CN107045576B - Comprehensive analysis and verification method for judging buffeting of wire feeding fan - Google Patents

Comprehensive analysis and verification method for judging buffeting of wire feeding fan Download PDF

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CN107045576B
CN107045576B CN201710254290.6A CN201710254290A CN107045576B CN 107045576 B CN107045576 B CN 107045576B CN 201710254290 A CN201710254290 A CN 201710254290A CN 107045576 B CN107045576 B CN 107045576B
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supply system
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CN107045576A (en
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何寅
吕伟
邵长岭
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China Tobacco Zhejiang Industrial Co Ltd
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Abstract

The invention relates to the field of wind-power cigarette feeding, in particular to a comprehensive analysis and verification method for buffeting judgment of a cigarette feeding fan. According to the method, constrained expected control is introduced into a comprehensive analysis and verification method for judging buffeting of the wire feeding fan, and the generation process of the buffeting of the fan is deduced through an expected control coefficient sigma and a modal quantization coefficient c, so that the problems that the reason of the buffeting of the fan is uncertain, the analysis is inaccurate and the verification is difficult to realize under the influences of factors such as short time, sporadic property and high frequency are solved well.

Description

Comprehensive analysis and verification method for judging buffeting of wire feeding fan
Technical Field
The invention relates to the field of wind-power cigarette feeding, in particular to a comprehensive analysis and verification method for buffeting judgment of a cigarette feeding fan.
Background
Tobacco shreds are one of the important raw materials for manufacturing cigarettes. In the cigarette production process, firstly, cut tobacco reaches a cut tobacco collecting box of a cigarette making machine through the processes of cutting, fermenting, humidifying, adding components, drying and the like through a conveying link; then the cigarette machine forms cigarette strips after forming through tobacco shreds, then the cigarette strips are cut into cigarettes with equal weight through a weight control system, and finally the cigarettes are formed into small packets and large strips through a packing machine. In the process, the cut tobacco is used as an important and unique circulating medium, so whether the quality and the quantity of the cut tobacco can be guaranteed or not in the conveying link is one of important factors for determining the high and low quality of cigarette products.
The wind-force send silk because it has response speed fast, dispose characteristics such as being nimble, reliability height and so on by most tobacco enterprises adopt, wind-force send silk rely on send silk fan to provide the negative pressure induced draft, send the pipe tobacco in the collection silk case to cigarette machine production cigarette through sending the pipeline, at this in-process, send silk fan to receive the influence of current fluctuation and the windage in the tuber pipe, send silk fan to produce buffeting, when the fan produced buffeting, the air current of the regular at the uniform velocity originally can become unstable, produce a lot of anomalous turbulence, be called "turbulent flow". Although the time for generating the turbulence is not enough relative to the time of the whole tobacco shred suction process, the abnormal phenomenon of tobacco shred conveying still can be caused, and the abnormal phenomenon is shown in the following steps: when the tobacco shred sucking speed is low, the phenomenon of less tobacco shreds or tobacco shred blockage is easily caused, and the cigarette making machine is finally stopped; when the air speed of the tobacco shred absorption is higher, the collision and friction between the tobacco shred and the pipe wall can be increased, the breakage of the tobacco shred is increased, and the process quality indexes such as the filament rate of the tobacco shred are directly influenced. In addition, frequent buffeting can damage fan blades and accelerate abrasion of moving parts in the fan. The buffeting frequency of a general fan is from low to high and occurs uninterruptedly, so how to combine the dynamic characteristics of the fan and avoid buffeting of the fan is a difficult problem in researching the stability of a wire feeding process, and a plurality of methods are provided for reducing buffeting by referring to other equipment. For example, the Anhui science and technology institute (Jones and Tiger, easy-to-surrept, etc.. Fan blade vibration active control analysis of intelligent materials [ J ]. detection and control, 2009, (9): 118-. The university of Guangdong industries (Lezhong kuan, Zhan Xin Zheng. study of buffeting in the theory of structure-changing control [ J ]. proceedings of Wuyi university, 2003,17(3):66-69) after analyzing the common four methods for attenuating buffeting, proposed a buffeting method based on the fuzzy nerve and utilized the simulation results for demonstration. In Beijing university of science and engineering (in Asia Man, Sunpbo, etc.; flexible spacecraft sliding mode variable structure control [ J ] based on novel approach law, space control, 2013,31(5):62-68), aiming at the problem of high-frequency buffeting of flexible spacecraft sliding mode variable structure control moment brought by applying a switching function, self-adaptive intelligent processing is provided for an improved index approach rate by applying fuzzy logic, so that the high-frequency buffeting of the control moment is restrained. The Harbin engineering university (Jinhong Chao, Rolingming, etc.; research on a novel saturation function method for suppressing sliding mode buffeting [ J ]. proceedings of Harbin engineering university, 2007,28(3): 288-. The university of mineral industry in China (Zheng Xiao, Sunwei, etc.. variable structure control a method for suppressing buffeting design [ J ]. Chinese scientific and technological paper on-line, 2011) designs a method for weakening buffeting by comparing the approach law with the traditional PID control method and the traditional variable structure control adopting a saturation function as a switching function, thereby obtaining a new method with good control effect. The university of west ampere electronic technology (study on characteristics of buffeting in Shen. sliding mode variable structure control and suppression [ D ]. school of academic degree of science of the university of west ampere electronic technology, 2012) proposes a stabilizing criterion and a variable structure switching gain adaptive adjustment method by adopting a generalized description function method, and is used for designing a backlash compensation controller and two types of second-order sampling variable structure controllers with small buffeting characteristics. The mechanical engineering college (Shetland, Chengyou, etc.. mechanical arm rapid sliding mode variable structure control with buffeting inhibition characteristics [ J ] motor and control bulletin, 2012,16(7):97-102) provides a sliding mode variable structure control strategy based on a novel sliding mode surface and a fuzzy power approach law, improves the convergence speed of the sliding mode variable structure in the sliding motion control stage, and can improve the approach motion speed of a system on the premise of ensuring the buffeting inhibition effect. The Fuzhou university mechanical engineering and automation college (Tongbao, Chenli, floating-base space robot rapid sliding mode variable structure control [ J ],2015,10(3):45-51) based on the fuzzy power approach law discusses a rapid sliding mode variable structure control method based on the fuzzy power approach law, and the method can enable the buffeting suppression effect of the mechanical arm to be obvious and simultaneously ensure the track tracking control effect of the system. Buffeting control [ J ],2005,45(1):34-42) of a sliding mode variable structure control system of Qinghua university (Yangpu, Zhang-Zeekao) gives quantitative relations among buffeting amplitude, period, approach rate parameters and change rates of control quantities by analyzing buffeting process controlled by a sliding mode variable structure under index approach rate so as to weaken buffeting of a stopper rod at certain amplitude and frequency. An index approach law is analyzed and designed by a mechanical arm sliding mode control method based on the approach law, wherein the mechanical arm sliding mode control method is used for researching [ J ],2013,27(1):62-66) of Hunan industry university (Huanghua, Liguang, and the like), and on the basis, the kinematics characteristics of the mechanical arm are researched and optimized, and buffeting of the mechanical arm in the motion process is reduced.
The buffeting is a common phenomenon in the running process of fan equipment, slight buffeting is a normal phenomenon, but if frequent or serious abnormal buffeting exists, the service life of internal parts of the fan blades can be influenced, and irreversible damage is caused. Because the fan is a closed operating environment, the buffeting of the fan gradually develops into a serious process from a slight state, when the serious buffeting occurs, the fan needs to be stopped for maintenance, parts are replaced, and production influence and economic loss are caused, so that how to judge the buffeting condition of the fan in advance to inhibit or eliminate the buffeting trend is one of measures for reducing the influence risk of the system fault of the fan. The above documents further adopt a method of adjusting an approach law to determine whether to reduce the amplitude, the period and the change rate of buffeting, which is suitable for objects with relatively strong anti-interference performance and intermittent disturbance, but because the influence of system parameters and external environments (current and strong magnetic field) of a fan is large, the anti-interference performance is relatively weak, and continuous disturbance which cannot be measured is easily generated, in a strict sense, the method of adjusting the approach law is adopted to determine that the method is meaningless for a fan system with unpredictable and continuous disturbance.
Disclosure of Invention
The invention provides a comprehensive analysis and verification method for judging buffeting of a wire feeding fan, which introduces constrained expected control into the comprehensive analysis and verification method for judging buffeting of the wire feeding fan, and deduces a generating process causing the buffeting of the fan through an expected control coefficient sigma and a modal quantization coefficient c, thereby better solving the problems of uncertain reasons of the buffeting of the fan, inaccurate analysis and difficult realization of verification under the influences of factors such as short time, sporadic nature, high frequency and the like.
The technical method adopted by the invention to solve the technical problems is as follows:
a comprehensive analysis and verification method for judging buffeting of a wire feeder comprises the following steps:
1) sampling process variables of instantaneous air pressure and air quantity of negative pressure air suction of a wire feeding fan randomly within a wire feeding period of equipment to obtain a sampling matrix W (N is S), wherein N is the number of sampling points, and S is the number of monitoring variables; repeating the production period T times to obtain corresponding data matrix W' (T N S)i) In which S isiThe number of sampling points in the ith dust removal period is;
2) the data matrix is measured and calculated according to a constraint variational principle to obtain a constraint control coefficient sigma aiming at buffeting of the wire feeding fan, namely
Figure BDA0001272950690000031
Regarding an air supply system of the wire feeding fan as constrained expected control, and adopting a bounded and infinite gain regulation control method for comprehensive analysis of an air supply process;
3) the air supply process is set as a two-order function, and an air supply system is regulated and controlled: when the fan works stably, y is equal to x, wherein y is equal to x0＝y,x0X, wherein y is amplitude, x is vibration frequency, and the start-stop switching condition is
Figure BDA0001272950690000032
Wherein sigma is a constraint control coefficient, and c is a modal quantization coefficient; if the fan generates buffeting, the changes of y0 and x0 deviate from the expectation of the air supply system, and the corresponding relation corresponds to the deviation error of the constraint type expectation control, namely the deviation error of the constraint type expectation control
Figure DEST_PATH_FDA0001341339840000013
Wherein VxσFor the value of the variation of the control coefficient, x, of the air supply systemcFor a pre-estimated value, x, after modal quantization of an air supply systemuDeviation error value of the air supply system; and designating the initial state of the air supply system as xoUnder the condition that x is less than 0 and sigma is more than 0oIs the initial state value of the air supply system;
3) if the air supply system can be regulated and controlled, the coefficient sigma designed according to the previous regulation and control method can ensure that the air supply system conforms to (x)0',xσ') initial value, i.e. at tRC＝tσ-t0Period t of timeσFor air supply system constraint control process time, t0Is the initial state time of the air supply system, tRCConstraining an expected control time for the air supply system; make the air supply system from (x)0',xσ') to a c-mode quantization state, which is convenient for the fan to conform to a constraint formThe quantitative state of the desired control, the process is as shown in FIG. 1;
4) said FIG. 1, in which (x)0',xσ') the slope of the line between the origin O (0,0) is denoted d ═ xσ/x0(ii) a σ >0 corresponds to Δ d ═ xσ-x0When the state of the fan air supply system approaches to a quantized state c, d is less than 0, so that the working condition modal convergence speed of the fan air supply system represented by x + dx ═ 0 is different from the working condition modal convergence speed represented by c, that is, the working condition modal convergence speed of the fan air supply system in a not-completely quantized state is greater than the working condition modal convergence speed represented by a constrained expected control state, and the buffeting of the fan is obvious; in the air supply system from (x)0',xσ') the convergence rate gradually decreases to be consistent with the convergence rate of c in the approach process towards c, namely d → c, the approach process is called balance, otherwise, buffeting is carried out;
5) c obtained by solving the coefficient sigma under the fan start-stop switching condition (sigma' is less than 0, sigma is more than 0) has the possibility of being different from the equivalent phenomenon of c designed under the condition of the working condition modal convergence of the air supply system, the possibility that sigma exceeds a limit value when the fan generates buffeting exists, so that the fan can not be ensured to be always in a stable state, and if the buffeting of the fan still occurs after the working condition modal convergence of the air supply system, the phenomenon that expected control can not be realized necessarily occurs;
6) when the phenomenon that the expected regulation is not achievable occurs, the slope d at the moment is not equal to c, and a straight line x' + cx ≠ 0 parallel to x + cx ═ 0, namely, the modal quantization state of the fan air supply system cannot meet the constraint condition, so that the air supply system cannot play the significance of the expected regulation; although its slope is not equal to the quantized coefficient c, x + cx ≠ 0 can be translated up and down; therefore, the slope can be made equal to c by using a translation method, and as a result, there are two possibilities for the change process of convergence (i.e., (x (t), x' (t))), as shown in fig. 2, wherein the 1 st possibility indicates that the fan buffeting can be regulated, and the 2 nd possibility indicates that the fan buffeting can not be regulated;
7) in the said fig. 2, curve 1 shows that the fan can be regulated when buffeting occurs, curve 2 shows that it can not be regulated, and during the fan air supply system approaching quantization c, because d >0 the air supply system convergence process must be diverged first, then evolves to another branch of quantization c, the process that the fan buffeting tends to be stable is a non-unidirectional convergence process;
8) the method for verifying the correctness of the analysis comprises two steps, wherein the first step is to determine a start-stop switching function sigma (x) of a fan air supply system; the second step is to achieve the desired control by satisfying the modal quantization state coefficient c;
the first step comprises the steps of:
1) in the first step, it is assumed that the target of the fan buffeting control problem, that is, the fan operating condition state, is expressed as: s ═ a (x) + b (y) × 0.5, where a (x) represents a vibration frequent change matrix, b (y) represents an amplitude change matrix, and c represents a modal quantization coefficient; since A (x) is an n × n dimensional matrix and B (y) is an n × m dimensional matrix, s is an n dimensional vector, c ∈ Rm×nAnd the equivalent function formed by the linear combination of the state variables is that the start-stop switching function sigma (x) of the fan air supply system is specified as: σ (x) ═ s ═ a (x) + b (y) × c;
2) in the function equation, the modal quantization coefficient c is equal to Rm×nIt is the linear combination coefficient of the switching function, and the controlled object can be expressed as a matrix:
Figure BDA0001272950690000041
wherein x1, x2 are the process variable of the instantaneous wind pressure and the amount of wind of the negative pressure induced draft that gather respectively when the fan takes place the buffeting, if at this moment in the collection process, supposing that the fan operating mode dynamic process of expectation is asymptotically stable, then corresponding sigma (x) is: σ (x) ═ c,1][x1,x2]TThe value ranges of x1 and x2 are called as the existence areas of a start-stop switching function sigma (x) of the fan air supply system and are marked as theta, and the value ranges of the fan modal quantization coefficients c relate to multiple aspects, such as stability of an expected fan buffeting regulation method, rapidity of a dynamic process of the expected regulation method and the like;
3) the value range of the fan modal quantization coefficient c meets the requirement of the method for asymptotic stability only by c being more than 0 if the buffeting of the fan is reduced, and according to the method, the buffeting of the fan modal quantization coefficient c is reducedThe range of possible changes of x1 and the requirement for rapidity of the dynamic process of the expected regulation and control method to reduce buffeting are met, for example, c is specified to be 0.5, and the fan operating condition state S is defined as: x is the number of2＝-0.5x1,-2＜x1< 2, which is the existence region theta of SσTwo line segments S1 and S2 obliquely symmetrical to the zero point, shown in FIG. 3, where θ isσIs the field of S; if sustained buffeting mitigation is desired and there is no particular requirement for method rapidity, then only c and c need be reduced>0, the method rapidity is far lower than that of an air supply system;
the second step comprises the steps of:
1) in the second step, there are two ways for c to pull the air supply system from x0 to S: pulling x to Sp when sigma (x) >0 or pulling x to SN when sigma (x) <0 is stable, wherein Sp is an estimated state and SN is a regulation state; pulling x to SN with σ (x) >0, or pulling x to Sp with σ (x) <0 as buffeting; although they all reach S, the dynamic process x0(t) is different; if stable, x0(t) unidirectional convergence without overshoot; if buffeting, x0(t) overshoot; whether steady or buffeting, depending on the method of determination of c;
2) the approach, using this condition, obtains the inequality of control as
Figure BDA0001272950690000051
An additional condition called the second step, according to which c can be solved, where c is assumed to be constant, and σ (x) ═ cxSubstituting this formula into the expression x ═ a (x) + b (x) + C, where x (t) is0)＝x0And substituting the error coefficient u at the same time to obtain an expression: σ (x) ═ ca (x) + cb (x) u, assume (cb (x))-1The error coefficient u' for which the constrained desired control can be found is: u ═ csgn (σ (x)), where u' satisfies
Figure BDA0001272950690000052
The requirements of (1);
3) the expression of the error coefficient u 'of the constrained anticipatory control, namely u' ═ csgn (sigma (x)), and the controlled object expression form closed-loop control;
4) the expression for the error coefficient u is exemplified, for example
Figure BDA0001272950690000053
u'＝[0.51]Putting an expression of the error coefficient u', and obtaining an example start-stop fan control expression as follows: u' ═ 0.5sgn (σ (x)); at this time, u' is expressed with the controlled object (i.e. x ═ a (x) + b (x)) + C, where x (t)0)＝x0) A closed loop control is formed.
The invention introduces the constrained expected control into the comprehensive analysis and verification method for judging the buffeting of the wire feeding fan, and deduces the generation process of the buffeting of the fan by the expected control coefficient sigma and the modal quantization coefficient c, thereby better solving the problems of uncertain reasons of the buffeting of the fan, inaccurate analysis and difficult realization of verification under the influences of factors such as short time, accidental and high frequency.
Drawings
FIG. 1 is a diagram illustrating a process of approaching a controllable state of the system.
FIG. 2 shows two possible graphs of the variation process (x (t), x' (t)).
Fig. 3 is a diagram of the system asymptotic stability process.
Fig. 4 is a block diagram of the present invention and system.
Detailed Description
As shown in fig. 4, the method for comprehensively analyzing and verifying buffeting of a wire feeder comprises a comprehensive analysis and verification method, wherein the comprehensive analysis comprises the following steps:
1) sampling process variables of instantaneous air pressure and air quantity of negative pressure air suction of a wire feeding fan randomly within a wire feeding period of equipment to obtain a sampling matrix W (N is S), wherein N is the number of sampling points, and S is the number of monitoring variables; repeating the production period T times to obtain corresponding data matrix W' (T N S)i) In which S isiThe number of sampling points in the ith dust removal period is;
2) the data matrix is measured and calculated according to a constraint variational principle to obtain a constraint control coefficient sigma aiming at buffeting of the wire feeding fan, namely
Figure BDA0001272950690000061
Regarding an air supply system of the wire feeding fan as constrained expected control, and adopting a bounded and infinite gain regulation control method for comprehensive analysis of an air supply process;
3) the air supply process is set as a two-order function, and an air supply system is regulated and controlled: when the fan works stably, y is equal to x, wherein y is equal to x0＝y,x0X, wherein y is amplitude, x is vibration frequency, and the start-stop switching condition is
Figure BDA0001272950690000062
Wherein sigma is a constraint control coefficient, and c is a modal quantization coefficient; if the fan generates buffeting, the changes of y0 and x0 deviate from the expectation of the air supply system, and the corresponding relation corresponds to the deviation error of the constraint type expectation control, namely the deviation error of the constraint type expectation control
Figure 55004DEST_PATH_FDA0001341339840000013
Wherein VxσFor the value of the variation of the control coefficient, x, of the air supply systemcFor a pre-estimated value, x, after modal quantization of an air supply systemuDeviation error value of the air supply system; and designating the initial state of the air supply system as xoUnder the condition that x is less than 0 and sigma is more than 0oIs the initial state value of the air supply system;
3) if the air supply system can be regulated and controlled, the coefficient sigma designed according to the previous regulation and control method can ensure that the air supply system conforms to (x)0',xσ') initial value, i.e. at tRC＝tσ-t0Period t of timeσFor air supply system constraint control process time, t0Is the initial state time of the air supply system, tRCConstraining an expected control time for the air supply system; make the air supply system from (x)0',xσ') to a c-mode quantization state, which is a quantization state that facilitates the ability of the wind turbine to comply with a contracted expected control, as shown in FIG. 1;
4) said FIG. 1, in which (x)0',xσ') slope of the line between the origin O (0,0)The ratio is expressed as d ═ xσ/x0(ii) a σ >0 corresponds to Δ d ═ xσ-x0When the state of the fan air supply system approaches to a quantized state c, d is less than 0, so that the working condition modal convergence speed of the fan air supply system represented by x + dx ═ 0 is different from the working condition modal convergence speed represented by c, that is, the working condition modal convergence speed of the fan air supply system in a not-completely quantized state is greater than the working condition modal convergence speed represented by a constrained expected control state, and the buffeting of the fan is obvious; in the air supply system from (x)0',xσ') the convergence rate gradually decreases to be consistent with the convergence rate of c in the approach process towards c, namely d → c, the approach process is called balance, otherwise, buffeting is carried out;
5) c obtained by solving the coefficient sigma under the fan start-stop switching condition (sigma' is less than 0, sigma is more than 0) has the possibility of being different from the equivalent phenomenon of c designed under the condition of the working condition modal convergence of the air supply system, the possibility that sigma exceeds a limit value when the fan generates buffeting exists, so that the fan can not be ensured to be always in a stable state, and if the buffeting of the fan still occurs after the working condition modal convergence of the air supply system, the phenomenon that expected control can not be realized necessarily occurs;
6) when the phenomenon that the expected regulation is not achievable occurs, the slope d at the moment is not equal to c, and a straight line x' + cx ≠ 0 parallel to x + cx ═ 0, namely, the modal quantization state of the fan air supply system cannot meet the constraint condition, so that the air supply system cannot play the significance of the expected regulation; although its slope is not equal to the quantized coefficient c, x + cx ≠ 0 can be translated up and down; therefore, the slope can be made equal to c by using a translation method, and as a result, there are two possibilities for the change process of convergence (i.e., (x (t), x' (t))), as shown in fig. 2, wherein the 1 st possibility indicates that the fan buffeting can be regulated, and the 2 nd possibility indicates that the fan buffeting can not be regulated;
7) in the said fig. 2, curve 1 shows that the fan can be regulated when buffeting occurs, curve 2 shows that it can not be regulated, and during the fan air supply system approaching quantization c, because d >0 the air supply system convergence process must be diverged first, then evolves to another branch of quantization c, the process that the fan buffeting tends to be stable is a non-unidirectional convergence process;
8) the method for verifying the correctness of the analysis comprises two steps, wherein the first step is to determine a start-stop switching function sigma (x) of a fan air supply system; the second step is to achieve the desired control by satisfying the modal quantization state coefficient c;
the first step comprises the steps of:
1) in the first step, it is assumed that the target of the fan buffeting control problem, that is, the fan operating condition state, is expressed as: s ═ a (x) + b (y) × 0.5, where a (x) represents a vibration frequent change matrix, b (y) represents an amplitude change matrix, and c represents a modal quantization coefficient; since A (x) is an n × n dimensional matrix and B (y) is an n × m dimensional matrix, s is an n dimensional vector, c ∈ Rm×nAnd the equivalent function formed by the linear combination of the state variables is that the start-stop switching function sigma (x) of the fan air supply system is specified as: σ (x) ═ s ═ a (x) + b (y) × c;
2) in the function equation, the modal quantization coefficient c is equal to Rm×nIt is the linear combination coefficient of the switching function, and the controlled object can be expressed as a matrix:
Figure BDA0001272950690000081
wherein x1, x2 are the process variable of the instantaneous wind pressure and the amount of wind of the negative pressure induced draft that gather respectively when the fan takes place the buffeting, if at this moment in the collection process, supposing that the fan operating mode dynamic process of expectation is asymptotically stable, then corresponding sigma (x) is: σ (x) ═ c,1][x1,x2]TThe value ranges of x1 and x2 are called as the existence areas of a start-stop switching function sigma (x) of the fan air supply system and are marked as theta, and the value ranges of the fan modal quantization coefficients c relate to multiple aspects, such as stability of an expected fan buffeting regulation method, rapidity of a dynamic process of the expected regulation method and the like;
3) if the value range of the fan modal quantization coefficient c is required to reduce the fan buffeting and meet the requirement of the method on the asymptotic stability, only c is greater than 0, the buffeting is reduced according to the possible change range of x1 and the requirement on the rapidity of the dynamic process of the expected regulation and control method, for example, c is specified to be 0.5, and the fan working condition state S is defined as: x is the number of2＝-0.5x1,-2＜x1< 2, which is the existence region theta of SσTwo line segments S1 and S2 obliquely symmetrical to the zero point, shown in FIG. 3, where θ isσIs the field of S; if sustained buffeting mitigation is desired and there is no particular requirement for method rapidity, then only c and c need be reduced>0, the method rapidity is far lower than that of an air supply system;
the second step comprises the steps of:
1) in the second step, there are two ways for c to pull the air supply system from x0 to S: pulling x to Sp when sigma (x) >0 or pulling x to SN when sigma (x) <0 is stable, wherein Sp is an estimated state and SN is a regulation state; pulling x to SN with σ (x) >0, or pulling x to Sp with σ (x) <0 as buffeting; although they all reach S, the dynamic process x0(t) is different; if stable, x0(t) unidirectional convergence without overshoot; if buffeting, x0(t) overshoot; whether steady or buffeting, depending on the method of determination of c;
2) the approach, using this condition, obtains the inequality of control as
Figure BDA0001272950690000082
An additional condition called the second step, according to which c can be solved, where c is assumed to be constant, and σ (x) ═ cxSubstituting this formula into the expression x ═ a (x) + b (x) + C, where x (t) is0)＝x0And substituting the error coefficient u at the same time to obtain an expression: σ (x) ═ ca (x) + cb (x) u, assume (cb (x))-1The error coefficient u' for which the constrained desired control can be found is: u ═ csgn (σ (x)), where u' satisfies
Figure BDA0001272950690000091
The requirements of (1);
3) the expression of the error coefficient u 'of the constrained anticipatory control, namely u' ═ csgn (sigma (x)), and the controlled object expression form closed-loop control;
4) the expression for the error coefficient u is exemplified, for example
Figure BDA0001272950690000092
u'＝[0.51]Putting an expression of the error coefficient u', and obtaining an example start-stop fan control expression as follows: u' ═ 0.5sgn (σ (x)); at this time, u' is expressed with the controlled object (i.e. x ═ a (x) + b (x)) + C, where x (t)0)＝x0) A closed loop control is formed.

Claims (1)

1. A comprehensive analysis and verification method for judging buffeting of a wire feeding fan is characterized by comprising a comprehensive analysis and verification method, wherein the comprehensive analysis comprises the following steps:
1) sampling process variables of instantaneous air pressure and air quantity of negative pressure air suction of a wire feeding fan randomly within a wire feeding period of equipment to obtain a sampling matrix W (N is S), wherein N is the number of sampling points, and S is the number of monitoring variables; repeating the production period T times to obtain corresponding data matrix W' (T N S)i) In which S isiThe number of sampling points in the ith dust removal period is;
2) the data matrix is measured and calculated according to a constraint variational principle to obtain a constraint control coefficient sigma aiming at buffeting of the wire feeding fan, namely
Figure FDA0002377029250000011
Regarding an air supply system of the wire feeding fan as constrained expected control, and adopting a bounded and infinite gain regulation control method for comprehensive analysis of an air supply process;
3) the air supply process is set as a two-order function, and an air supply system is regulated and controlled: when the fan works stably, y is equal to x, wherein y is equal to x0＝y,x0X, wherein y is amplitude, x is vibration frequency, and the start-stop switching condition is
Figure FDA0002377029250000012
Wherein sigma is a constraint control coefficient, and c is a modal quantization coefficient; if the fan generates buffeting, y0And x0Will deviate from the air supply system expectation and the corresponding relation corresponds to deviation error of the constraint expectation control, i.e.
Figure FDA0002377029250000013
Wherein VxσFor the value of the variation of the control coefficient, x, of the air supply systemcFor a pre-estimated value, x, after modal quantization of an air supply systemuDeviation error value of the air supply system; and designating the initial state of the air supply system as xo<0 and σ>Under the condition of 0, wherein xoIs the initial state value of the air supply system;
if the air supply system can be regulated and controlled, the coefficient sigma designed according to the previous regulation and control method can ensure that the air supply system conforms to (x)0',xσ') initial value, i.e. at tRC＝tσ-t0Period t of timeσFor air supply system constraint control process time, t0Is the initial state time of the air supply system, tRCConstraining an expected control time for the air supply system; make the air supply system from (x)0',xσ') to a c-mode quantization state, which is a quantization state that facilitates the ability of the wind turbine to comply with a contracted expected control;
4)(x0',xσ') the slope of the line between the origin O (0,0) is denoted d ═ xσ/x0；σ>0 corresponds to △ d ═ x σ -x0>0, d is necessary to be present during the period that the state of the fan air supply system approaches the quantization state c<0, so that the working condition modal convergence speed of the fan air supply system represented by x + dx being 0 is different from the working condition modal convergence speed represented by c, that is to say, the working condition modal convergence speed of the fan air supply system in a not-completely quantized state is greater than the working condition modal convergence speed represented by a constrained expected control state, and the buffeting of the fan is more obvious; in the air supply system from (x)0',xσ') the convergence rate gradually decreases to be consistent with the convergence rate of c in the approach process towards c, namely d → c, the approach process is called balance, otherwise, buffeting is carried out;
5) c obtained by solving the coefficient sigma under the fan start-stop switching condition (sigma' <0, sigma >0) has the possibility of being different from the equivalent phenomenon of c designed under the condition of the working condition modal convergence of the air supply system, and the situation that the fan is always in a stable state cannot be ensured because sigma when the fan generates buffeting is possible to exceed a limit value, and if the fan buffeting still occurs after the working condition modal convergence of the air supply system, the phenomenon that expected control cannot be realized necessarily occurs;
6) when the phenomenon that expected control cannot be realized occurs, the slope d at the moment is not equal to c, and a straight line x' + cx ≠ 0 parallel to x + cx ═ 0, namely, the modal quantization state of the fan air supply system cannot meet the constraint condition, so that the air supply system cannot play the significance of expected regulation and control; although its slope is not equal to the quantized coefficient c, x + cx ≠ 0 can be translated up and down; therefore, the slope can be made equal to c by using a translation method, and the result is a change process of convergence, namely (x (t), x' (t)), and there are two possibilities, wherein the 1 st possibility indicates that the buffeting of the fan can be regulated and controlled, and the 2 nd possibility indicates that the buffeting of the fan can not be regulated and controlled;
7) the curve 1 shows that the fan can be regulated and controlled when the buffeting happens, the curve 2 shows that the fan cannot be regulated and controlled, and when the fan air supply system approaches to the quantization c, the convergence process of the fan air supply system must be diverged firstly when d is larger than 0, and then the convergence process evolves to the other branch of the quantization c, so that the process that the buffeting of the fan tends to be stable is a non-unidirectional convergence process;
8) the method for verifying the correctness of the analysis comprises two steps, wherein the first step is to determine a start-stop switching function sigma (x) of a fan air supply system; the second step is to achieve the desired control by satisfying the modal quantization state coefficient c;
the first step comprises the steps of:
1) in the first step, it is assumed that the target of the fan buffeting control problem, that is, the fan operating condition state, is expressed as: s ═ a (x) + b (y) × 0.5, where a (x) represents a vibration frequent change matrix, b (y) represents an amplitude change matrix, and c represents a modal quantization coefficient; since A (x) is an n × n dimensional matrix and B (y) is an n × m dimensional matrix, s is an n dimensional vector, c ∈ Rm×nAnd the equivalent function formed by the linear combination of the state variables is that the start-stop switching function sigma (x) of the fan air supply system is specified as: σ (x) ═ s ═ a (x) + b (y) × c;
2) in the function equation, the modal quantization coefficient c is equal to Rm×nIt is the linear combination coefficient of the switching function, which isThe control objects may be represented as a matrix:
Figure FDA0002377029250000021
wherein x1、x2The process variables of the instantaneous wind pressure and the wind volume of the negative pressure induced draft collected when the fan generates buffeting are respectively, if the process is collected at the moment, the expected dynamic process of the fan working condition is assumed to be asymptotically stable, and the corresponding sigma (x) is as follows: σ (x) ═ c,1][x1,x2]T0, wherein x1And x2The value range of the method is called as the existence area of a start-stop switching function sigma (x) of the fan air supply system and is marked as theta, and the value range of the fan modal quantization coefficient c relates to multiple aspects including stability of the fan buffeting expectation regulation method and rapidity of a dynamic process of the expectation regulation method;
3) if the value range of the fan modal quantization coefficient c is required to reduce the buffeting of the fan and meet the requirement of the method on asymptotic stability, only c is required>0, according to x1Reducing buffeting according to the possible change range and the requirement on rapidity of the dynamic process of the expected regulation and control method, wherein if c is specified to be 0.5, the working condition state S of the fan is defined as: x is the number of2＝-0.5x1,-2<x1<2, which is the existence region theta of SσIn two line segments S obliquely symmetrical to the zero point1And S2，θσIs the field of S; if sustained buffeting mitigation is desired and there is no particular requirement for method rapidity, then only c and c need be reduced>0, the method rapidity is far lower than that of an air supply system;
the second step comprises the steps of:
1) in the second step, c is to move the air supply system from x0There are two ways to pull on S: sigma (x)>0 pulls x to SpUpper, or σ (x)<0 pulls x to SNIs stable in the above, wherein SpTo estimate the state, SNIs in a regulation state; sigma (x)>0 pulls x to SNUpper, or σ (x)<0 pulls x to SpThe upper part is buffeting; although they all reach S, the dynamic process x0(t) is different; if stable, x0(t) unidirectional convergence without overshoot; if buffeting, x0(t) overshoot; whether steady or buffeting, depending on the method of determination of c;
2) the approach, using this condition, obtains the inequality of control as
Figure FDA0002377029250000022
An additional condition called the second step, according to which c can be solved, where c is assumed to be constant, and σ (x) ═ cxSubstituting this formula into the expression x ═ a (x) + b (x) + C, where x (t) is0)＝x0And substituting the error coefficient u at the same time to obtain an expression: σ (x) ═ ca (x) + cb (x) u, assume (cb (x))-1The error coefficient u' for which the constrained desired control can be found is: u ═ csgn (σ (x)), where u' satisfies
Figure FDA0002377029250000023
The requirements of (1);
3) the expression of the error coefficient u 'of the constrained anticipatory control, namely u' ═ csgn (sigma (x)), and the controlled object expression form closed-loop control;
4) the expression of the error coefficient u is exemplified and will be
Figure FDA0002377029250000031
u'＝[0.5,1]Putting an expression of the error coefficient u', and obtaining a control expression of the start-stop fan as follows: u' ═ 0.5sgn (σ (x)); at this time, u' is expressed with the controlled object, i.e. x ═ a (x) + b (x) + C, where x (t)0)＝x0And closed-loop control is formed.
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