Realization of fuzzy PID temperature control algorithm (a): The concept of parameter self-tuning fuzzy PID algorithm

Last semester has basically realized the PID temperature control algorithm, in order to write a small paper, the first thing this semester to do is to realize the fuzzy PID temperature control algorithm.

The main difference between the structure of fuzzy control system and the conventional feedback control system is that the controller is mainly composed of fuzzy, fuzzy inference machine and three function modules and knowledge base (including database and rule library). The specific implementation process is as follows:

(1) pretreatment:

Input data is often a specific data that is measured by measuring equipment, and preprocessing is the classification or definition of the nature of the data before they enter the controller. The preprocessing process is also a quantization process, which divides the input data into several digital levels in a discrete space. For example, suppose a feedback error is 4.5 and the error space is ( -5,-4 ... 4,5), the Quantizer will make it close to its nearest level, rounded to 5. The scale of the quantization of the quantizer is the quantization factor. The quantization process is a way to reduce the amount of data, but if the quantization is too coarse, the controller will oscillate or even lose balance.

(2) fuzziness

In the fuzziness, it is necessary to determine the membership function of the fuzzy subsets corresponding to the values of the language variables in the fuzzy set theory domain. Membership function is generally based on the experience of the operator to determine, in the commissioning of the development or even controller operation needs to be constantly revised and optimized to meet the requirements of control. The membership function has many shapes, but the key factor that affects the performance of fuzzy controller is the situation of each fuzzy set coverage theory, and the shape of membership function has no big difference in achieving the control requirements, in order to make the mathematical expression and operation simple, the general selection of Triangle, trapezoidal membership function. However, the width of the membership function has a large effect on performance, the shape of membership function is steep, the output change is more drastic, the control sensitivity is high; When the membership function is flat, the output change is slower and the stability of the system is good. Therefore, when the subordinate function is selected, the subordinate function with the shape of the steeper form is used when the deviation is small or near 0, and the smooth membership function is adopted in the area with the larger deviation, so that the system has good robustness. And in the actual work, there should not be three membership functions intersect state. Generally, the maximum value of the intersection of any two fuzzy subsets is taken between 0.4~0.8. In addition, the position distribution of the subordinate function also has some influence on the control performance, when the function is evenly distributed in the whole domain, the control effect is not good, so the general will be 0 fixed, the other fuzzy subsets to 0 sets close, in order to achieve a better control effect.

(3) Design control rules table

The conditions and conclusions of the rule to use a number of variables, the controller is used to solve multi-input and multi-output and single-input single-output problem, the traditional single-input single-output problem is based on error E adjustment control signal, sometimes also need to change the speed of error and cumulative error, but we also call a single input single output system, because These three quantities are derived from the measurement of errors. To put it simply, our control objects are regulated around a standard value, and our statements and studies are limited to single-input single-output systems.

Rule format: Basically, a fuzzy language controller contains rules in the form of LIWKHQ, but there are other rule formats. In most systems, rules are presented in this form:

If A is NB and B are NB, then C is NB (2-11)

tags of zero,pos,nag--fuzzy sets in the formula: Z, PB, nm--0 points, positive and negative

(4) Inference machine

The rule only reflects that the control signal is calculated by an equal amount of error and error rate. The inference decision is the core of fuzzy control, it uses the information in Knowledge base and fuzzy operation mode, simulates the method of reasoning decision of human, and activates the corresponding control rule under certain input conditions to give the appropriate fuzzy control output.

This part can be realized by designing the software of different inference algorithms in computer, and can also be realized by using the hardware IC chip which is designed by fuzzy inference. Because of the high price of hardware IC based on fuzzy inference, most fuzzy controller is implemented by software on computer.

(5) Precision

The result obtained by fuzzy inference is a fuzzy quantity, which is a set of fuzzy vectors with multiple membership values. The output signal of the control system is a definite measure, therefore, in the fuzzy control application, the fuzzy output of the controller must be converted into a definite value, that is, the process of precision. There are two common methods of precision, namely the maximum membership degree method and the center of gravity method. For the maximum membership degree method, if the membership function of the output fuzzy set has only one peak, the maximal value of the membership function is the exact value, and the element with the highest degree of membership in the fuzzy sub-set is selected as the control amount. If there are multiple maximum values in the output fuzzy vector, the average value of these elements is generally taken as the control amount. The advantage of the maximum membership method is that the calculation is simple, but because the method uses less information, it will cause some control deviation, and it is generally applied to the occasions where the precision of control is not high.

The center of gravity method is the precise value of fuzzy inference output for the centers of Fuzzy membership function curve and horizontal axis area, for discrete domain with n output quantization series:

Here Xi is a different point in the discrete space, I (xi) is its membership in the membership function, the expression can be understood as the center of gravity in the setting of the subordinate. For a continuous situation, you can make and replace the integral to calculate. The computational amount is relatively high, but the algorithm is relatively accurate, so it is also one of the most commonly used algorithms.

Maximum Membership degree method, this method is the simplest, as long as in the inference conclusion of the fuzzy set of the highest degree of membership of the element as output can be. This method does not consider the shape of the membership function.

(6) Post-processing

The system control output value is only relative, not the actual control amount, the relative control amount and the actual project required value has a proportional relationship, and then after the process, to multiply the output scale factor, and give a practical unit like voltage, meters, kilograms, such as ( -2,2) represents the voltage ( -10 v,10v).

The above is the main content of fuzzy control algorithm. The most important feature of fuzzy control algorithm is that the control effect can be realized without fully knowing the mathematical model of a system. Therefore, the mathematical model is difficult to determine the system has a great advantage, but because there is no integral term in the fuzzy control algorithm, so the control result is prone to static error. In order to eliminate this defect, we can combine the fuzzy control algorithm and PID algorithm to get the parameter self-tuning fuzzy PID algorithm.

The block diagram of the parametric self-tuning fuzzy-PID algorithm is as follows:

The concrete implementation measure is to set the initial value of the PID controller (the specific value can refer to the debugging results of the previous semester), and then get the corresponding adjustment value according to the fuzzy rules, then add the final PID parameters.

KP = KP ' + Qp * KP (KP ': initial value QP: Proportional coefficient kp: the KP adjustment value obtained by the fuzzy rule)

ki = Ki ' + Qi * ki

kd = kd ' + Qd * KD

The above is the theory of the parameter self-tuning fuzzy PID algorithm all content.

Reference: Wang Peng. Research and application of ceramic heating temperature control technology [D]. Shenzhen.

Realization of fuzzy PID temperature control algorithm (a): The concept of parameter self-tuning fuzzy PID algorithm