CN113279997B - Aero-engine surge active control system based on fuzzy switching of controller - Google Patents
Aero-engine surge active control system based on fuzzy switching of controller Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
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Abstract
The invention relates to an aircraft engine surge active control system based on fuzzy switching of controllers, which is based on the principle of fuzzy switching, selects a basic controller most suitable for the current state to perform switching control according to the working state of a gas compressor, and can realize large-range, self-adaptive and performance-optimized surge active control. The controller designed by the invention realizes large-scale surge active control in a fuzzy switching mode, enlarges the effective working range of the controller and improves the reliability of the controller; the designed controller can be suitable for active control of surge caused by various inducers, so that the self-adaptability of the controller is improved, and the actual working condition of the engine is more approximate; certain optimization indexes are added in the design process of the controller, so that the optimal control under the corresponding optimization target can be realized; the invention can be slightly modified on the basis of the existing controller to achieve the required control effect, and is simpler and easier to implement compared with the existing intelligent control method.
Description
Technical Field
The invention belongs to the field of modeling and control of an aero-engine, and relates to an aero-engine surge active control system based on fuzzy switching of a controller.
Background
At present, high-performance aircraft engines are developing towards the aspects of high thrust-weight ratio, high speed, high reliability and the like, and higher requirements are also put forward on the pneumatic stability of the gas compressor. The improvement of the thrust-weight ratio of the high-performance engine leads to the improvement of the single-stage pressure ratio of the air compressor, the load of the air compressor is higher and higher, the problem of the aerodynamic stability of the aircraft engine is gradually prominent, and the thrust-weight ratio becomes one of important factors for limiting the development of the engine. In a traditional compressor surge control method, the core idea is to ensure that enough surge margin is provided at a working point when the working point of a compressor is designed. Therefore, slight disturbance can occur at the working point of the compressor, and the compressor can still be kept in a stable working space. The method has high reliability, but is often over conservative when the working point is selected, and the engine stability is replaced on the premise of sacrificing the engine performance. At this time, the advantages of the surge active control method are gradually reflected.
The active control method inhibits the generation and development of instability states such as surge of a gas compressor by means of control measures such as pre-stage gas injection, gas discharge adjustment and the like, so that the stable working range of the engine is expanded, and the working point of the engine is moved to a position with higher performance. The current surge active control methods can be classified into the following three categories: a mode-based control method, a nonlinear control method, and an intelligent control method. The methods can inhibit the occurrence of instability states such as compressor surge and the like under certain conditions, but compared with the traditional control method, the reliability is lower, and if the controller fails, the surge is directly caused, which is one of the reasons why the active control method is not practically applied for a long time. Meanwhile, most of the existing active control methods only aim at a destabilization state or a destabilization inducement and do not have good adaptability; in addition, most active control methods are often designed only for local operating points, and cannot realize active control of surge in a large range. In the existing active control method, the unstable state such as surging can be effectively inhibited as a standard, performance loss and the like generated to an engine after a controller takes action are not considered, and an optimal control strategy is not obtained under the same performance.
Disclosure of Invention
Aiming at the problems of low reliability, insufficient self-adaptability, small working range and the like in an active control method in the prior art, the invention provides an aircraft engine surge active control system based on fuzzy switching of a controller.
The technical scheme adopted by the invention is as follows:
an aircraft engine surge active control system based on fuzzy switching of a controller mainly comprises a basic controller design module, a fuzzy switching module and a control signal fusion module, wherein the design process of each part comprises the following steps:
s1 designing N according to the stability requirement in the surge active control and combining the traditional Lyapunov stability theorycA basic controller. Wherein, the basic controller is used for generating the basic control signal u of the fuzzy switching controller designed by the inventionbaseThe control signals are fused into the actual control signal u of the controller through fuzzy switching in the subsequent stepsout. The specific implementation process is as follows:
s1.1 design N by using mode control method based on Lyapunov stability theorycA basic controller, and NcNot less than 2. In each basic controller, the average flow coefficient phi and the disturbance first-order mode A of the compressor can be respectively used as feedback quantities to determine the feedback quantity and the control quantity u required by the compressorcThe relationship of (1), namely:
ubase，1＝k1(Φ-Φ0)
ubase，2＝k2A
ubase，Nc＝kNc(-Φ+Φ0+A)
in the formula, k1，k2，...，kNcIs a controller parameter to be determined; u. ofbase，jIndicating the basic control signal, phi, output by the jth basic controller0The average flow coefficient of the compressor in steady state operation is obtained;
the method for determining the controller parameters comprises the following steps: based on a traditional gas compressor Moore-Greitzer model, after linearization processing is carried out on the model, the controller parameters can be obtained by combining the Lyapunov stability theory.
S1.2 determination of NcWorking range of the basic controller: when the working state of the compressor is in the working range of the basic controller, the basic controller can ensure the stable operation of the compressor through tip air injection, and the working range of the basic controller can be expressed by the size of disturbance borne by the compressor. In addition, basic controllers are required to be designed with different operating ranges. For example, in the basic controller design process, choose differentThe parameter variables (average flow phi and first-order mode A) of the compressor are used as feedback variables of a basic controller, and the basic controller working in a small disturbance range and a large disturbance range is designed respectively.
S1.3 according to NcThe working range of the basic controllers is sequenced according to the size of the working disturbance range, namely, the controllers in the working range are converted according to the sequence along with the increase of the disturbance on the air compressor. Wherein the order of the ith basic controller is denoted rankiAnd rankiIs 1 to NcIs an integer of (1).
S2 designing fuzzy switching module.
The fuzzy switching module obtains the selection tendency c of the basic controller through the traditional fuzzy reasoning according to the state variable x of the gas compressortre. The compressor state variable x is a physical quantity capable of reflecting the working state of the compressor, and the state variables include but are not limited to the average flow rate and the average pressure rise of the compressor. Said basic controller selection tendency ctreIs a parameter in the range of 0-1, and is used for representing the weight occupied by a certain basic controller.
The design of the fuzzy switching module needs to determine a state variable x input by the module, fuzzy division of module input and output, a fuzzy rule used by fuzzy reasoning and a defuzzification method, and the specific design process is as follows:
s2.1, determining a state variable x (average flow phi and a first-order mode A) capable of representing the working state of the compressor as the input of the fuzzy switching module.
S2.2, fuzzy division is carried out on the state variable x input by the fuzzy switching module, and N is obtained by dividing each variableaA fuzzy set; preference of basic controller to output ctreCarrying out fuzzy division to obtain NbA fuzzy set. Determining membership functions f of input variables belonging to respective fuzzy setsin，(i，C)(xi) And the membership function f of the output variable belonging to each fuzzy setout，B(ctre)。
Membership mu of input variables belonging to different fuzzy setsin，(i，C)Can be calculated by:
μin，(i，C)＝fin，(i，C)(xi)
wherein x isiIs the value of the ith input variable; c is dividing a fuzzy set; f. ofin，(i，C)A membership function of an ith input variable belonging to a fuzzy set C; mu.sin，(i，C)The calculated degree of membership of the ith input variable in the fuzzy set C.
Membership mu of output variable belonging to different fuzzy setsout，BCan be calculated by:
μout，B＝fout，B(ctre)
wherein, ctreA selection tendency for the output; b is dividing a fuzzy set; f. ofout，B(ctre) Represents the output ctreOutputting membership function in fuzzy set B; mu.sout，BThen a calculated preference c is selectedtreMembership in fuzzy set B.
Function of degree of membership f abovein，(i，C)And fout，BGenerally including but not limited to the following:
(1) gaussian type membership function
The Gaussian membership function is determined by two parameters sigma and epsilon, and the expression is as follows:
in the formula, xinFor the variable to be fuzzified, the parameter sigma is used for adjusting the width of the membership function, the parameter epsilon is used for determining the center of the curve, and the calculation result of f is xinDegree of membership.
(2) Trapezoidal membership function
The trapezoidal membership function can be determined by four parameters a, b, c, d, which are expressed as:
in the formula, xinThe parameters a and d are the left and right vertexes of the lower bottom of the trapezoid respectively, and the parameters b and c are the left and right vertexes of the upper bottom of the trapezoid respectively.
(3) Triangular membership function
The triangular membership function is determined by 3 parameters, and the expression is as follows:
in the formula, xinThe parameters a and c are the left and right vertexes of the triangle base, and the parameter b represents the upper vertex of the triangle.
S2.3, establishing a fuzzy rule table of a fuzzy switching module, and designing NrulesThe bars are fuzzy rules.
Fuzzy rules may be expressed in the format of if-then, i.e.:
If x1∈C1，x2∈C2，…，xn∈Cnthenctre∈B
wherein, C1Representing the fuzzy set to which the 1 st input variable belongs in the fuzzy rule, C representing the fuzzy set to which the 2 nd variable belongs, and so on; b represents the output c in this fuzzy ruletreThe fuzzy set to which it belongs.
In the fuzzy rule, (x)1∈C1，x2∈C2，…，xn∈Cn) Is a priori condition of the fuzzy rule, the prior membership degree mu of the fuzzy rulerule，iCan be calculated as:
wherein the content of the first and second substances,
i.e. the membership of the input variable calculated in S2.2 in the fuzzy set；NinsThe number of input variables in the fuzzy rule is shown; mu.srule，iI.e. the calculated prior membership of the ith fuzzy rule.
S2.4, performing defuzzification on the output of the fuzzy switching module, wherein the defuzzification result is the controller selection tendency c calculated by the fuzzy switching moduletre. The output result is defuzzified by using a gravity center method, and the calculation process is as follows:
(1) calculating the prior membership mu of each fuzzy rulerule，iNamely:
(2) calculating controller selection tendency c using centroid methodtre：
Wherein, murule，iAnd murule，jRespectively calculating prior membership degrees of the ith fuzzy rule and the jth fuzzy rule;
and
respectively outputting membership functions of a fuzzy set B in the ith fuzzy rule and the jth fuzzy rule; c. CtreA trend is selected for the calculated controller.
S3 designing a control signal fusion module. The input of the control signal fusion module comprises a controller selection trend ctreAnd a basic control signal u generated by the basic controllerbaseOutput as the fused control signal uout. The control signal fusion module selects the trend c according to the input controllertreCalculating the weight w of each basic controlleriAnd then on the basis of the calculated weights for the basic control signal ubasePerforming weighted fusion to obtainActual control signal u of the controllerout。
The method for designing the control signal fusion module needs to determine the fusion weight of the controller and a weighted fusion method, and comprises the following specific steps:
s3.1 designing the controller fusion weight. According to the number N of basic controllerscFor selection tendency ctreAnd carrying out fuzzy division, wherein the obtained fuzzy center of concentration can be calculated by the following formula:
in the formula, ciIs the ith fuzzy set center; n is a radical ofcIs the number of basic controllers; rankiFor the order determined in step S1.3 for the ith controller, taking values from 1 to NcIs an integer of (1). For example, in NcWhen 3, the fuzzy set center c1＝0、c2＝0.5、c3＝1。
Weight w corresponding to ith controlleriCan be calculated according to the following formula:
wi＝fw，i(ctre)
wherein, ctreSelecting a trend for the fusion module input, i.e. the controller; f. ofw，iMembership functions corresponding to the ith controller, wherein the membership functions can be selected from the forms mentioned in step S2.2; w is aiNamely the calculated weight corresponding to the ith controller.
S3.2, carrying out weighted fusion on the basic control signals to obtain the actual control signals u of the basic controllerout。
Actual control signal u of the basic controlleroutCan be obtained by weighted fusion of the following formula:
wherein u isbase，jA basic control signal representing the output of the jth basic controller;wiand wiRespectively representing the weight of the ith corresponding to the jth basic controller; n is a radical ofcThe number of basic controllers; u. ofoutThe control quantity actually output by the controller after fusion, namely the control quantity output by the fuzzy switching controller designed by the invention.
The main design and calculation processes of the aircraft engine surge active control system based on fuzzy switching of the controller are designed.
The invention has the beneficial effects that: according to the surge active control method based on fuzzy switching of the controller, the limitation of the surge active control method based on a single controller is overcome, the problem that the single controller cannot meet the requirement of realizing various disturbances is solved, and the effective working range of the surge active controller is expanded. The method can realize self-adaptive adjustment of the weight of each basic controller according to the size of the disturbance, so that the compressor can better adapt to various external disturbances, the stable work of the axial flow compressor of the aero-engine in a wider working range is realized, the success rate of active surge control and the stability of the compressor are improved to a great extent, and the safety and the reliability of the aero-engine are improved.
Drawings
FIG. 1 is a flow chart of an active control system design for aircraft engine surge based on controller fuzzy switching;
FIG. 2 is a schematic structural diagram of an aircraft engine surge active control system based on fuzzy switching of a controller;
FIG. 3 is a block diagram of an active control system for aircraft engine surge based on controller fuzzy switching in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of the fuzzy set and fuzzy rules of the input and output of the fuzzy switching module; wherein, the graph (a) is the fuzzy set division of the average flow coefficient phi, the graph (b) is the fuzzy set division of the first-order modal amplitude A, and the graph (c) is the fuzzy switching module output selection trend ctreThe fuzzy set of (a) is divided, and the graph (d) is a fuzzy switching rule used by the fuzzy switching module;
FIG. 5 is a schematic diagram of fuzzy set partitioning for the control signal fusion module;
FIG. 6 is a surge active control process under a small disturbance condition, wherein (a) is a change process of a local compressor flow coefficient when the fuzzy switching controller and the basic controller provided by the invention perform control in the same working range; FIG. b is a graph of the jet flow coefficients generated by the fuzzy switching controller and the basic controller; graph (c) blurs the switching signal generated by the switching module for this time.
Fig. 7 shows the surge active control process in the case of moderate disturbances, where the meanings of graph (a), graph (b) and graph (c) are the same as described in fig. 6.
Fig. 8 is a surge active control process in the case of large disturbances, where the significance of graph (a), graph (b) and graph (c) is the same as described in the above graphs.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and embodiments thereof.
The control system mainly comprises a basic controller design module, a fuzzy switching module and a control signal fusion module, and a design flow chart of the aircraft engine surge active control system based on the fuzzy switching of the controller is shown in figure 1.
FIG. 2 is a schematic structural diagram of an aircraft engine surge active control system based on fuzzy switching of a controller. As can be seen from the figure, the controller mainly comprises a fuzzy switching module, a control signal fusion module, a basic controller and the like. The fuzzy switching module further comprises three parts of state variable fuzzification, fuzzy rule reasoning and defuzzification. The fuzzy switching controller generates a controller selection trend c through a fuzzy switching moduletreThe control signal fusion module is used for controlling the selection tendency ctreAnd a basic control signal ubaseObtaining the actual control signal u of the controller by weighted fusionout。
Fig. 3 is a block diagram of an active aircraft engine surge control system based on fuzzy controller switching in the present embodiment.
The specific implementation process comprises the following steps:
s1 basic controller design: according to the stability requirement in the surge active control, the traditional Lyapunov stability theory is combined, and 3 basic controllers are designed, specifically as follows:
s1.1, 3 basic controllers are designed by adopting a mode control method based on the Lyapunov stability theory, the average flow coefficient phi and the disturbance first-order mode A of the gas compressor are respectively used as feedback quantities, and the feedback quantity and the control quantity u required by the gas compressor are determinedbase，jIn FIG. 3 the basic controller designs N according to the design step S1.1c3 basic controllers. Selecting a pressure rise psi generated by a gas injection valve of a gas compressorjAs the control amount, a control law of the basic controller can be obtained:
the controller 1: u. ofbasr，1＝k1(Φ-Φ0)
The controller 2: u. ofbase，2＝k2A
The controller 3: u. ofbase，3＝k3(-Φ+Φ0+A)
Wherein phi is the average flow coefficient of the compressor; a is a first-order modal amplitude; phi0The average flow coefficient of the balance point of the compressor is obtained; k is a radical of1、k2、k3Is the controller parameter to be determined. From Lyapunov's stability theory, it can be determined that k is the same in this example1、k2、k3The values of (A) are as follows: k is a radical of1＝-0.1，k2＝0.1，k3＝0.1。
The method for determining the controller parameters comprises the following steps: based on a traditional gas compressor Moore-Greitzer model, after linearization processing is carried out on the model, the controller parameters can be obtained by combining the Lyapunov stability theory. The embodiment of the invention listed here takes the Moore-Greitzer model of the compressor as the controlled object, and the Moore-Greitzer model of the compressor is as follows:
in the equation, A (xi) is first-order modal amplitude, phi (xi) is average flow coefficient of the compressor, psi (xi) is average pressure rise coefficient of the compressor, and phi (xi) is average pressure rise coefficient of the compressorT(xi) is the average flow coefficient of the downstream valve of the compressor; other parameters in the equation are inherent parameters of the compressor, and the following values are selected here:
ΨC0＝0.30，H＝0.14，W＝0.25，lC＝8.0，α＝1/3.5，m＝1.75。
s1.2 determines the operating range of 3 basic controllers: when the working state of the compressor is in the working range of the basic controller, the basic controller can ensure the stable operation of the compressor through tip air injection, and the working range of the basic controller can be expressed by the size of disturbance borne by the compressor. The above three basic controller performance characteristics are shown in table 2.
TABLE 2 basic controller Performance characteristics
S1.3, sequencing the basic controllers according to the working ranges of the 3 basic controllers, namely, switching the controllers in the working ranges according to the sequence along with the increase of the disturbance on the air compressor. Wherein, the order of the ith basic controller is denoted as tankiAnd rankiIs an integer of 1 to 3. As can be seen from table 2, the 3 basic controllers have respective operating ranges. As the compressor experiences increased disturbances, the controller in the operating range is switched from controller 1 to controller 3 and then to controller 2. Thus, the order of the basic controllers can be written as follows:
the controller 1: rank1＝1
The controller 2: rank2＝3
The controller 3: rank3＝2
S2 designing fuzzy switching module.
Fig. 4 is a schematic diagram of a fuzzy set and fuzzy rules of input and output of the fuzzy switching module, which embodies a design process of the fuzzy switching module. Wherein, the graph (a) is the fuzzy set division of the average flow coefficient phi, the graph (b) is the fuzzy set division of the first-order modal amplitude A, and the graph (c) is the fuzzy switching module output controller selection tendency ctreThe graph (d) is a fuzzy switching rule used in the fuzzy switching module.
The fuzzy switching module obtains the selection tendency c of the basic controller through the traditional fuzzy reasoning according to the state variable x of the gas compressortre. The compressor state variables x include, but are not limited to, the compressor mean flow Φ and the mean pressure rise Ψ. Said basic controller selection tendency ctreIs a parameter in the range of 0-1, and is used for representing the weight occupied by a certain basic controller.
S2.1, determining the average flow phi and the first-order mode A which can represent the working state of the compressor as the input of the fuzzy switching module.
S2.2 fuzzy partition is performed on the state variable x input by the fuzzy switching module, as shown in fig. 4 (a):
carrying out fuzzy division on the average flow coefficient phi and the first-order modal amplitude A to obtain Na5 fuzzy sets. The membership function uses a prompt membership function and a triangle membership function, and the selected membership function parameters are respectively shown in table 3 and table 4 (the formats are uniform, and the triangle membership function in the table is regarded as a trapezoid membership function with the upper end and the lower end coincident). The fuzzy set partition of the average flow coefficient Φ and the first-order modal amplitude a is shown in the graph (a) and the graph (b), respectively.
TABLE 3 mean flow coefficient fuzzy set membership function parameters
| Fuzzy set | a | b | | d |
| Z | ||||
| 0 | 0 | 0 | 0.15 | |
| PZ | 0.1 | 0.25 | 0.25 | 0.4 |
| PS | 0.25 | 0.4 | 0.4 | 0.43 |
| PM | 0.43 | 0.6 | 0.6 | 0.63 |
| PB | 0.63 | 0.8 | 1 | 1 |
TABLE 4 first order modal amplitude fuzzy set membership function parameters
| Fuzzy set | a | b | | d |
| Z | ||||
| 0 | 0 | 0 | 0.15 | |
| PZ | 0.05 | 0.18 | 0.18 | 0.34 |
| PS | 0.2 | 0.35 | 0.35 | 0.55 |
| PM | 0.4 | 0.55 | 0.55 | 0.75 |
| PB | 0.63 | 0.75 | 1 | 1 |
Selection tendency c for fuzzy switching module outputtreCarrying out fuzzy division to obtain Nb5 fuzzy sets. The membership function is a triangular membership function, and the selected membership function parameters are shown in table 5. Tendency to choose ctreThe fuzzy set partition is shown in figure (c).
TABLE 5 fuzzy set membership function parameters for selection trends
S2.3, establishing a fuzzy rule table, as shown in FIG. 4 (d):
according to the performance characteristics of the basic controller, the controller gradually transits from average flow coefficient feedback to comprehensive feedback and then gradually transits to first-order modal amplitude feedback according to the working range of the basic controller along with the continuous increase of the disturbance on the gas compressor. At the same time, setting the following selection tendency ctreThe used basic controller is gradually transited to the comprehensive feedback from the average flow coefficient feedback and then gradually transited to the first-order modal amplitude feedback. Thus, when fuzzy rule design is performed, fuzzy rule design can be performedPreference c following the greater disturbance to the compressortreThe larger the principle, i.e. the tendency c to be selected as the mean flow coefficient Φ and the first-order modal amplitude A increase continuouslytreGradually transits from the fuzzy set S to the fuzzy set B. The fuzzy rule table corresponding to the above principle is shown in fig. 4 (d).
S2.4, performing defuzzification on output of the fuzzy switching module to obtain a selection tendency ctre. The process of defuzzification is illustrated herein by specific examples.
Taking the average flow coefficient Φ equal to 0.275 and the first-order mode a equal to 0.387 as examples:
(1) calculating the prior membership mu of each fuzzy rulerule，i
The following fuzzy rules are used as examples herein, namely
ifΦ∈PZ，A∈PSthenctre∈MS
Its a priori membership rules may be calculated as
(2) Calculating controller selection tendency c using centroid methodtre
After determining prior membership of each fuzzy rulerule，iThe controller selection tendency c can be calculated according to the method of center-of-gravity defuzzification in S2.4tre。
S3, designing a control signal fusion module, and fig. 5 is a schematic diagram of fuzzy set division of the control signal fusion module.
S3.1, designing controller fusion weight, wherein in the diagram of FIG. 5, a fuzzy set P represents the weight of average flow coefficient feedback, a fuzzy set PA represents the weight of comprehensive feedback, and a fuzzy set A represents the weight of first-order modal amplitude feedback, and both the fuzzy set P and the fuzzy set PA use a triangular membership function. In this embodiment, three basic controllers are used, NcAccording to step 3Step S3.1 may determine that the fuzzy centroids are: c. C1＝0、c2＝0.5、c 31. The control signal fusion module fuzzy set membership function parameters are shown in table 6.
TABLE 6 fuzzy set membership function parameters of control signal fusion module
| Fuzzy set | a | | c |
| P | |||
| 0 | 0 | 0.3 | |
| PA | 0.2 | 0.5 | 0.8 |
| A | 0.7 | 1 | 1 |
S3.2, carrying out weighted fusion on the signals of the basic controllers, calculating the weight corresponding to each basic controller according to the fuzzy membership of the control signal fusion module which marks 6 in S3.1, thereby obtaining the control quantity actually output by the fused controllers, namely designing the fuzzy switching controller for the inventionControl quantity u of outputoutThe calculation results are shown in fig. 6, 7 and 8.
An example is also used herein to further illustrate the process of controlling signal weighted fusion:
in step S2.4 of the specific embodiment, the selection tendency c of the controller is calculatedtre0.286. According to the method in S3.2, the weights corresponding to the basic controllers can be obtained as follows:
w1＝fw，1(ctre)＝0.0457
w2＝fw，2(ctre)＝0
w3＝fw，3(ctre)＝0.288
in this case, the outputs of the basic controllers are respectively
ubase，1＝k1(Φ-Φ0)＝0.737
ubase，2＝k2A＝1.285
ubase，3＝k3(-Φ+Φ0+A)＝1.369
The fused controller output is
The simulation calculation results of this embodiment are shown in fig. 6, 7 and 8: FIG. 6 is a diagram of the active surge control process under a small disturbance condition, where the disturbance is generated by a small initial disturbance, and a diagram (a) is a variation process of a compressor flow coefficient when the fuzzy switching controller and the basic controller proposed by the present invention implement control; FIG. b is a graph of the jet flow coefficients generated by the fuzzy switching controller and the basic controller; graph (c) the selection tendency c generated by the fuzzy switching module at this timetre. It can be seen from the figure that under the action of the fuzzy switching controller, the control effect is consistent with or even slightly better than that of the basic controller, and the air injection quantity of the air injection valve can be basically consistent. Meanwhile, the selection tendency c generated by the fuzzy switching moduletreBasic maintenanceAt a lower level, i.e. a controller with the average flow coefficient Φ as a feedback quantity, this is consistent with the performance characteristics and operating range of the basic controller during the design process.
Fig. 7 shows the active control of surge in the case of a medium disturbance, which is caused by a large initial disturbance, wherein the meanings of the graphs (a), (b) and (c) are the same as those described in fig. 6. Under the condition of moderate disturbance, the fuzzy switching controller can also realize the active surge control effect consistent with that of the basic controller, but the air injection quantity generated by the fuzzy switching controller by using the air injection valve is obviously less than that of the basic controller, so that the fuzzy switching controller can realize a more optimized or even optimal control strategy under the required performance index. Controller selection tendency ctreThe controller is gradually transited from the comprehensive feedback to the average flow coefficient feedback at the moment, which also accords with the performance characteristics and the working range of the basic controller in the design process.
Fig. 8 shows the active control of surge in the case of a large disturbance, which is generated by placing a distortion plate in front of the compressor, wherein the meanings of the graphs (a), (b) and (c) are the same as those described in the above figures. The distortion sheet can make the air inlet flow field of the air compressor change obviously, and has great influence on the stable work of the air compressor. Under the condition, the fuzzy switching controller can achieve the same or better performance as the basic controller in the process of active surge control, and the air injection quantity generated by the air injection valve is obviously reduced compared with the basic controller, so that the influence of the control process on the working performance of the engine is smaller. In this state, the controller selection tendency c can be clearly observedtreIn the change process between the basic controllers, the selection tendency is gradually reduced along with the disturbance of the compressor, which shows that the controller is gradually transited to the average flow coefficient feedback from the first-order modal amplitude feedback through the comprehensive feedback at the moment. From the above process, it can be seen that the active surge control method based on fuzzy switching can control the stable operation of the compressor under the conditions of large disturbance and various surge inducers, and the reliability and the adaptability of the controller are very importantIs a significant improvement.
The above-mentioned embodiments only express the embodiments of the present invention, but not should be understood as the limitation of the scope of the invention patent, it should be noted that, for those skilled in the art, many variations and modifications can be made without departing from the concept of the present invention, and these all fall into the protection scope of the present invention.
Claims (4)
1. The aircraft engine surge active control system based on fuzzy switching of the controller is characterized by mainly comprising a basic controller design module, a fuzzy switching module and a control signal fusion module, wherein the design process of each part comprises the following steps:
s1 design N based on stability requirements in active surge controlcA basic controller for generating a basic control signal u for the fuzzy switching controllerbaseThe realization process is as follows:
s1.1 design N by using mode control method based on Lyapunov stability theorycA basic controller, and NcNot less than 2; in each basic controller, the average flow coefficient phi and the disturbance first-order mode A of the compressor can be respectively used as feedback quantities to determine the feedback quantity and the control quantity u required by the compressorcThe relationship of (1), namely:
ubase，1＝k1(Φ-Φ0)
ubase，2＝k2A
in the formula (I), the compound is shown in the specification,
is a controller parameter to be determined; u. ofbase，jIndicating the basic control signal, phi, output by the jth basic controller0The average flow coefficient of the compressor in steady state operation is obtained;
s1.2 determination of NcWorking range of the basic controller: when the working state of the compressor is in the working range of the basic controller, the basic controller can ensure the stable operation of the compressor through tip air injection, and the working range of the basic controller is expressed by the size of disturbance borne by the compressor; in the design process of the basic controller, different compressor parameter variables are selected as feedback variables of the basic controller, the basic controller working in a small disturbance range and a large disturbance range is designed respectively, and the basic controller with different working ranges is obtained, wherein the compressor parameter variables comprise an average flow coefficient phi and a disturbance first-order mode A;
s1.3 according to NcThe working range of each basic controller is sequenced according to the size of the working disturbance range, namely, the basic controllers in the working range are converted according to the sequence along with the increase of the disturbance on the air compressor; wherein the order of the ith basic controller is denoted rankiAnd rankiIs 1 to NcAn integer of (d);
s2 designing a fuzzy switching module: the fuzzy switching module obtains the selection tendency c of the basic controller through fuzzy reasoning according to the state variable x of the gas compressortreFor representing the weight occupied by a certain basic controller; the fuzzy switching module is designed by determining a state variable x input by the module, fuzzy division of module input and output, a fuzzy rule used by fuzzy reasoning and a defuzzification method, and the specific design process is as follows:
s2.1, determining a state variable x capable of representing the working state of the gas compressor as the input of a fuzzy switching module;
s2.2, fuzzy division is carried out on the state variable x input by the fuzzy switching module, and N is obtained by dividing each variableaA fuzzy set; basic controller selection trends for output ctreCarrying out fuzzy division to obtain NbA fuzzy set; determining membership functions f of input variables belonging to respective fuzzy setsin，(i，C)(xi) And the membership function f of the output variable belonging to each fuzzy setout，B(ctre)；
Membership mu of input variables belonging to different fuzzy setsin，(i，C)Can be calculated by:
μin，(i，C)＝fin，(i，C)(xi)
wherein x isiIs the value of the ith input variable; c is dividing a fuzzy set; f. ofin，(i，C)A membership function of an ith input variable belonging to a fuzzy set C; mu.sin，(i，C)Calculating the membership degree of the ith input variable in the fuzzy set C;
membership mu of output variable belonging to different fuzzy setsout，BCan be calculated by:
μout，B＝fout，B(ctre)
wherein, ctreA selection tendency for the output; b is dividing a fuzzy set; f. ofout，B(ctre) Represents the output ctreOutputting membership function in fuzzy set B; mu.sout，BThen a calculated preference c is selectedtreMembership in fuzzy set B;
s2.3, establishing a fuzzy rule table of a fuzzy switching module, and designing NrulesA bar fuzzy rule;
fuzzy rules may be expressed in the format of if-then, i.e.:
If x1∈C1，x2∈C2，…，xn∈Cnthen ctre∈B
wherein, C1Denotes the fuzzy set, C, to which the 1 st input variable belongs in this fuzzy rule2Representing the fuzzy set to which the 2 nd input variable belongs, and so on; b represents the output c in this fuzzy ruletreThe fuzzy set to which it belongs;
in the fuzzy rule, (x)1∈C1，x2∈C2，…，xn∈Cn) Is a priori condition of the fuzzy rule, the prior membership degree mu of the fuzzy rulerule，iCan be calculated as:
wherein the content of the first and second substances,
that is, the membership degree of the input variable calculated in S2.2 in the fuzzy set; n is a radical ofinsThe number of input variables in the fuzzy rule is shown; mu.srule，iThe prior membership degree of the ith fuzzy rule is calculated;
s2.4, performing defuzzification on the output of the fuzzy switching module, wherein the defuzzification result is the selection tendency c of the basic controller calculated by the fuzzy switching moduletre(ii) a The output result is defuzzified by using a gravity center method, and the calculation process is as follows:
(1) calculating the prior membership mu of each fuzzy rulerule，iNamely:
(2) calculating basic controller selection trends c using the center of gravity methodtre：
Wherein, murule，iAnd murule，jRespectively calculating prior membership degrees of the ith fuzzy rule and the jth fuzzy rule;
and
respectively outputting membership functions of a fuzzy set B in the ith fuzzy rule and the jth fuzzy rule; c. CtreSelecting a trend for the calculated base controller;
s3 designing a control signal fusion module; the control signalThe input of the number fusion module comprises a basic controller selection trend ctreAnd a basic control signal u generated by the basic controllerbaseOutput as the fused control signal uout(ii) a The control signal fusion module selects the trend c according to the input basic controllertreCalculating the weight w of each basic controlleriAnd then on the basis of the calculated weights for the basic control signal ubaseCarrying out weighting fusion to finally obtain the actual control signal u of the basic controllerout；
The design of a control signal fusion module needs to determine the fusion weight of a basic controller and a weighted fusion method, and the specific steps are as follows:
s3.1, designing a fusion weight of a basic controller; according to the number N of basic controllerscFor selection tendency ctreFuzzy division is carried out, and the obtained fuzzy set center is calculated by adopting the following formula:
in the formula, ciIs the ith fuzzy set center; n is a radical ofcIs the number of basic controllers; rankiFor the order determined in step S1.3 for the ith basic controller, taking values from 1 to NcAn integer of (d); for example, in NcWhen 3, the fuzzy set center c1＝0、c2＝0.5、c3＝1；
Weight w corresponding to ith basic controlleriCalculated according to the following formula:
wi＝fw，i(ctre)
wherein, ctreSelecting trends for the fusion module inputs, i.e., the base controller; f. ofw，iMembership functions corresponding to the ith basic controller, wherein the membership functions can be selected from the forms mentioned in the step S2.2; w is aiThe calculated weight corresponding to the ith basic controller is obtained;
s3.2, carrying out weighted fusion on the basic control signals to obtain the reality of the basic controllerBoundary control signal uout；
Actual control signal u of the basic controlleroutThe method is obtained by weighted fusion of the following formula:
wherein u isbase，jA basic control signal representing the output of the jth basic controller; w is aiAnd wjRespectively representing the weight of the ith corresponding to the jth basic controller; n is a radical ofcThe number of basic controllers; u. ofoutThe control quantity is actually output by the fused basic controller, namely the control quantity output by the fuzzy switching controller.
2. The active aircraft engine surge control system based on fuzzy controller switching of claim 1, wherein in step S1.1, the controller parameter determination method comprises the following steps: based on a traditional gas compressor Moore-Greitzer model, after linearization processing is carried out on the model, the controller parameters can be obtained by combining the Lyapunov stability theory.
3. The active control system for aircraft engine surge based on controller fuzzy switching as claimed in claim 1, wherein in step S2, said compressor state variables x comprise average compressor flow and average pressure rise.
4. The active control system for aircraft engine surge based on controller fuzzy switching as claimed in claim 1, wherein in step S2, said basic controller selects trend ctreIs in the range of 0 to 1.
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