter changes; in addition, the use of fuzzy reasoning and fuzzy rules is helpful to adapt to the changes in latency to a certain extent, and effectively compensate for the pure lag of objects under more complex circumstances.

3D Fuzzy Controller: one is to use error E, error change EC and error change rate ECC as three-dimensional variables, which can solve the contradiction between fast response and stability requirements of traditional two-dimensional fuzzy controllers; another method is to use E, EC and error accumulation and Σ E, which is equivalent to a variable gain PID controller and improves the steady-state precision of fuzzy control.

Multi-variable fuzzy control: Generally, the structure decomposition and hierarchical structure are used to combine multiple simple fuzzy controllers and take into account the relationship between multiple rule sets.

2. Adaptive and Self-learning fuzzy control:

Self-Tuning Fuzzy Controller: a self-tuning fuzzy controller that modifies control rules. Based on the evaluation of response performance indicators, the fuzzy set translation or membership function parameters are used, to partially or comprehensively modify the control rules. You can also adjust the Rules table or the membership function itself. A self-tuning Fuzzy Controller Based on the Fuzzy Model, including the linguistic Method for Identifying System Models Using Fuzzy Sets theory, the System Fuzzy Relationship Model Identification Method Based on reference fuzzy sets, and the establishment of a Fuzzy Rule Model Using I/O data, it serves as the basis for self-tuning controller design.

Parameter Self-Tuning Fuzzy Control: Fuzzy Control of Self-adjusting proportional factor, introducing the performance measurement and proportional factor adjustment functions, changing the parameters of the fuzzy controller online, this greatly enhances the adaptability to environment changes. PID self-tuning control based on fuzzy inference, such as Parameter Self-tuning fuzzy PD control and similar PI and PID control.

Model reference adaptive fuzzy controller: uses the deviation between the output of the Reference Model and the output of the control system to modify the output of the fuzzy controller, including the proportional factor, deblur policy, and fuzzy control rules.

Fuzzy Control with self-learning function: including a variety of fuzzy control methods with external disturbance impact or repetitive task performance and self-learning function, as well as self-optimized Fuzzy Controller, etc, the key lies in the design of learning and optimization algorithms, especially to improve the speed and efficiency.

Self-Organizing Fuzzy Controller: Fuzzy Model Reference learning control combining the reference model and self-organizing mechanism, and more advanced self-organizing forms such as adaptive hierarchical fuzzy control have great development potential.

3. The combination of fuzzy control and other intelligent control methods:

Although fuzzy control still has a lot of controversy in terms of concept and theory, since 1990s, due to the participation of many famous scholars in the world and the success of a large number of engineering applications, especially for complex systems that cannot use classical and modern control theories to establish accurate mathematical models, the results are remarkable, which leads to more extensive and in-depth research, in fact, fuzzy control has been determined as an important branch of intelligent control.

4. Expert Fuzzy Control:

The expert system can express and utilize the heuristic knowledge required to control complex processes and objects, and pay attention to the need for multi-level and classification of knowledge. This makes up for the defect that the structure of the fuzzy controller is too simple and the rules are relatively simple, fuzzy control is endowed with higher intelligence. The combination of the two can also possess complex process control knowledge, and can effectively use this knowledge in more complex situations.

5. Neural Network-Based Fuzzy Control:

Neural Networks implement local or all fuzzy logic control functions. For example, if a neural network is used to implement fuzzy control rules or fuzzy reasoning, the latter usually requires more than three layers of Network. Adaptive Neural Network Fuzzy Control, the learning function of neural networks is used as model identification or controller. The membership functions and inference rules based on fuzzy neural networks are obtained, and fuzzy neural networks with fuzzy connection strength are used, all of them are applied in control. The controller design method combining fuzzy system and genetic algorithm provides a new idea.

In addition, the research on Fuzzy Prediction Control, fuzzy variable structure method, fuzzy system modeling, parameter identification, and fuzzy pattern recognition are also at the forefront.

Iv. Prospect of Fuzzy Control

Fuzzy control is still a controversial field. Since its development history is not long enough, theoretically systematic and perfect, technical maturity and standardization are still not enough, and it needs to be further improved.

There are still some important theoretical questions about fuzzy systems. Two important questions are: how to obtain Fuzzy Rules and membership functions, which are based entirely on experience at present, and how to ensure the stability of the fuzzy system.

In general, the main topics for strengthening research on the theory and application of fuzzy control are:

It is suitable for stability analysis methods, stability evaluation theory systems, controller robustness analysis, and system controllability and Observability determination methods to solve common engineering problems.

Research on the design method of fuzzy control rules, including the setting method of fuzzy set membership function, quantization level, optimal selection of sampling period, rule coefficient, the minimum implementation, automatic generation of rules and membership function parameters, and so on. Further, we need to provide a systematic design method for the fuzzy controller.

The determination of the optimal parameter adjustment theory of the fuzzy controller, and the learning method and Algorithm for correcting the inference rules.

Fuzzy Dynamic Model Identification Method.

The design method of the Fuzzy Prediction System and the method to increase the computing speed.

The combination of neural networks and fuzzy control is expected to develop a new intelligent control theory.

Research on the improvement of fuzzy control algorithms: due to the wide range of fuzzy logic, there are a large number of concepts and principles. However, these concepts and principles can be applied in a few fuzzy logic systems. This attempt needs to be further explored.

Research on Optimal Fuzzy Controller Design: the design basis of the control rules is standardized based on the appropriately proposed performance indicators, and the optimum is achieved in a certain sense.

 

Information Source (author): Yan Yong

 

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