CN105179166B - A kind of wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection - Google Patents

A kind of wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection Download PDF

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CN105179166B
CN105179166B CN201510566054.9A CN201510566054A CN105179166B CN 105179166 B CN105179166 B CN 105179166B CN 201510566054 A CN201510566054 A CN 201510566054A CN 105179166 B CN105179166 B CN 105179166B
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energy conversion
pitch
hydraulic
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岳继光
刘志刚
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Tongji University
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Abstract

A kind of wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection, including：1) mechanism model of wind energy conversion system hydraulic variable-pitch servo-drive system is combined, the simulation system fragility of digitized processing is treated by continuous time analog domain Analysis of Magnitude-Frequency Characteristic method validation, to ensure the validity of subsequent digitation system stability design；2) system discrete time frequency-domain analysis model is established based on sample frequency 1/T and according to system digitalized z-transform and bilinearity w conversion；3) by MATLAB instruments and according to optimal fragility phase margin section, optimum sampling frequency separation is obtained according to system discrete time frequency-domain analysis model；4) the optimum sampling frequency separation bound of acquisition is substituted into system discrete time frequency-domain analysis model, the fragility design of checking digital display circuit.By selecting suitable PLC sampling units, effective cost control is realized, and avoids sampling frequently or lags caused system oscillation, ensures the stability and reliability of system operation.

Description

A kind of wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection
Technical field
The invention belongs to wind-force machine hydraulic system technical field, is related to the wind energy conversion system hydraulic pressure based on system vulnerability principle and becomes System for rotating sample frequency system of selection.
Background technology
Running environment residing for a kind of wind energy conversion system hydraulic control system is more special, and geographical position is remote, and maintenance difficulty is high, Breakdown loss is big, therefore objectively requirement should have higher stability.
Fragility refers to that system due to itself intrinsic weakness or leak, lacks necessity when external environment condition changes Adaptability and robustness, so as to cause systematic function decline in addition failure consequence.Under normal circumstances, the stability of system can Judged using phase margin, the fragility power of system can be using phase margin as quantizating index；Phase margin is bigger, system it is crisp Weak property is stronger, and systematic function is better.
The design method of this class large-scale control system of wind-force machine hydraulic system, current research are primarily intended to high frequency Shandong The design of rod, the design of middle low frequency characteristic is often have ignored, cause system to lose most basic work good characteristic in itself. Selection for PLC sampling units, current research also without clear and definite guiding method, make every effort to sampling frequency as fast as possible Rate, but who does not know so produce unnecessary cost increase, even causes system can not normal work because of sampling too fast Make.
Because the amplitude versus frequency characte of continuous control system is difficult to the fragility of reflection numerical control system directly perceived, therefore it is necessary to seek Look for a kind of method for analyzing discrete digital system stability margin.
The content of the invention
It is an object of the invention to provide a kind of wind energy conversion system hydraulic variable-pitch systematic sampling based on system vulnerability principle Frequency selecting method, solve under the extreme running environment of wind mill pitch-variable servo-drive system based on system digitalized stability Design Problem.
It is well known that continuous control system, which is converted to numerical control system, has to pass through sampling element；Therefore, when continuous control When the stability margin of system processed determines, as long as reasonably selecting sample frequency, the fragility of numerical control system can be with connecting Continuous control system is consistent.
To reach above-mentioned purpose, solution of the invention is：
A kind of wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection based on system vulnerability principle, including it is following Step：
Step (1)：According to dynamics, flow be continuous etc., equation, description wind energy conversion system hydraulic variable-pitch servo-drive system mathematics close System, determines system mechanism model；
Step (2)：Obtained by the performance parameter of displacement transducer, servo amplifier and driver, servo valve and hydraulic cylinder Obtain the model of each function link of wind energy conversion system hydraulic variable-pitch servo-drive system；
Step (3)：With reference to system in step (1) mechanism model and step (2) in each function Link Model, obtain wind-force Machine hydraulic variable-pitch servo closed-loop model parameter simultaneously establishes final mask structure；
Step (4)：Phase margin index definition system vulnerability model in system stability margin；
Step (5)：The system vulnerability model checking system that the system model and step (4) obtained according to step (3) obtains System continuous time analog domain stability, foundation is provided for following digital domain stability Design；
Step (6)：On the basis of step (5), by MATLAB instruments, pass through optimum phase nargin section and bilinearity W converts to obtain system digitalized optimum sampling frequency separation.
Further：Also include step (7)：According to the optimum sampling frequency range bound obtained in step (6) in two-wire Property w transform domains in verify digital display circuit stability Design, so far complete based on fragility principle digital display circuit sample frequency choosing Select, that is, determine PLC sampling unit performance indications.
In view of the Low Medium Frequency characteristic of system, i.e., the performance parameter designed fragility as Low Medium Frequency stability characteristic (quality). While guarantee system has enough robustness, the fragility that Low Medium Frequency characteristic is shown as to system is analyzed and designed It is particularly important, the sample frequency selection based on this completion digital display circuit.Due to the fortune residing for such wind energy conversion system hydraulic control system Row environment is more special, and geographical position is remote, and maintenance difficulty is high, and breakdown loss is big, should have higher stability.
The establishment of wind energy conversion system hydraulic variable-pitch servo-drive system mathematical modeling in step (1).For typical wind energy conversion system hydraulic pressure Feather servo-drive system is made up of AC speed regulating mechanism, pump control actuating unit, sampling transmission mechanism and PLC controlling organizations.Can root According to the flow equation Q of servo valveL=kqxv-kcpL, the continuity flow equation of hydraulic chamberWith equilibrium equation F=A1P1-A2P2=A1PL=(m+M) s2y+Bcsy+ky+ FLEstablish the mathematical modeling of asymmetry hydraulic cylinder；Wherein QLFor control valve load flow, kqFor the flow gain of guiding valve, kcFor The flow-pressure coefficient of guiding valve, xvFor spool displacement, PLFor the load pressure of system of valve controlling cylinder, CtcAlways revealed for oil cylinder Coefficient, CtaCoefficient, P are revealed for systemsFor oil supply source pressure, V1For rodless cavity volume, βeFor effective volume modulus of elasticity, η is liquid The ratio between cylinder pressure rod chamber area A2 and rodless cavity area A1, s are Laplace transformation operator, and y is hydraulic cylinder travel, and F is valve draining pressure The driving force of cylinder system, A1For the transversal effective area area of rodless cavity, A2For the transversal effective area of rod chamber area, P1For without bar Cavity pressure, P2For rod chamber pressure, m is the quality of piston rod, and M is the quality of load, BcFor piston and the viscous damping system of load Number, k be load spring rate, FLTo act on any outer load force on piston, wherein the mathematical modeling for closing oar process iskqFor the discharge coefficient of servo valve, A1It is horizontal for rodless cavity Cut effective area area, whFor hydraulic natural frequency, ξhFor hydraulic damping ratio.The mathematical modeling for opening oar process isWhereinFor the discharge coefficient of servo valve, A2To there is bar The transversal effective area of cavity area, whFor hydraulic natural frequency, ξhFor hydraulic damping ratio.
The fragility of simulation system is characterized in step (5) by the stability margin of continuous time analog domain, and is made with this The foundation analyzed and designed for following digital system vulnerability.
The conversion of bilinearity w domains is introduced in step (6), frequency response method is expanded into descreted-time control system, is characterized Digital display circuit amplitude versus frequency characte, and then obtain fragility quantizating index.Wherein bilinearity w becomes z-plane unit circle internal maps of changing commanders To w Left half-planes.It is grinding for w planes and s planes from s plane to z-plane and from z-plane to the synthetic effect of w plane transformations It is similar to study carefully region.Because distortion caused by being converted from s plane to z-plane, is partly mended by the conversion of z-plane to w planes Repay.For the Bode diagram of the two in the difference of high band, may be interpreted as：First, that studied is only 0≤ω≤ωs/2 Frequency range, it is corresponding with 0≤v≤+ ∞；Secondly, the v=+ ∞ of w planes and ω=ω of s planess/ 2 is corresponding, i.e. pole LimitWithIt is corresponding, and the latter is a constant value.It is special in continuous domain and the amplitude-frequency of discrete domain to compare the system Linearity curve, and have ωs/ 2=2 π fs/ 2 ＞ ωc, therefore understand that w domains frequency characteristic is consistent with analog domain frequency characteristic, and its sign Frequency range meets discrete digital domain system vulnerability analysis demand.
By optimizer system stable phase angle nargin section in step (7), by MATLAB instruments, obtained based on special algorithm The optimum sampling frequency separation of digital display circuit.Its algorithm steps is：
(a) according to sampling unit precision set travel through initial value, step-length, and input system analog domain open-loop transfer function and Experience sampling period maximum；
(b) calls z domains, w domains transforming function transformation function to complete the conversion of ssystem transfer function successively；
(c) using MATLAB Analysis of Magnitude-Frequency Characteristic function obtain phase margin value and with above and below optimum angle nargin section Limit is made comparisons；
(d) if the current phase margin values of form section with upper traversing result phase margin value and do not include optimal phase The position nargin section upper limit or lower limit, then continue to travel through next time, and circulation performs step (b), (c), until it is determined that optimum sampling is all Phase bound, algorithm are so far completed.
Code realization of the algorithm steps (a) (b) (c) (d) based on Matlab softwares, i.e., described algorithm steps (a) (b) (c) algorithm of (d) based on MATLAB function custom features realizes that code is as follows：
[Tmax,Tmin]=sampling_period (num, den, T0,TL,Tstep)
Fori=T0:Tstep:Tmax
Ifi==T0 Pm_0=90；Tmin=0；Tmax=0； end
W=logspace (- 1,6,200)；
Sys=tf (num, den)；
T=i；
[sysd]=c2d (sys, T, ' zoh')；
Opt=d2cOptions (' Method', ' tustin', ' PrewarpFrequency', T)；
Sysc=d2c (sysd, opt)；
[mag, phase, w]=bode (sysc, w)；
[Gm, Pm, Wcg, Wcp]=margin (mag, phase, w)；
ifPm<45&&Pm_0>45 Tmin=T； end
ifPm<60&&Pm_0>60 Tmax=T； end
Pm_0=Pm；
ifTmax>0&&Tmin>0 i=TL； end end.
To realize goal of the invention, step (1)-(6) in above content are basic step, can be right by increasing step (7) Sampled result based on algorithm design gained is verified, ensures the correctness and validity of design.
The time sequencing of each step performs according to step number, and wherein step (2) can be advanced to the first order, on each The key element of step, is further described below：
Step (1), traditional modeling method are that the mathematical modeling of object, also referred to as machine are established on the basis of theory analysis Logos；For complication system, then using the method for system identification, established from experimental observed data can reflect system input- The model of output relation, i.e. experimental method.Dynamics and Flow continuity equation are to determine rational content, hydraulic variable-pitch system modelling It is the key point of subsequent design, more favourable support can be provided for follow-up design by the accuracy for improving modeling.
Step (2), in order to which the physical model of reality is abstracted into accurate mathematical modeling, do not influenceing the base of systematic function On plinth, each element of feather cylinder device is done to hypothesis (detailed content is referring to embodiment) displacement sensing of correlation Device, servo amplifier and driver, servo valve and hydraulic cylinder are the fundamentals of system modelling, it is necessary to physics according to each key element Performance parameter and operation principle are converted into mathematical modeling, the modeling for overall system.
Step (3), the derivation and simplification of system mathematic model are completed according to Such analysis, and complete mathematical model parameter Calculate.
Step (4) and (5), analysis system progressive die near-field amplitude versus frequency characte, the discrete of system is established according to z domains, w domain theories Spatial model, to obtain fragility characterization value.
Step (6), completes the congruity theory analysis of system, and system is obtained most according to traversal optimizing algorithm logical design Good sampling period interval value.
Step (7), it is special that system continuous domain, discrete domain amplitude-frequency are substituted into based on the sampling period interval value obtained in step (6) Property analysis method in obtain system interval value amplitude versus frequency characte, by existing theoretical checking with ensure system vulnerability design Correctness and validity.
Due to using such scheme, the beneficial effects of the invention are as follows：This method clear logic, scalability is strong, passes through choosing Suitable PLC sampling units are selected, realize effective cost control, and avoids sampling frequently or lags caused system oscillation, Ensure the stability and reliability of system operation.
Brief description of the drawings
Fig. 1 is embodiment wind energy conversion system hydraulic variable-pitch servo-drive system hydraulic structure figure of the present invention.
Wherein:Fluid provides pressure source Ps by hydraulic pump；Overflow valve ensures that the oil pressure in hydraulic circuit is not higher than setting Maximum pressure；The effect of accumulator 1,2 is when wind energy conversion system breaks down and during emergency shutdown, there is provided hydraulic oil enters hydraulic pressure Cylinder；Now use 3-position 4-way servo valve and HY-YG100 type asymmetrical cylinders.
Fig. 2 is embodiment four-way valve control asymmetrical cylinder systematic schematic diagram of the present invention
Fig. 3 is embodiment wind energy conversion system hydraulic variable-pitch servo system control block diagram of the present invention.
Fig. 4 is wind energy conversion system hydraulic variable-pitch servo-drive system sample frequency choosing of the embodiment of the present invention based on fragility principle Selection method algorithm flow chart.
Embodiment
The present invention will be further described with reference to the accompanying drawings.
A kind of wind energy conversion system hydraulic variable-pitch servo-drive system sample frequency system of selection based on fragility principle of the present invention, Comprise the following steps：
Step (1)：According to dynamics, flow be continuous etc., equation, description wind energy conversion system hydraulic variable-pitch servo-drive system mathematics close System, determines system mechanism model；
Step (2)：Obtained by the performance parameter of displacement transducer, servo amplifier and driver, servo valve and hydraulic cylinder Obtain the model of each function link of wind energy conversion system hydraulic variable-pitch servo-drive system；
Step (3)：With reference to system in step (1) mechanism model and step (2) in each function Link Model, obtain wind-force Machine hydraulic variable-pitch servo closed-loop model parameter simultaneously establishes final mask structure；
Step (4)：Phase margin index definition system vulnerability model in system stability margin；
Step (5)：The system vulnerability model checking system that the system model and step (4) obtained according to step (3) obtains System continuous time analog domain stability, foundation is provided for following digital domain stability Design；
Step (6)：On the basis of step (5), by MATLAB instruments, pass through optimum phase nargin section and bilinearity W converts to obtain system digitalized optimum sampling frequency separation；
Step (7)：Optimum sampling frequency range bound according to being obtained in step (6) is tested in bilinearity w transform domains Digital display circuit stability Design is demonstrate,proved, so far completes the digital display circuit sample frequency selection based on fragility principle, that is, determines that PLC is adopted Sample unit performance index.
Specifically：
1) traditional modeling method is that the mathematical modeling of object is established on the basis of theory analysis, also referred to as mechanism method；Pin To complication system, then using the method for system identification, system Input output Relationship can be reflected by being established from experimental observed data Model, i.e. experimental method.Refering to pertinent literature, asymmetrical cylinder is also referred to as single-rod piston formula hydraulic cylinder, during modern project uses Referring now still to asymmetric cylinder near equalization point linearization technique, obtain three fundamental equations：
(1) flow equation of valve：QL=kqxv-kcpL
(2) the flow continuity equation of hydraulic cylinder works chamber：
(3) equilibrium equation：F=A1P1-A2P2=A1PL=Ms2y+Bsy+Ky+F1
Wherein QLFor control valve load flow, kqFor the flow gain of guiding valve, kcFor the flow-pressure coefficient of guiding valve, xvFor Spool displacement, PLFor the load pressure of system of valve controlling cylinder, CieCoefficient, C are always revealed for oil cylindertaCoefficient, P are revealed for systems For oil supply source pressure, V1For rodless cavity volume, βeFor effective volume modulus of elasticity, m is the quality of piston rod, and s calculates for Laplace transformation Son, y are hydraulic cylinder travel, and F is the driving force of system of valve controlling cylinder, A1For the transversal effective area area of rodless cavity, A2To there is bar The transversal effective area of cavity area, P1For rodless cavity pressure, P2For rod chamber pressure, M is the quality of load, and B is piston and load Viscous damping coefficient, K be load spring rate, F1To act on any outer load force on piston.
The mathematical modeling of asymmetrical cylinder is established, is emulated with MATLAB, and considers temperature for system emphatically The influence of model, establish the actual mathematical model for considering that temperature influences.So as to preferably use MATLAB to carry out related emulation With design.
2) in order to which the physical model of reality is abstracted into accurate mathematical modeling, on the basis of systematic function is not influenceed, Each element of feather cylinder device is done into hypothesis below：
(1) model simplification of proportional amplifier and proportioning valve is a ratio system xv=k3U, (wherein xvFor valve element position Move, u is control voltage, k3For ratio) this is due to that played a leading role in the range of system operating frequency is valve control cylinder mode, Its intrinsic frequency is usually corner frequency minimum in system, and the corner frequency of proportional reversing valve is far above valve control cylinder mode Corner frequency；
(2) frequency range of the duty-cycle system of displacement transducer is much higher, therefore is replaced with a proportional component：U=kfy (wherein u is feedback voltage, kfFor feedback factor, y is hydraulic cylinder displacement)；
(3) control valve is preferable (disregarding the radial clearance between valve element, valve pocket) zero lap four port valve, and four throttle Window is matching and symmetrical (the area gradient w of i.e. each restriction is equal), and flow coefficient C d is equal；
(4) flowing of window of throttling be turbulent flow, and the compressibility of fluid influence in valve can be ignored；
(5) control valve has preferable responding ability；
(6) hydraulic energy source is preferable constant pressure source, and charge oil pressure Ps is constant, and return pressure Po is zero；
(7) the inside and outside leakage of hydraulic cylinder is Laminar Flow；
Using the method analysis system of linearisation dynamic characteristic when, ignore and the nonlinear loads such as Coulomb friction be present.
First, defined according to control valve load flow：
Here control valve is thought of as perfect symmetry zero lap valve, does not consider the leakage between its valve port, therefore Xv>When 0, Q4= 0；Xv<When 0, the load flow of Q2=0 event valves is：
Secondly load pressure PL is defined：
When hydraulic cylinder moves right：
The driving force of F --- system of valve controlling cylinder, N
PL--- the load pressure of system of valve controlling cylinder, Pa；
--- the ratio between hydraulic cylinder rod chamber area A2 and rodless cavity area A1.
When hydraulic cylinder is moved to the left：
Each parameter definition is identical with (1) formula.
3) being closed by feather cylinder device exemplified by oar process mathematical model derives has：
Feather cylinder device pass oar process hydraulic cylinder piston rod is protruding, propeller pitch angle increase.[18] this time-varying oar It is the process that the hydraulic cylinder piston rod shown in Fig. 2 .3 moves right away from cylinder device motion.Now according to hydraulic valve stream Amount definition：
Δ p --- pressure differential, Pa
Cd--- hydraulic valve restriction discharge coefficient；ρ --- fluid density, kg/m3
Ai--- orifice area changes；W --- hydraulic valve choke area gradient, m
During closing oar,xv>The flow equation of 0 servo valve control mouth：
Ps--- oil supply source pressure, Pa
According to Flow continuity equation, the flow equation for obtaining the cylinder of asymmetrical cylinder two is：
Q1--- rodless cavity flow, m3/s
Q2--- rod chamber flow, m3/s
βe--- effective volume modulus of elasticity, Pa
Cic--- hydraulic cylinder interior leakage reveals coefficient, m5/(N·s)
Cec--- hydraulic cylinder outward leakage coefficient, m5/(N·s)
V1--- rodless cavity volume, m3
V2--- rod chamber volume, m3
Obtained by formula (2.3)：
Ignore leakage and liquid hold effect caused by flow when：
Obtained by formula (2.4)：
Therefore obtained by formula (2.5), (2.6)：
Simultaneous formula (2.1) and (2.7) solve：
By load flow definition, and bring formula (2.4) (2.8) into and abbreviation obtains：
Wherein：--- oil cylinder always reveals coefficient, m5/(N·s)
--- system reveals coefficient, m5/(N·s)
By load flow definition, and bring formula (2.3) into, obtain another expression of load flow：
Above formula (2.10) is linearized：
QL=kqxv-kcpL (2.11)
Wherein：--- the flow gain of guiding valve, m2/s；
--- the flow-pressure coefficient of guiding valve, m5/(N·s)
The stress equation of hydraulic cylinder piston is：
Wherein：F --- driving force caused by hydraulic cylinder, N
Bc--- piston and the viscous damping coefficient of load, N/ (m/s)
The spring rate of k --- load, N/m
FL--- any outer load force acted on piston, N
The quality of m --- piston rod, kg
The quality of M --- load, kg
Formula (2.9), (2.10), (2.12) are that feather hydraulic cylinder moves right the fundamental equation of non-linear hour；In order to With the control theory research feather cylinder device of classics, corresponding mathematical modulo is established using the equation group after linearisation Type.Formula (2.9), (2.11), (2.12) are that the Basic equation group linearized when feather hydraulic cylinder moves right is as follows：
Laplace transform is carried out to equation group to obtain：
The Basic equation group that feather cylinder device opens the linearisation of oar process mathematical model can similarly be obtained：
Laplace transform is carried out to above equation group to obtain：
4) feather cylinder device mathematical modeling simplifies
Oar is closed according to feather cylinder device and opens the lienarized equation group of oar process, can obtain hydraulic cylinder displacement y with Relation between spool displacement Xv and outer load force FL：
Close oar process：
Wherein：kce=kc+Ctc--- total flow-pressure coefficient, m5/(N·s)
me=m+M --- gross mass, kg
Now, piston rod moves right：V1=V10+A1Y, due to V10>>A1Y, so V1≈V10.And fans load is with used Property load based on, the rigidity k ≈ 0 of load,Therefore obtain closing the final reduced form of oar process mathematical model：
Wherein：--- hydraulic natural frequency, rad/s
--- hydraulic damping ratio, zero dimension
Open oar process：
Wherein：kce=kc′+Ctc' --- it is total discharge coefficient, m5/(N·s)
me=m+M --- it is gross mass, kg
Now, piston rod is to left movement：V2=V20-A2Y is due to V20>>A2Y, so V2≈V20.And fans load is with inertia Based on load, the rigidity k ≈ 0 of load,Obtain out the final simplified style of oar process mathematical model：
Wherein：--- hydraulic natural frequency, rad/s
--- hydraulic damping ratio, zero dimension
5) feather cylinder device mathematical model parameter calculates
In feather cylinder device Derivation of Mathematical Model, its linearization procedure and simplified process are all based on piston rod The middle low amplitude vibrations near its equilbrium position.The concept of hydraulic cylinder spring rate is described in document [10] and is drawn a conclusion：When When piston deviates equilbrium position, the increase of hydraulic cylinder spring rate, intrinsic frequency increase.Therefore it can be obtained by its spring rate expression formula Piston-initial-position.
Hydraulic cylinder spring rateIf hydraulic cylinder total kilometres are L, piston displacement y, then V1=A1Y, V2=A2(L-y).Then obtain the relation of hydraulic cylinder spring rate and its piston displacement：The method that extreme value is sought by higher mathematics, whenWhen, hydraulic cylinder bullet Spring rigidity is minimum, when hydraulic cylinder piston connection inertia mass load, intrinsic frequency(m1 is piston and load quality Reduced value) it is now minimum.Then
Because feather cylinder device oil viscosity, leakage coefficient etc. are affected by temperature.When determining systematic parameter Should be in a certain temperature.The present invention uses HY-YG100 type hydraulic cylinders at a temperature of certain, and design parameter is shown in Table 1：
The feather cylinder device parameter of table 1
It can be calculated according to the data of table 1：
Rodless cavity area
Rod chamber area
Area ratio
Rodless cavity initial volume
Rod chamber initial volume
(1) oar process is closed：
The discharge coefficient of valveIt is and load pressure PLIt is relevant, zero-bit flow system is commonly used in engineering Number estimation
The flow-pressure coefficient of valveIt is, work related with load pressure and spool displacement Frequently with new definition in journeyWherein rcRadial clearance/m between valve element and valve pocket, rc=5 × 10-5；μ power Viscosity/PaS, μ=137 × 10-4Therefore
Hydraulic natural frequency
Hydraulic damping ratio
Close oar process piston rod displacement is with spool displacement relational expression：
(2) oar process is opened：
The discharge coefficient of valveWith load pressure PLIt is relevant, zero-bit stream is commonly used in engineering Measure parameter estimation
The flow-pressure coefficient k of valvec′≈kc=3.581 × 10-10
Intrinsic frequency
Hydraulic damping ratio
Open oar process piston rod displacement is with spool displacement relational expression：
6) wherein servo valve driving hydraulic cylinder link mathematical modeling is clear and definite, for servo valve amplification, shift transmission and The quantization of controller link can be obtained by data below.
The servo valve actuator pick-up relation of table 2
System realizes generally use PID controller, and it has four parameters undetermined：P, I, D and calculus time T.This hair The bright analysis on system vulnerability temporarily only introduces proportional component P herein.Therefore, based on system block diagram can set controller parameter as K, servo valve amplifier gain are K1, displacement transducer gain is K2, then have：
Wind energy conversion system hydraulic variable-pitch system open loop transmission function can be obtained and closed loop transfer function, difference is as follows：
7) progressive die near-field amplitude versus frequency characte
Known system open loop transmission function, the continuous time frequency domain analysis based on system can be crisp to the analog domain of the system Weak property does preliminary analysis.The oar process amplitude versus frequency characte expression of wind energy conversion system hydraulic variable-pitch pass is defined to obtain according to frequency domain analysis Formula：
Its cross-over frequency w is calculated using amplitude expressioncHave：
Solve：ωc=53.73rad/s, is substituted into system phase expression formula and can obtain the phase margin of system and be：
The Bode diagram of the system can be obtained based on MATLAB instruments, and thus draws emulation stability margin numerical value, itself and meter It is consistent to calculate result.Calculating based on above stability margin, it is known that the system has stable system architecture in analog domain, is to being System is digitized and its premise of vulnerability analysis.
8) system digitalized and fragility characterizes
The frequency response design method to digital display circuit mainly includes direct frequency response method and Bilinear transformation method at present. Because direct frequency response method loses the simplicity of logarithmic coordinates, therefore digital display circuit is realized using Bilinear transformation method herein Stability analysis, the fragility of digital display circuit is represented by its phase margin.
Discrete domain Analysis of Magnitude-Frequency Characteristic problem can be by the way that the pulsed transfer function of z-plane to be transformed to w planes method To solve.This conversion is generally termed w conversion, is a kind of bilinear transformation, is defined as follows：
Wherein, T is the sampling period of studied descreted-time control system.By by the given pulse transmission in z-plane Into the rational function on w, frequency response method is able to expand to descreted-time control system functional transformation.Closed based on the mapping System, line translation gradually can be entered to it so that wind-force machine hydraulic system closes oar process transmission function as an example.The sampling of field of signal processing Frequency is generally higher, and the sample frequency of digital control field is generally relatively low.According to system block diagram, distinguish before and after its controller Dosing sampling switch and zero-order holder can be digitized, and according to correlating transforms principle, can obtain the system open loop transmission function Z-transform and w transformation results in sampling period T=0.01s.
By s domains Analysis of Magnitude-Frequency Characteristic principle, can obtain w domains amplitude versus frequency characte relational expression is：
And then when can obtain sampling period T=0.01s according to amplitude, phase formula system discrete domain amplitude versus frequency characte.Its Middle cross-over frequency and phase margin are respectively：
vc=53.91rad/s γ=72.8 °
9) consistency analysis
Become by w and change commanders z domain mappings into w domains, the amplitude versus frequency characte in z domains is characterized with w domains amplitude versus frequency characte, therefore it need to be entered Row consistency analysis, i.e., compared with the amplitude versus frequency characte under continuous time frequency domain, to ensure that w domains amplitude versus frequency characte characterizes dispersion number The validity of word Amplitude Frequency Characteristic.
- the ω of s planess/2≤ω≤ωs/ 2 frequency bands are mapped to-∞ ＜ v ＜+∞ scopes, and wherein v is the void in w planes Quefrency.For the vulnerability analysis of system, Phase margin is under the jurisdiction of system Low Medium Frequency characteristic, therefore frequency after compression Characteristic disclosure satisfy that the demand of system vulnerability analysis.
Once becoming the pulsed transfer function G (z) that changes commanders by w transforms to G (w), so that it may is considered as the transmission letter on w Number, i.e., traditional frequency response method can be used for w planes, so as to which original frequency response design method is applied into discrete time In control system.As described above, v is a virtual frequency, by replacing w with jv, then can using legacy frequencies response method come Draw the Bode diagram on w.W planes G (jv) is corresponding with s planes G (jw), but the frequency axis of w planes is deformation, just like formula Shown corresponding relation：
That is bilinearity w becomes z-plane unit circle internal maps of changing commanders to w Left half-planes.Put down from s plane to z-plane and from z Face is that w planes are similar with the survey region of s planes to the synthetic effect of w plane transformations.Because become from s plane to z-plane Distortion caused by changing, partly fallen by the conversion compensation of z-plane to w planes.For the Bode diagram of the two high band difference, It may be interpreted as：First, that studied is only 0≤ω≤ωs/ 2 frequency ranges, it is corresponding with 0≤v≤+ ∞；Secondly, w The v=+ ∞ of plane and ω=ω of s planess/ 2 is corresponding, i.e. the limitWithIt is corresponding, and the latter is One constant value.It need to point out that the two values are typically unequal, for zero pole point angle, | G (jv) | at v=+ ∞ it is non-zero Value means that G (w) includes equal number of zero point and limit.It is bent in the amplitude versus frequency characte of continuous domain and discrete domain to compare the system Line, and have ωs/ 2=2 π fs/ 2 ＞ ωc, therefore understand that w domains frequency characteristic is consistent with analog domain frequency characteristic, and the frequency of its sign Scope meets discrete digital domain system vulnerability analysis demand.
10) optimum interval analysis and calculating
By to discrete digital domain Analysis of Magnitude-Frequency Characteristic under Different sampling period, from T=0.01s to T=0.1s, being System phase margin is intended to 0 ° from γ=72.8 °.As can be seen here, the sampling period influences very big on the fragility of digital display circuit.By Characterized in the fragility of system by phase margin, and the response speed of phase margin reflection system.Phase margin is less than normal, can lead Cause system vulnerability deficiency；Phase margin is bigger than normal, and system response can be caused slow.So optimum phase angle nargin section of system It correspond to optimal sampling period section.The phase margin of usual system is at least 45 °, and optimum phase nargin is 60 °.
Inverse logic based on Analysis of Magnitude-Frequency Characteristic calculates optimum sampling cycle section and the drawbacks of calculating is excessively complicated be present；Institute By MATLAB instruments, a larger sampling period scope is traveled through using the false position of positive logic, to obtain optimum sampling Computation of Period is then the method recommended herein.Wherein, MATLAB is used for the accuracy of Amplitude Frequency Characteristic Analysis function in 1.3 sections In verified；Larger sampling period range lower limit can be determined that the traversal step-length of false position is also should by sampling unit precision Sampling precision value, its upper limit can then be set according to engineering experience, can flexibly be changed in calculating process.The algorithm logic is as follows：
(1) initial value, step-length, and input system analog domain open-loop transfer function and warp are traveled through according to sampling unit precision set Test sampling period maximum；
(2) z domains, w domains transforming function transformation function is called to complete the conversion of ssystem transfer function successively；
(3) using MATLAB Analysis of Magnitude-Frequency Characteristic function obtain phase margin value and with optimum angle nargin section bound Make comparisons；
(4) if current phase margin value forms section with upper traversing result phase margin value and do not include optimum phase The nargin section upper limit or lower limit, then continue to travel through next time, circulation performs step (2) (3), until it is determined that on the optimum sampling cycle Lower limit, algorithm are so far completed.Because the premise of digital display circuit vulnerability analysis is that system has stable analog domain amplitude versus frequency characte, So certainly exist optimal sampling period section.According to algorithm above flow, MATLAB can be obtained and encapsulate function (such as preceding institute State).
11) model is verified
By taking wind energy conversion system hydraulic variable-pitch system switching oar process as an example, seek its optional sampling cycle section, it may be verified that should The correctness of method.According to the wind energy conversion system hydraulic variable-pitch system switching oar model of foundation and the initial analysis of its digital display circuit As a result, it is as follows to can obtain relevant parameter：
Close oar process：
Num=[52.6]；
Den=[1/363.91^2,2*0.1266/363.91,1,0]；
T0=0.01s；
TL=0.1s；
Tstep=0.001s；
Can obtain its output result based on traversal optimizing method is：
Tmax=0.026s；Tmin=0.019s；
Open oar process：
Num=[42.14]；
Den=[1/339.228^2,2*0.0721/337.228,1,0]；
T0=0.01s；
TL=0.1s；
Tstep=0.001s；
Can obtain its output result based on traversal optimizing method is：
Tmax=0.034s；Tmin=0.021s；
It can be seen from above the result, it is consistent with digital display circuit Analysis of Magnitude-Frequency Characteristic result.Further, since wind energy conversion system Hydraulic variable-pitch system comprising opening oar and closing two asymmetric processes of oar, shares a set of sampling unit simultaneously, is one typical Hybrid system, so, the optimum sampling cycle section corresponding to the digitlization of the hybrid system need to be that two above process is optimal Sampling period section common factor, namely：
[0.019,0.026] ∩ [0.021,0.034]=[0.021,0.026]
Model above checking uses sampling unit of the precision for 1ms, can if being analyzed for the sampling unit of other precision Adjust accordingly to complete the design of digital display circuit fragility.
The above-mentioned description to embodiment is understood that for ease of those skilled in the art and using this hair It is bright.Person skilled in the art obviously easily can make various modifications to these embodiments, and described herein General Principle is applied in other embodiment without by performing creative labour.Therefore, the invention is not restricted to implementation here Example, for those skilled in the art according to the announcement of the present invention, not departing from improvement that scope made and modification all should be Within protection scope of the present invention.

Claims (9)

  1. A kind of 1. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection, it is characterised in that：Comprise the following steps：
    Step (1)：Wind energy conversion system is described according to the flow equation of valve, the flow continuity equation of hydraulic cylinder works chamber and equilibrium equation Hydraulic variable-pitch servo-drive system mathematical relationship, determines system mechanism model；
    Step (2)：Wind is obtained by the performance parameter of displacement transducer, servo amplifier and driver, servo valve and hydraulic cylinder The model of each function link of power machine hydraulic variable-pitch servo-drive system；
    Step (3)：With reference to system in step (1) mechanism model and step (2) in each function Link Model, obtain wind energy conversion system liquid Buckling pitch servo closed-loop model parameter simultaneously establishes final mask structure；
    Step (4)：Phase margin index definition system vulnerability model in system stability margin；
    Step (5)：The system vulnerability model checking system that the system model and step (4) obtained according to step (3) obtains connects Continuous time simulation domain stability, foundation is provided for following digital domain stability Design；
    Step (6)：On the basis of step (5), by MATLAB instruments, become by optimum phase nargin section and bilinearity w Get system digitalized optimum sampling frequency separation in return.
  2. 2. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterised in that：Also include Step (7)：Optimum sampling frequency range bound according to being obtained in step (6) verifies numeral system in bilinearity w transform domains System stability Design, the digital display circuit sample frequency selection based on fragility principle is so far completed, that is, determines PLC sampling units Can index.
  3. 3. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterised in that：Consider The Low Medium Frequency characteristic of system, i.e., the performance parameter designed fragility as Low Medium Frequency stability characteristic (quality), ensureing that system has Shandong While rod, the fragility that Low Medium Frequency characteristic is shown as to system is analyzed and designed, based on this completion digital display circuit Sample frequency selects.
  4. 4. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterised in that：Step (1) establishment of wind energy conversion system hydraulic variable-pitch servo-drive system mathematical modeling in, for by AC speed regulating mechanism, pump control actuating unit, Transmission mechanism and the typical wind energy conversion system hydraulic variable-pitch servo-drive system of PLC controlling organizations composition are sampled, according to the stream of servo valve Measure equation：QL=kqxv-kcpLThe continuity flow equation of hydraulic chamber： And equilibrium equation：F=A1P1-A2P2=A1PL=Ms2y+Bsy+Ky+F1Establish the mathematical modeling of asymmetry hydraulic cylinder；Wherein QLFor control valve load flow, kqFor the flow gain of guiding valve, kcFor the flow-pressure coefficient of guiding valve, xvFor spool displacement, PLFor The load pressure of system of valve controlling cylinder, CieCoefficient, C are always revealed for oil cylindertaCoefficient, P are revealed for systemsFor oil supply source pressure, V1For rodless cavity volume, βeFor effective volume modulus of elasticity, m is the quality of piston rod, and s is Laplace transformation operator, and y is hydraulic cylinder Stroke, F be system of valve controlling cylinder driving force, A1For the transversal effective area area of rodless cavity, A2Have for rod chamber area is transversal Imitate area, P1For rodless cavity pressure, P2For rod chamber pressure, M is the quality of load, and B is the viscous damping system of piston and load Number, K be load spring rate, F1To act on any outer load force on piston, wherein the mathematical modeling for closing oar process iskqFor the discharge coefficient of servo valve, A1It is horizontal for rodless cavity Cut effective area area, whFor hydraulic natural frequency, ξhFor hydraulic damping ratio；The mathematical modeling for opening oar process isWhereinFor the discharge coefficient of servo valve, A2To there is bar The transversal effective area of cavity area, whFor hydraulic natural frequency, ξhFor hydraulic damping ratio.
  5. 5. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterised in that：Step (5) fragility of simulation system is characterized in by the stability margin of continuous time analog domain, and in this, as following digital system The foundation for vulnerability analysis and the design of uniting.
  6. 6. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterised in that：Step (6) conversion of bilinearity w domains is introduced in, frequency response method is expanded into descreted-time control system, characterizes digital display circuit amplitude-frequency Characteristic, and then obtain fragility quantizating index；Wherein bilinearity w becomes z-plane unit circle internal maps of changing commanders to w Left half-planes； It is that w planes are similar with the survey region of s planes to the synthetic effect of w plane transformations from s plane to z-plane and from z-plane； Distortion caused by being converted from s plane to z-plane, partly fallen by the conversion compensation of z-plane to w planes；Even if the baud of the two There is difference in figure, also can confirm that w domains frequency characteristic is consistent with analog domain frequency characteristic in high band, and the frequency range of its sign Meet discrete digital domain system vulnerability analysis demand.
  7. 7. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 2, it is characterised in that：Step (7) by optimizer system stable phase angle nargin section in, by MATLAB instruments, the optimum sampling frequency zones of digital display circuit are obtained Between.
  8. 8. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 7, it is characterised in that：The calculation Method step is：
    (a) travels through initial value, step-length, and input system analog domain open-loop transfer function and experience according to sampling unit precision set Sampling period maximum；
    (b) calls z domains, w domains transforming function transformation function to complete the conversion of ssystem transfer function successively；
    (c) obtains phase margin value using MATLAB Analysis of Magnitude-Frequency Characteristic function and made with optimum angle nargin section bound Compare；
    (d) if the current phase margin values of and upper traversing result phase margin value form section not include optimum phase abundant The section upper limit or lower limit are spent, then continues to travel through next time, circulation performs step (b), (c), until it is determined that on the optimum sampling cycle Lower limit, algorithm are so far completed.
  9. 9. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 8, it is characterised in that：The calculation Algorithm of the method step (a) (b) (c) (d) based on MATLAB function custom features realizes that code is as follows：
    [Tmax,Tmin]=sampling_period (num, den, T0,TL,Tstep)
    For i=T0:Tstep:Tmax
    If i==T0 Pm_0=90；Tmin=0；Tmax=0；end
    W=logspace (- 1,6,200)；
    Sys=tf (num, den)；
    T=i；
    [sysd]=c2d (sys, T, ' zoh')；
    Opt=d2cOptions (' Method', ' tustin', ' PrewarpFrequency', T)；
    Sysc=d2c (sysd, opt)；
    [mag, phase, w]=bode (sysc, w)；
    [Gm, Pm, Wcg, Wcp]=margin (mag, phase, w)；
    if Pm<45&&Pm_0>45 Tmin=T；end
    if Pm<60&&Pm_0>60 Tmax=T；end
    Pm_0=Pm；
    if Tmax>0&&Tmin>0i=TL；end end.
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