Adaptive Fuzzy Control of Pneumatic Position Servo Li Yuxiang, Li Xiuren, Li Xuegui (Department of Mechanical Engineering and Automation, Tianjin Textile Institute, Tianjin 300160) The adverse effects of nonlinearity and variability of cylinder seal friction improve the positioning accuracy and reliability of the system. The program is also simple, practical and easy to master.
Electro-hydraulic servo systems have long been widely used in the field of automation, and the application of pneumatic servo control is far less extensive than the application of hydraulic servo control. In fact, in many light-load, high-speed work, pneumatic servo control is more advantageous. However, due to the compressibility of the gas, the non-linearity of the flow and pressure, and the complexity of the sealing friction, the accuracy and reliability of the pneumatic servo are greatly limited. It is difficult to further improve the accuracy and reliability of existing pneumatic servo systems with conventional control methods. In recent years, the combination of pneumatic technology and microcomputer technology has strongly promoted the development of electrical servo control technology. This paper discusses the use of adaptive fuzzy PD controller to form a linear drive cylinder position servo system, which effectively improves the positioning accuracy and reliability of the pneumatic servo system.
1 system composition experimental device shown in Figure 1. The control signal output by the computer controls the pressure servo valve V and the two chambers of the cylinder respectively through voltage/current conversion. The control current allows the output pressure of the servo valve to be adjusted within the range of 0-6 M Pa. . The small two-position three-way solenoid valve V controls the sliding seat brake. The continuity of V is controlled by a computer. The pressure in the two chambers of the cylinder is detected by two pressure sensors. The current signal output by the sensor is fed back to the computer via current/voltage conversion. Computer control systems include conversion and conversion. The linear drive cylinder is a rodless cylinder with a stroke of 800 mm and a bore of 25 mm. Since the cylinder structure is symmetrical, the left and right movement characteristics are the same. The stroke position of the cylinder slide is detected by the grating and fed back to the computer to form a closed loop system. The microcomputer control program is programmed in C language with a sampling period of 4 ms. During this time, the computer calculates the voltage signal of the servo valve and performs position control according to the fuzzy control rule and the position signal. The voltage signal adjustment range is 5 control principle as shown in Figure 2. The system output is compared with the command value to obtain the deviation signal e(t). Then all the way through the proportional link ke, the other through the differential link and the proportional link Δe, respectively, get the normalized control deviation e and its time differential Δe.
Taking k max allows the input variable to take values ​​in the normalized area ( 1, 1). The normalized input deviation after transformation and its time differential are: where e is the normalized transformed adjustment deviation k is the sampling ordinal number 1, and the instruction variable y is the adjustment variable T is the sampling period Δe is the time differential of the normalized transformed adjustment deviation.
The e and Δe obtained after the normalization process are the input variables of the fuzzy control. The fuzzy control first obfuscates the input signal, and then infers according to the established fuzzy rule, and then obtains the output control signal through the defuzzification process. The control signal is inversely transformed by the proportional link k and then transmitted to the experimental platform. . The position signal output from the test bench is fed back to the comparison link.
2 Fuzzy control analysis According to the fuzzy set theory to determine the membership level of the input variable, the input variable is first divided into 7 fuzzy sets, namely: NB - negative large PM - positive PB - positive. Then define the corresponding triangle and polyline membership functions, as shown in Figure 3. In theory, changing the normalization system can change the sensitivity of the system within the variable interval. Generally speaking, the larger the normalization coefficient, the higher the sensitivity of the system [1]. There is no membership function of the same width, and the distribution of the fuzzy set changes with the change of the variable. Adjusting the value of the variable can change the sensitivity of the system near 0 to improve the positioning accuracy of the system.
The fuzzy set of the fuzzy controller output u (k T) is a single element set. The membership functions of the nine single element sets are shown in Figure 4. The negative value is small - NV S and is very small - the value of PV S is determined by the fuzzy adaptive process adjustment, the purpose is to compensate the friction of the cylinder. The frictional force includes friction between the piston and the cylinder wall and between the carriage and the guide rail. The fuzzy control rule describes the actual application of the system by the language rules between the input variable and the output variable. These relationships can be written in accordance with the if rules in fuzzy set theory: where XE and ΔE are linguistic variables that normalize the input, and U is the linguistic variable of the normalized output.
The basis of the August 2000 issue of the Journal of Tianjin Textile Institute consists of 7×7 related fuzzy rules, as shown in Table 1.
Using the SUMRPO D reasoning method [2], the corresponding membership level of each rule is obtained by the method of finding the algebraic product: where _ is the membership level of the r-th rule, _ is the membership level of the fuzzy quantity, and _ is Δe The membership level of the fuzzy amount Y. After fuzzification, after inference and judgment, an unambiguous program is needed to output the exact value to control the actuator. In this paper, the fuzzy process uses the centroid method to calculate the exact value of the output: where m is the value. Except that M is a variable, the other seven are fuzzy controller adjustment values ​​taken as variables to compensate for friction.
3 The adaptive compensation experiment of friction shows that friction is a complex and variable function. The amount of friction varies with speed, acceleration, two chamber pressure, piston position and dwell time. Especially when the piston is close to the command position, there may be insufficient displacement or overshoot due to the frictional force. If proper compensation is not performed, the control accuracy will be seriously affected. In this experiment, the adaptive adjustment of the value ±M of the two fuzzy sets NV S and PV S output by the fuzzy controller with the nonlinear function M value is also established based on the fuzzy logic, and the process is the same as described above.
The three membership functions are shown in Figure 5.
The rule base for determining output variables is shown in Table 2.
Through the above analysis and calculation process, we obtain the nonlinear control characteristic diagram of the adaptive fuzzy PD control system as shown in Fig. 6. It can be seen that the input and output exhibit a strong nonlinearity near the value of zero.
The membership function graph 4 experiment and conclusion The cylinder position servo request system can quickly, accurately and stably reproduce the input command position. Practice has proved that the size of the proportional link coefficient k affects the system response time. Choose a different k value, the system response is shown in Figure 7.
It can be seen that when k≥0.1, the system response curve does not exhibit overshoot oscillation. When k = 0.1, the shortest time for the system to have no overshoot response is obtained. The command stroke displacement is 600 mm, and the overshoot response time is 0. 5 s. 800 positioning points are randomly selected to measure the positioning error.
The error distribution of the statistical results is shown in the histogram of Figure 8. The maximum error is 5. Improving the accuracy and reliability of pneumatic servo control is an important issue in the field of pneumatic technology. It is difficult to control such a nonlinear system with conventional linear control methods. Due to the compressibility of the gas and the variability of the sealing friction, the control difficulty is also increased, and the promotion and application of the electric servo is also limited. The use of fuzzy controllers and necessary corrections is a simple and practical way to achieve nonlinear system control, especially easy for engineers to master. This experiment proves that this method effectively improves the speed, control accuracy and reliability of the electrical position servo system.
Small relationships are not consistent, so you need to use the whole of them to participate in the ordering of graphics. When the shape is drawn during the display process, the four faces are sequentially drawn in order of the distance from the center of the four sides to the distance of the viewpoint, so that the entire figure can be drawn in the correct display order.
4 Display results of the unit body structure According to the above method, the unit body structure is as shown in FIG. 5 and FIG. 6, and the viewpoint positions are different, and the display results are different.
[1] Zhang Jiaguang, Zhang Changgui. Computer Graphics (New Edition) [M]. Beijing: Tsinghua University Press, 1994.
Tang Rongxi. Computer Graphics Tutorial [M]. Beijing: Science Press, Journal of Tianjin Textile Institute, August 2000
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