CN103034126A - Controlling system and controlling method of axial off-center magnetic bearing of outer rotor of constant current source - Google Patents

Abstract

The invention discloses a controlling system and a controlling method of an axial off-center magnetic bearing of an outer rotor of a constant current source. The controlling system is a closed-loop system formed by a variable universe fuzzy controller, a force/current converting module, a power amplifier module, a prototype body and a displacement detection module, wherein the variable universe fuzzy controller, the force/current converting module, the power amplifier module, the prototype body and the displacement detection module are sequentially connected. The variable universe fuzzy controller is composed of a fuzzy controller and a telescopic factor fuzzy controller, wherein the fuzzy controller and the telescopic factor fuzzy controller are connected in parallel, and the fuzzy controller comprises a proportion integration differentiation (PID) fractional order controller based on online adjustment of fuzzy setting rules. Deviation e obtained by comparison of a displacement output signal and a given reference location signal and ec which is the change rate of e are both used as input variables of the fuzzy controller and the telescopic factor fuzzy controller. The telescopic factor fuzzy controller converts the input variables into fuzzy quantities through fuzzy calculation, and carries out Fuzzy inference calculation of the output quantities according to the telescopic factor rule and outputs the telescopic factor and feedbacks the telescopic factor to the fuzzy controller. The controlling system and the controlling method of the axial off-center magnetic bearing of the outer rotor of the constant current source have strong restraining capability for nonlinearity, and ensure system stability better.

Description

Control System and Control Method of Constant Current Source Offset External Rotor Axial Magnetic Bearing

technical field

The invention belongs to the technical field of control, and in particular relates to the design of a control system and a control method of a non-mechanical contact magnetic suspension bearing (magnetic bearing).

Background technique

Magnetic bearing is a new type of support bearing that uses magnetic field force to suspend the rotor in space so that it has no mechanical contact with the stator. It has the advantages of no friction, no wear, no lubrication and sealing, high speed, high precision and long life. The magnetic bearing system is mainly composed of two parts: the mechanical structure of the magnetic bearing and the control system. The mechanical structure affects the working performance of the entire magnetic bearing system. The corresponding control system and its control method determine the dynamic performance, stiffness, damping and Stability, so the magnetic bearing mechanical structure and control system restrict whether a complete magnetic bearing system can achieve the best working condition.

For the mechanical structure of the constant current source biased outer rotor axial magnetic bearing, please refer to the magnetic bearing in the patent application number 201210247525.6 titled "A Constant Current Source Biased External Rotor Axial Magnetic Bearing". The cost of the magnetic bearing and the reduction of power consumption of the magnetic bearing are the goals, but the magnetic bearing only involves the mechanical structure, and does not involve its corresponding control system and its control method. Since the levitation force generated by the magnetic bearing has serious nonlinear characteristics, the stable control of the levitation force is a key problem to be solved, and it is particularly important to solve the problem of nonlinear control of the levitation force.

The controller is the core component of the control system, which directly affects the performance of the entire control system, and the control method of the entire control system is also embodied in the core algorithm of the controller. At present, PID controllers are mostly used to control magnetic bearings, but PID controllers rely too much on the model parameters of the control object, and their robustness is poor. It is difficult to meet the precise control requirements of the system simply by using the PID controller. The fractional-order PID controller (PI ^λ D ^μ controller), which originated from the PID controller but is different from the traditional PID controller, is the promotion and development of the conventional integer-order PID controller. The dynamic system described by the fractional-order mathematical model needs to be are more precise than those described by integer-order models. Since the fractional-order PID controller introduces the differential order coefficient λ and the integral order coefficient μ , there are two more adjustable parameters, so the adjustment range of the controller parameters becomes larger.

In recent years, there have been more and more researches and applications of fuzzy control methods. The fuzzy controller developed by using fuzzy logic itself has intelligent reasoning function and nonlinear characteristics, especially the PID controller based on the online adjustment of fuzzy tuning rules, which can be very It is better to overcome the adverse effects of uncertain factors such as model parameter changes and nonlinearity in the magnetic bearing system, and obtain better control effects. However, because there are two more adjustable parameters in the PID controller under online adjustment based on fuzzy tuning rules, it will lead to an increase in the number of rules, which in turn increases the complexity of the control system, and affects the accuracy and real-time performance of the control system.

Contents of the invention

The purpose of the present invention is to provide a variable domain fuzzy fractional order PID control system for the constant current source biasing the outer rotor axial magnetic bearing to overcome the shortcomings of several existing magnetic bearing control systems and nonlinear control methods , with better robustness, anti-interference, adaptability and better control accuracy. The invention also provides a control method of the control system at the same time, which can obtain satisfactory control precision, reduce the number of rules, realize parameter online adjustment, and achieve good control effect.

In order to achieve the above object, the technical scheme adopted by the control system of the constant current source biasing outer rotor axial magnetic bearing of the present invention is: the control system is composed of a variable universe fuzzy controller, a force/current conversion module, a power amplification module, a constant The flow source bias outer rotor axial magnetic bearing prototype body and the displacement detection module are sequentially connected to form a closed-loop system. The variable domain fuzzy controller is composed of a fuzzy controller and a scaling factor fuzzy controller connected in parallel. The fuzzy controller includes a fuzzy tuning based on The PID fractional-order controller under regular online adjustment, the displacement detection module is composed of eddy current displacement sensor and displacement interface circuit connected sequentially; the axial position of the prototype body is detected by displacement sensor, and the detected displacement signal is processed by displacement interface circuit to output displacement The output signal z and the displacement output signal z are compared with the given reference position signal z* to obtain the deviation e and its rate of change e _c , and both the deviation e and its rate of change e _c are input to the variable universe fuzzy controller. The output force signal Fz _* of the domain fuzzy controller is transformed into the control current reference signal by the force/current conversion module, and the control current reference signal is input into the power amplification module and then output the control current to drive the prototype body.

The technical scheme adopted by the control method of the control system of the constant current source biasing outer rotor axial magnetic bearing of the present invention includes the following steps:

(1) In the variable universe fuzzy controller, the deviation e and its rate of change e _c are used as the input variables of the fuzzy controller and the scaling factor fuzzy controller; the scaling factor fuzzy controller first transforms the input variable into Fuzzy quantity, and then fuzzy inference calculation of the fuzzy output according to the expansion factor rule, and finally calculate the expansion factor a ₁ ( t ) of the output deviation e and the expansion factor a ₂ ( t ) of the deviation change rate e _c through defuzzification , the exact amount of the expansion factor β ( t ) of the output volume F _Z *, and feed back the exact amount to the fuzzy controller;

(2) The fuzzy controller converts the input variable into a fuzzy quantity through fuzzy calculation, and the output after fuzzy processing is used as the input quantity processed by the fractional-order PID controller under the online adjustment of fuzzy tuning rules, and the proportional coefficient K is adjusted in real time _p , integral coefficient K _i , differential coefficient K _d , differential order coefficient λ , and integral order coefficient μ , the output of the PID fractional-order controller undergoes fuzzy reasoning and defuzzification to output force signal F _z *.

The beneficial effect of the present invention compared with prior art is:

1. Because the fractional-order PID controller has two more adjustment degrees of freedom λ and μ than the integer-order PID controller, the fractional-order controller is insensitive to object parameter changes and has a strong ability to suppress nonlinearity. Therefore, when the magnetic When the parameters of the bearing model change, the stability of the system can be better guaranteed.

2. Fractional calculus is more flexible than the design of traditional controllers, and the change of differential and integral order is easier to change the frequency domain response characteristics of the system than changing the coefficients of proportional, integral and differential, so it can be better designed. Stick control system.

3. Since the fractional-order PID controller does not have the function of online parameter tuning like the conventional PID controller, it cannot meet the system's self-tuning requirements for parameters under different working conditions, thus affecting the further improvement of its control effect. Combining fuzzy control and PID control not only has the advantages of flexible fuzzy control and strong adaptability, but also has the characteristics of high precision of fractional-order PID control, and makes the PID controller adapt to the change of the controlled object to obtain better control performance.

4. Integrating the idea of variable universe into the fuzzy fractional-order PID controller, adjusting the universe in real time through the nonlinear expansion factor can significantly reduce the number of initial rules and effectively improve the control accuracy at the desired control point. Therefore, the self-adaptive fuzzy controller is designed by using the fuzzy variable universe, and the high-precision control effect can be achieved by using a simple domain division, which can just make up for the shortcomings of the complicated fuzzy rules caused by adding two more parameters to the fuzzy fractional-order PID controller. . On the premise that the form of fuzzy rules remains unchanged, the domain of discourse and controller output can be adjusted online according to the error. The domain of discourse shrinks as the error becomes smaller, or expands as the error increases, so as to achieve the purpose of improving control accuracy.

Description of drawings

Fig. 1 is the overall block diagram of the control system of the constant current source bias outer rotor axial magnetic bearing of the present invention;

In the figure: Aa . Variable universe fuzzy controller; a . Fuzzy controller; a 1. Fuzzification; a 2. Fuzzy tuning rules; a 3. PID fractional order controller; Fuzzy controller; A1. Fuzzification; A2. Fuzzy tuning rules; A3. Fuzzy reasoning; A4. Defuzzification; b . Force/current conversion module; c . Power amplification module; d . Prototype body; e 1. Displacement sensor; e 2. Displacement interface circuit;

8. Switching power amplifier; 9. Constant current source.

Detailed ways

As shown in Figure 1, the control system of the present invention for biasing the axial magnetic bearing of the outer rotor with a constant current source consists of a variable universe fuzzy controller A a , a force/current conversion module b , a power amplification module c , and a prototype body d (that is, the constant current source Offset outer rotor axial magnetic bearing) and the displacement detection module f are sequentially connected to form a closed-loop system. Variable domain fuzzy controller A a is composed of fuzzy controller a and scaling factor fuzzy controller A in parallel. The fuzzy controller a includes a PID fractional-order controller a3 under online adjustment based on the fuzzy tuning rule a2 . The power amplification module c is composed of a switching power amplifier 8 and a constant current source 9 . The displacement detection module f is composed of an eddy current displacement sensor f1 and a displacement interface circuit f2 connected in sequence. The output signal of the variable universe fuzzy controller A a is transformed into the control current reference signal by the force/current conversion module b , and the control current reference signal is input into the power amplification module c and then outputs the control current to drive the prototype body d. The axial position of the prototype body d (that is, the axial magnetic bearing of the outer rotor biased by the constant current source) is detected by the displacement sensor f1 , the detected displacement signal is processed by the displacement interface circuit f2 , and the modulated displacement output signal z is output , the displacement output signal z is compared with the given reference position signal z*, and the obtained deviation e and its rate of change e _c are input to the variable universe fuzzy controller A a .

In the variable universe fuzzy controller A a , the deviation e and its rate of change e _c are used as the input variables of the fuzzy controller a and the scaling factor fuzzy controller A.

，则偏差e的可变论域即可形成，即通过“伸缩”因子α(x)变换为[ -α(x )E, α(x )E ]。这种规则的在线生成可降低对控制器初始规则数量的要求，恰好弥补控制器中由于采用分数阶PID所产生的额外两个可调参数λ和μ所造成的规则复杂性。因此，使本发明的可变论域的模糊控制器的控制效果大为改善，整个算法较为简捷, 实时性较好，精度高。 Scalability factor fuzzy controller A first converts the input variable into fuzzy quantity through fuzzy A1 calculation. The specific steps of fuzzy A1 are as follows: first define the domain of input and output variables, and then set "negative large (NB)", "negative medium (NM)", "negative small (NS)", "zero (ZO)", The seven linguistic variables of "positive small (PS)", "positive middle (PM)" and "positive big (PB)" are the corresponding linguistic variables, that is, the fuzzification is completed. Then the fuzzy inference calculation A3 is performed on the output of the fuzzy A1 according to the expansion factor rule A2. Among them, the formation rule of the expansion factor rule A2 is: under the premise that the formation (shape) of the fuzzy tuning rule a2 of the fuzzy controller a remains unchanged, the domain of discourse shrinks according to the decrease of _the deviation, and can also be expanded according to the increase of the deviation. Inflated, and then the contraction factor rule A2 can be formed. If the initial universe of discourse is defined as [ - E, E ], the variable universe of discourse can be formed by shrinking or expanding the value of the initial universe of discourse through the operation method of linear transformation according to the expansion factor rule A2. For example: define α( e ) as a continuous function of the deviation variable e ,

, then the variable universe of deviation e can be formed, that is, transformed into [ -α( x )E, α( x )E ] through the "stretching" factor α( x ). The on-line generation of such rules can reduce the requirement on the number of initial rules of the controller, and just make up for the complexity of the rules caused by the additional two adjustable parameters λ and μ in the controller due to the use of fractional-order PID. Therefore, the control effect of the fuzzy controller of the variable universe of the present invention is greatly improved, the whole algorithm is relatively simple, the real-time performance is good, and the precision is high.

When e and ec are relatively large, the control system of the present invention mainly aims at _rapidly reducing errors and speeding up dynamic response. Therefore, a larger control amount should be taken to rapidly reduce e and e _c , so the input domain should be larger at this time, that is, the input domain should be "inflated" than the initial domain, and the output The domain of discourse can basically remain unchanged; when e and e _c are small, the control system of the present invention is gradually in a stable state, and the main goal is to further reduce the deviation and realize the operation of the system without static error. Therefore, the output domain of discourse at this time should be larger, that is, the output domain of discourse should be "inflated" than the initial domain of discourse, and at the same time, the input domain of discourse should be smaller, that is, the input domain of discourse should be smaller than the initial domain of discourse. Domain should be "contracted". In the calculation of fuzzy reasoning A3, the two fuzzy controllers in the variable domain fuzzy controller Aa both contain 49 control rules. According to the established expansion factor rule A2, combined with the fuzzy experience and expert knowledge of the traditional magnetic bearing control system, list the expansion factor a ₁ ( t ), a ₂ ( t ), β ( t ) fuzzy control rule table, and then get Scaling factor a ₁ ( t ) (scaling factor of deviation e ), a ₂ ( t ) (scaling factor of deviation change rate e _c ), β ( t ) (scaling factor of output F _Z *) blur amount, and finally It is calculated by defuzzification A4, and the precise quantities of three scaling factors a ₁ ( t ), a ₂ ( t ), β ( t ) are output, and the precise quantities are fed back to the fuzzy controller a . a ₁ ( t ) and a ₂ ( t ) adjust the discourse domain of the two input quantities e and e _c of the fuzzy controller in real time, and β ( t ) adjust the discourse domain of the output quantity F _Z * of the fuzzy controller in real time adjust. Among them, defuzzification A4 is a process from fuzzy set to ordinary set, and its function is to convert the known fuzzy set obtained by fuzzy reasoning into corresponding precise quantities that can be directly used for control and output through appropriate methods. According to the actual control object, the present invention uses the center of gravity method to defuzzify, which is convenient for calculation and has high precision.

The fuzzy controller a also converts the input variables into fuzzy quantities by calculating the fuzzy a 1 firstly, and the fuzzy a 1 in the fuzzy controller a is the same as the fuzzy A1 in the scaling factor fuzzy controller A. In addition to the two input quantities of fuzzy controller a , except e and e _c , the scaling factor outputted by fuzzy controller A1 is also used as the input of fuzzy controller a . The output processed by fuzzy a 1 is used as the input processed by the fractional-order PID controller a 3 under the online adjustment of the fuzzy tuning rule a 2 based on real-time adjustment, and the proportional coefficient K _p , the integral coefficient K _i , and the differential coefficient K are adjusted in real time _d , the differential order coefficient λ , the size of the integral order coefficient μ , and then the output of the PID fractional-order controller a 3 undergoes fuzzy reasoning a 4 and defuzzification a 5 to output the force signal F _z *, the force signal F _z * is Output of variable domain fuzzy controller Aa . The method of fuzzy inference a4 and defuzzification a5 is the same as the method of fuzzy inference a3 and defuzzification a4 in scaling factor fuzzy controller A.

The PID fractional- order controller a 3 under online adjustment based on the fuzzy tuning rule a 2 should consider the stability, response speed, overshoot and stability accuracy of the system, and the method of setting the control parameters is as follows: In the fractional-order PID controller a 3 below, the five PID parameter values K _p , K _i , K _d , λ, μ are used as the control variables. When the deviation e is large, the control value is selected to eliminate the deviation quickly , to ensure that the system has better fast-tracking performance and avoid large overshoots at the same time. When the deviation e is small, the control quantity should be selected to prevent overshoot, with the system stability as the main starting point, and at the same time, it is necessary to prevent the system from oscillating near the set value. Reasonable fuzzy rules can be established according to engineering technical knowledge and practical operation experience. On this basis, in addition to the two input quantities e and e _c of the fuzzy controller a , the three scaling factors a ₁ ( t ), a ₂ ( t ) and β ( t ) output by the scaling factor fuzzy controller A1 Also as the input of the fuzzy controller a , the universe of discourse can be adjusted in real time through the nonlinear shrinkage factor. The variable universe model fuzzy controller A a can significantly reduce the number of initial rules and effectively improve the control precision at the desired control point. Then make fuzzy reasoning according to the reduced fuzzy control rules to change the value of PID parameters online, and adjust the size of K _p , K _i , K _d , λ , μ in real time, so as to realize the self-tuning of PID parameters, and obtain a variable universe fuzzy controller The output force signal F _z * of A a . Among them, the fractional-order differential and integral in the PID fractional-order controller a3 uses the Oustaloup algorithm to discretize into the order of the approximate model in the frequency range, and completes the fuzzy PID fractional-order control according to the fuzzy reasoning process and the discrete model equation A digital implementation of a 3.

Finally, the variable universe fuzzy controller A a outputs the force signal F _z *, and then outputs the control current reference signal i _z * through the force/current conversion module b . Then the switching power amplifier 8 outputs the control current iz to drive the axial control coil of the constant current source to bias the axial magnetic bearing of the outer rotor (that is, the prototype body d) , and the constant current source 9 provides the bias current i to the bias coil of the constant current source _{z 0} , to realize the closed-loop control of the axial magnetic bearing of the outer rotor biased by the constant current source.

In order to obtain satisfactory control accuracy, reduce the number of rules, realize parameter online adjustment, and achieve good control effect, the present invention adopts an additional controller, that is, the expansion factor controller, to form a variable theory together with the traditional fuzzy controller domain fuzzy controller. The expansion factor controller can change the domain of discussion of the system fuzzy controller in real time, which makes up for the deficiency that the traditional single fuzzy controller cannot adjust parameters online. Variable domain fuzzy control is to use expert experience and knowledge to establish fuzzy control rules, and use fuzzy reasoning to adjust the domain of the system fuzzy controller in real time, so that the domain of the system fuzzy controller is optimal in each control process. It greatly reduces the dependence on expert experience and knowledge, and improves the adaptive ability and robustness of the fuzzy system.

The present invention uses a fractional-order PID controller (PI ^λ D ^μ controller) to replace the conventional integer-order PID controller, and combines the advantages of variable domain fuzzy control and fractional-order PID controller control to make the constant current source bias the outer rotor The axial magnetic bearing system realizes the stable control of its levitation force, has better static and dynamic stability, enhances the self-adaptive ability of the system and has strong robustness to external disturbances.

As described above, the present invention can be realized. Other changes and modifications made by those skilled in the art without departing from the spirit and protection scope of the present invention are still included in the protection scope of the present invention.

Claims (4)

1. A control system for biasing the axial magnetic bearing of the outer rotor with a constant current source, which is characterized in that: the control system is composed of a variable domain fuzzy controller (A a ), a force/current conversion module, a power amplification module, a constant The flow source biased outer rotor axial magnetic bearing prototype body and the displacement detection module are sequentially connected to form a closed-loop system. The variable domain fuzzy controller (A a ) is composed of the fuzzy controller ( a ) and the scaling factor fuzzy controller (A). Composed in parallel, the fuzzy controller ( a ) includes a PID fractional-order controller ( a3 ) under online adjustment based on fuzzy tuning rules, and the displacement detection module is composed of eddy current displacement sensors and displacement interface circuits connected in sequence; the axial position of the prototype body It is detected by a displacement sensor, and the detected displacement signal is processed by the displacement interface circuit to output the displacement output signal z , and the displacement output signal z is compared with the given reference position signal z* to obtain the deviation e and its rate of change e _c , and the deviation e and The rate of change e _c is input to the variable universe fuzzy controller (A a ), and the output force signal F _z * of the variable universe fuzzy controller (A a ) becomes the control current reference signal after being transformed by the force/current conversion module. The current reference signal is input to the power amplifier module and then output to control the current to drive the prototype body. 2. A control method for a control system as claimed in claim 1, characterized in that it comprises the steps of: (1) In the variable universe fuzzy controller (A a ), the deviation e and its rate of change e _c are used as the input variables of the fuzzy controller ( a ) and the scaling factor fuzzy controller (A); the scaling factor fuzzy controller (A) First convert the input variable into a fuzzy quantity through fuzzy calculation, then perform fuzzy inference calculation on the fuzzy output quantity according to the expansion factor rule (A2), and finally calculate the expansion factor a ₁ of the output deviation e through defuzzification ( t ), the expansion factor a ₂ ( t ) of the deviation change rate e _c , the precise amount of the expansion factor β ( t ) of the output F _Z *, and the precise amount is fed back to the fuzzy controller ( a ); (2) Fuzzy controller ( a ) converts the input variable into fuzzy quantity through fuzzy calculation, and the output quantity after fuzzy processing is used as fuzzy tuning rule ( a 2) fractional order PID controller under online adjustment ( a 3 ) processing input, real-time adjustment of proportional coefficient K _p , integral coefficient K _i , differential coefficient K _d , differential order coefficient λ , and integral order coefficient μ , the output of the PID fractional-order controller ( a 3 ) passes through Fuzzy inference and defuzzification output force signal F _z *. 3. The control method according to claim 2, characterized in that: the concrete steps of said fuzzification are: first define the domain of discourse of the input and output variables, then set the language variables, and finally the output of the fuzzification according to the expansion factor rule (A2) Perform fuzzy inference calculations. 4. The control method according to claim 2, characterized in that: the formation rule of the expansion factor rule (A2) is: under the premise that the fuzzy tuning rule ( a2 ) of the fuzzy controller ( a ) is formed unchanged, the theory The domain shrinks according to the decrease of the deviation, and expands according to the increase of the deviation; when the value of the deviation e and its rate of change e _c is large, the input domain takes the larger domain, and the output domain remains unchanged; when the deviation e and When the change rate e _c value is small, the output domain takes a larger one, and the input domain takes a smaller one.

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