CN105179166A - Sampling frequency selection method of wind turbine hydraulic pitch change system - Google Patents

Abstract

The invention discloses a sampling frequency selection method of a wind turbine hydraulic pitch change system. The method comprises the following steps: 1) the vulnerability of an analog system to be digitally processed is verified by combining with a mechanism model of a wind turbine hydraulic pitch change servo system through a continuous time analog domain magnitude-frequency characteristic analysis method to guarantee the effectiveness of subsequent digital system stability design; 2) a system discrete time frequency domain analysis model is built based on a sampling frequency 1/T according to the system digital z conversion and the bilinear w conversion; 3) an optimal sampling frequency section is obtained by a MATLAB tool according to an optimal vulnerability phase margin section and the system discrete time frequency domain analysis model; and 4) top and bottom limitations of the obtained optimal sampling frequency section are substituted into the system discrete time domain frequency analysis model to verify the digital system vulnerability design. As a proper PLC sampling unit is selected, the effective cost control is realized, the system oscillation caused by frequent or lag sampling is prevented, and the system operation stability and reliability are guaranteed.

Description

The system of selection of a kind of wind energy conversion system hydraulic variable-pitch system sampling frequency

Technical field

The invention belongs to wind energy conversion system hydraulic system technical field, relate to the wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection based on system vulnerability principle.

Background technique

Running environment residing for one class wind energy conversion system hydraulic control system is more special, and geographical position is remote, and maintenance difficulty is high, and breakdown loss is large, therefore objectively requirement should have higher stability.

Fragility refers to that system is due to self intrinsic weakness or leak, lacks necessary adaptability and robustness when external environment condition changes, thus causes systematic function to decline the consequence even lost efficacy.Under normal circumstances, the stability of system can utilize phase margin to judge, the fragility power of system can phase margin be quantizating index; Phase margin is larger, and the fragility of system is stronger, and systematic function is better.

The design method of this class large-scale control system of wind energy conversion system hydraulic system, the design of high frequency robustness is mainly tended in current research, often have ignored the design of medium and low frequency characteristic, causes system itself to lose the most basic work good characteristic.For the selection of PLC sampling unit, current research does not have clear and definite guiding method yet, makes every effort to sample frequency fast as far as possible, but who does not know that can produce unnecessary cost like this increases, and causes system normally to work because sampling is too fast even.

Amplitude versus frequency characte due to continuous control system is difficult to the fragility intuitively reflecting numerical control system, therefore is necessary to find a kind of method analyzing discrete digital system stability nargin.

Summary of the invention

The object of the present invention is to provide a kind of wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection based on system vulnerability principle, based on system digitalized stability Design problem under the extreme running environment of solution wind mill pitch-variable servo-system.

As everyone knows, continuous control system is converted to numerical control system and has to pass through sampling element; Therefore, when the stability margin of continuous control system is determined, as long as reasonably select sample frequency, namely the fragility of numerical control system can be consistent with continuous control system.

For achieving the above object, solution of the present invention is:

Based on a wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection for system vulnerability principle, comprise the following steps:

Step (1): according to equations such as dynamics, flow are continuous, describe wind energy conversion system hydraulic variable-pitch servo-system mathematical relationship, certainty annuity mechanism model;

Step (2): the model being obtained each function link of wind energy conversion system hydraulic variable-pitch servo-system by the performance parameter of displacement transducer, servoamplifier and driver, servovalve and oil hydraulic cylinder;

Step (3): each function Link Model in the mechanism model of system and step (2) in integrating step (1), obtains wind energy conversion system hydraulic variable-pitch servo closed-loop model parameter and establish final mask structure;

Step (4): according to the phase margin index definition system vulnerability model in system stability nargin;

Step (5): the system vulnerability model verification system analog domain continuous time stability that the system model obtained according to step (3) and step (4) obtain, for following digital territory stability Design provides foundation;

Step (6): on the basis of step (5), by MATLAB instrument, obtains system digitalized optimum sampling range between a frequency by optimum phase nargin interval and bilinearity w conversion.

Further: also to comprise step (7): the optimum sampling frequency range upper and lower according to obtaining in step (6) verifies number system stability Design in bilinearity w transform domain, so far the number system sample frequency completed based on fragility principle is selected, and namely determines PLC sampling unit performance index.

Consider the Low Medium Frequency characteristic of system, by the performance parameter that fragility designs as Low Medium Frequency stability characteristic (quality).While the system of guarantee has enough robustness, it is also particularly important that the fragility showing as Low Medium Frequency characteristic to system carries out design and study, and the sample frequency completing number system based on this is selected.Running environment residing for such wind energy conversion system hydraulic control system is more special, and geographical position is remote, and maintenance difficulty is high, and breakdown loss is large, should have higher stability.

The establishment of wind energy conversion system hydraulic variable-pitch servo-system mathematical model in step (1).Typical wind energy conversion system hydraulic variable-pitch servo-system is made up of AC variale speed mechanism, pump control power mechanism, sampling transmission mechanism and PLC control mechanism.Can according to the flow equation Q of servovalve _l=k _qx _v-k _cp _l, the continuity flow equation in hydraulic work chamber with equilibrium equation F=A ₁p ₁-A ₂p ₂=A ₁p _l=(m+M) s ²y+B _csy+ky+F _lset up the mathematical model of asymmetry oil hydraulic cylinder; Wherein Q _lfor control valve load flow, k _qfor the flow gain of guiding valve, k _cfor the flow-pressure coefficient of guiding valve, x _vfor spool travel, P _lfor the induced pressure of system of valve controlling cylinder, C _tcfor oil cylinder always reveals coefficient, C _tafor system reveals coefficient, P _sfor oil supply source pressure, V ₁for rodless cavity volume, β _efor effective volume Young's modulus, η is the ratio of oil hydraulic cylinder rod chamber area A 2 and rodless cavity area A 1, and s is Laplace transformation operator, and y is hydraulic cylinder travel, and F is the driving force of system of valve controlling cylinder, A ₁for the transversal useful area area of rodless cavity, A ₂for the transversal useful area of rod chamber area, P ₁for rodless cavity pressure, P ₂for rod chamber pressure, m is the quality of piston rod, and M is the quality of load, B _cfor the viscous damping coefficient of piston and load, k is the spring rate of load, F _lfor acting on any outer load force on piston, the mathematical model of wherein closing oar process is $\frac{Y\left(s\right)}{x_v}=\frac{\frac{k_q}{A_1}}{s(\frac{s^2}{w_h^2}+2\frac{{\mathrm{\ξ}}_h}{w_h}s+1)}=\frac{263}{s(\frac{s^2}{{363.91}^2}+\frac{2\×0.1266}{363.91}s+1)},$ K _qfor the flow coefficient of servovalve, A ₁for the transversal useful area area of rodless cavity, w _hfor frequency of the natural hydraulic mode, ξ _hfor hydraulic damping ratio.The mathematical model opening oar process is $\frac{Y\left(s\right)}{x_v}=\frac{\frac{{k_q}^{\′}}{A_2}}{s(\frac{s^2}{w_h^2}+2\frac{{\mathrm{\ξ}}_h}{w_h}s+1)}=\frac{210.7}{s(\frac{s^2}{{337.228}^2}+\frac{2\×0.0721}{337.228}s+1)},$ Wherein for the flow coefficient of servovalve, A ₂for the transversal useful area of rod chamber area, w _hfor frequency of the natural hydraulic mode, ξ _hfor hydraulic damping ratio.

In step (5) by continuous time analog domain stability margin characterize the fragility of analog system, and in this, as the foundation of following digital system vulnerability analysis and design.

Introduce the conversion of bilinearity w territory in step (6), frequency response method is expanded to descreted-time control system, characterize number system amplitude versus frequency characte, and then obtain fragility quantizating index.Wherein bilinearity w converts z-plane unit circle internal maps to w Left half-plane.From s plane to z-plane and from z-plane to the synthetic effect of w plane transformation, be that w plane is similar with the survey region of s plane.This is because convert the distortion caused from s plane to z-plane, partly compensated by the conversion of z-plane to w plane.For the two Bode Plot in the difference of high band, may be interpreted as: first, that study is only 0≤ω≤ω _s/ 2 frequency ranges, it is corresponding with 0≤v≤+ ∞; Secondly, the v=+ ∞ of w plane and the ω=ω of s plane _s/ 2 is corresponding, i.e. the limit with corresponding, and the latter is a constant value.Relatively this system is at the amplitude-versus-frequency curve of continuous domain and discrete domain, and has ω _s/ 2=2 π f _s/ 2 > ω _c, therefore known w territory frequency characteristic is consistent with analog domain frequency characteristic, and its frequency range characterized meets discrete digital domain system vulnerability analysis demand.

Interval by optimizer system stable phase angle nargin in step (7), by MATLAB instrument, obtain the optimum sampling range between a frequency of number system based on special algorithm.Its algorithm steps is:

(a). according to sampling unit precision set traversal initial value, step-length, and input system analog domain open loop transfer function and experience sampling period maximum value;

(b). call the conversion of z territory, w territory transforming function transformation function completion system transfer function successively;

(c). utilize MATLAB Analysis of Magnitude-Frequency Characteristic function to obtain phase margin value and make comparisons with the interval upper and lower of optimum angle nargin;

(d). if current phase margin value and a upper traversing result phase margin interval that value is formed do not comprise the interval upper limit of optimum phase nargin or lower limit, then continue to travel through next time, circulation performs step (b), (c), until determine optimum sampling cycle upper and lower, algorithm so far completes.

Described algorithm steps (a) (b) (c) (d) is based on the codes implement of Matlab software, and namely described algorithm steps (a) (b) (c) (d) is as follows based on the code of the algorithm of MATLAB function custom feature:

[T _max,T _min]＝sampling_period(num,den,T ₀,T _L,T _step)

fori＝T0:Tstep:Tmax

ifi＝＝T0Pm_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>45Tmin＝T；end

ifPm<60&&Pm_0>60Tmax＝T；end

Pm_0＝Pm；

ifTmax>0&&Tmin>0i＝T _L；endend。

For realizing goal of the invention, step (1)-(6) in above content are basic step, by increasing step (7), can verify the sampled result based on this algorithm design gained, ensure correctness and the 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, about the key element of each step, further illustrates as follows:

Step (1), traditional modeling method is on the basis of theory analysis, sets up the mathematical model of object, also claims mechanism method; For complex system, then adopt the method for system identification, from experimental observed data, set up the model that can reflect system Input output Relationship, i.e. experimental method.Dynamics and Flow continuity equation are for determine rational content, and hydraulic variable-pitch system modelling is the key point of subsequent design, can be by improving the validity of modeling the support that follow-up design provides more favourable.

Step (2), in order to the physical model of reality is abstracted into accurate mathematical model, on the basis of not influential system performance, each element of feather cylinder device is done the fundamental that relevant hypothesis (detailed content is see embodiment) displacement transducer, servoamplifier and driver, servovalve and oil hydraulic cylinder are system modellings, needs are converted into mathematical model, for the modeling of overall system according to the physical function parameter of each key element and working principle.

Step (3), according to derivation and the simplification of Such analysis completion system mathematical model, and completes the calculating of mathematical model parameter.

Step (4) and (5), analytical system progressive die near-field amplitude versus frequency characte, sets up the discrete space model of system, to obtain fragility characterization value according to z territory, w domain theory.

Step (6), the congruity theory analysis of completion system, obtains the optimum sampling cycle interval value of system according to the logic design of traversal optimizing algorithm.

Step (7), the interval value amplitude versus frequency characte obtaining system in system continuous domain, discrete domain Analysis of Magnitude-Frequency Characteristic method is substituted into, by the checking of existing theory to guarantee the correctness that system vulnerability designs and validity based on the sampling period interval value obtained in step (6).

Owing to adopting such scheme, the invention has the beneficial effects as follows: this method clear logic, extensibility is strong, by selecting suitable PLC sampling unit, realize effective cost control, and avoid frequent or delayed caused system oscillation of sampling, ensure stability and the reliability of system cloud gray model.

Accompanying drawing explanation

Fig. 1 is the invention process example wind energy conversion system hydraulic variable-pitch servo-system hydraulic structure figure.

Wherein: fluid provides pressure source Ps by oil hydraulic pump; Oil pressure in relief valve guarantee oil hydraulic circuit is not higher than the maximum pressure of setting; The effect of pressure-stored tank 1,2 be when wind energy conversion system break down and emergency shutdown time, provide hydraulic oil to enter oil hydraulic cylinder; Now adopt 3-position 4-way servovalve and HY-YG100 type asymmetrical cylinder.

Fig. 2 is the invention process example four-way valve control asymmetrical cylinder systematic schematic diagram

Fig. 3 is the invention process example wind energy conversion system hydraulic variable-pitch servo system control block diagram.

Fig. 4 is the wind energy conversion system hydraulic variable-pitch servo-system sample frequency system of selection algorithm flow chart of the invention process example based on fragility principle.

Embodiment

Below in conjunction with accompanying drawing illustrated embodiment, the present invention is further illustrated.

A kind of wind energy conversion system hydraulic variable-pitch servo-system sample frequency system of selection based on fragility principle of the present invention, comprises the following steps:

Step (1): according to equations such as dynamics, flow are continuous, describe wind energy conversion system hydraulic variable-pitch servo-system mathematical relationship, certainty annuity mechanism model;

Step (2): the model being obtained each function link of wind energy conversion system hydraulic variable-pitch servo-system by the performance parameter of displacement transducer, servoamplifier and driver, servovalve and oil hydraulic cylinder;

Step (3): each function Link Model in the mechanism model of system and step (2) in integrating step (1), obtains wind energy conversion system hydraulic variable-pitch servo closed-loop model parameter and establish final mask structure;

Step (4): according to the phase margin index definition system vulnerability model in system stability nargin;

Step (5): the system vulnerability model verification system analog domain continuous time stability that the system model obtained according to step (3) and step (4) obtain, for following digital territory stability Design provides foundation;

Step (6): on the basis of step (5), by MATLAB instrument, obtains system digitalized optimum sampling range between a frequency by optimum phase nargin interval and bilinearity w conversion;

Step (7): the optimum sampling frequency range upper and lower according to obtaining in step (6) verifies number system stability Design in bilinearity w transform domain, so far the number system sample frequency completed based on fragility principle is selected, and namely determines PLC sampling unit performance index.

Concrete:

1) traditional modeling method is on the basis of theory analysis, sets up the mathematical model of object, also claims mechanism method; For complex system, then adopt the method for system identification, from experimental observed data, set up the model that can reflect system Input output Relationship, i.e. experimental method.Consult pertinent literature, asymmetrical cylinder also claims single-rod piston formula oil hydraulic cylinder, and modern project still with reference to asymmetric cylinder linearization technique near equinoctial point, obtains three fundamental equations in using:

(1) flow equation of valve: Q _l=k _qx _v-k _cp _l

(2) the flow continuity equation in hydraulic cylinder works chamber: $Q_L=C_{ie}{P}_L+C_{ta}{P}_s+\frac{V_1}{(1+m^3){\mathrm{\&beta;}}_e}{\mathrm{sP}}_L+A_{1}sy$

(3) equilibrium equation: F=A ₁p ₁-A ₂p ₂=A ₁p _l=Ms ²y+Bsy+Ky+F ₁

Wherein Q _lfor control valve load flow, k _qfor the flow gain of guiding valve, k _cfor the flow-pressure coefficient of guiding valve, x _vfor spool travel, P _lfor the induced pressure of system of valve controlling cylinder, C _iefor oil cylinder always reveals coefficient, C _tafor system reveals coefficient, P _sfor oil supply source pressure, V ₁for rodless cavity volume, β _efor effective volume Young's modulus, m is the quality of piston rod, and s is Laplace transformation operator, and y is hydraulic cylinder travel, and F is the driving force of system of valve controlling cylinder, A ₁for the transversal useful area area of rodless cavity, A ₂for the transversal useful area of rod chamber area, P ₁for rodless cavity pressure, P ₂for rod chamber pressure, M is the quality of load, and B is the viscous damping coefficient of piston and load, and K is the spring rate of load, F ₁for acting on any outer load force on piston.

Set up the mathematical model of asymmetrical cylinder, use MATLAB to emulate, and consider emphatically the impact of temperature for system model, set up the actual mathematical model considering temperature impact.Thus MATLAB can be used better to carry out relevant simulation and design.

2) in order to the physical model of reality is abstracted into accurate mathematical model, on the basis of not influential system performance, each element of feather cylinder device is done following hypothesis:

(1) model simplification of proportional amplifier and Proportional valve is a ratio system x _v=k ₃u, (wherein x _vfor spool travel, u is control voltage, k ₃for ratio) this be due to active within the scope of system operating frequency be valve control cylinder mode, its natural frequency is generally corner frequency minimum in system, and the corner frequency of proportional reversing valve is far above the corner frequency of valve control cylinder mode;

(2) frequency range of the Duty cycle system of displacement transducer is much higher, therefore replaces by a proportional component: u=k _f(wherein u is feedback voltage to y, k _ffor feedback factor, y is oil hydraulic cylinder displacement);

(3) control valve is desirable (namely disregarding the radial clearance between spool, valve pocket) zero lap four port valve, and four throttling windows are coupling and symmetrical (namely the area gradient w of each restriction is equal), and flow coefficient C d is equal;

(4) flowing of throttling window is turbulent flow, and the compressibility of fluid impact in valve is negligible;

(5) control valve has desirable response capability;

(6) hydraulic energy source is desirable [constant, and charge oil pressure Ps is constant, and return pressure Po is zero;

(7) the inside and outside leakage of oil hydraulic cylinder is Laminar Flow;

When adopting the dynamic characteristic of linearizing methods analyst system, ignore nonlinear loads such as there is Coulomb friction.

First, define according to control valve load flow:

$\left\{\begin{array}{cc}{Q}_L=Q_1-Q_3& x_v>0\\ Q_L=Q_4-Q_2& x_v<0\end{array}\right.$

Here control valve is thought of as perfect symmetry zero lap valve, does not consider the leakage between its valve port, therefore during Xv>0, Q4=0; During Xv<0, the load flow of Q2=0 event valve is:

$\left\{\begin{array}{cc}{Q}_L=Q_1& x_v>0\\ Q_L=Q_3& x_v<0\end{array}\right.$

Secondly definition induced pressure PL:

When oil hydraulic cylinder moves right:

$P_L=\frac{F}{A_1}=\frac{P_1{A}_1-P_2{A}_2}{A_1}=P_1-{\mathrm{\&eta;P}}_2---\left(1\right)$

The driving force of F---system of valve controlling cylinder, N

P _l---the induced pressure of system of valve controlling cylinder, Pa;

---the ratio of oil hydraulic cylinder rod chamber area A 2 and rodless cavity area A 1.

When oil hydraulic cylinder is moved to the left:

$P_L=\frac{F}{A_2}=\frac{P_2{A}_2-P_1{A}_1}{A_2}=P_2-\frac{1}{\mathrm{\&eta;}}{P}_1---\left(2\right)$

Each parameter definition is identical with (1) formula.

3) be derived as example with feather cylinder device pass oar process mathematical model to have:

It is protruding that feather cylinder device closes oar process hydraulic cylinder piston rod, and propeller pitch angle increases.[18] now feather cylinder device motion is the process that the hydraulic cylinder piston rod shown in Fig. 2 .3 moves right.Now define according to hydrovalve flow:

$Q=g\&times;\sqrt{\mathrm{\&Delta;}p}$

$g=C_d\&times;A_i\&times;\sqrt{\frac{2}{\mathrm{\&rho;}}}=C_d\&times;w\&times;x_v\&times;\sqrt{\frac{2}{\mathrm{\&rho;}}}$

Δ p---pressure difference, Pa

C _d---hydrovalve restriction flow coefficient; ρ---fluid density, kg/m ³

A _i---orifice area changes; W---hydrovalve choke area gradient, m

Close in oar process, the flow equation of xv>0 servo valve control mouth:

$\left\{\begin{array}{c}{Q}_1=C_d{\mathrm{wx}}_v\sqrt{\frac{2}{\mathrm{\&rho;}}(P_s-P_1)}\\ Q_2=C_d{\mathrm{wx}}_v\sqrt{\frac{2}{\mathrm{\&rho;}}{P}_2}\end{array}\right.---\left(1.3\right)$

P _s---oil supply source pressure, P _a

According to Flow continuity equation, the flow equation obtaining asymmetrical cylinder two cylinder is:

$\left\{\begin{array}{c}{Q}_1=C_{ic}(P_1-P_2)+C_{ec}{P}_1+\frac{V_1}{{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_1+{\stackrel{\&CenterDot;}{V}}_1\\ Q_2=C_{ic}(P_1-P_2)-C_{ec}{P}_2-\frac{V_2}{{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_2-{\stackrel{\&CenterDot;}{V}}_2\end{array}\right.---\left(2.4\right)$

Q ₁---rodless cavity flow, m ³/ s

Q ₂---rod chamber flow, m ³/ s

β _e---effective volume Young's modulus, P _a

C _ic---hydraulic cylinder interior leakage dew coefficient, m ⁵/ (Ns)

C _ec---oil hydraulic cylinder outward leakage coefficient, m ⁵/ (Ns)

V ₁---rodless cavity volume, m ³

V ₂---rod chamber volume, m ³

Obtained by formula (2.3): $\frac{Q_1}{Q_2}=\sqrt{\frac{P_s-P_1}{P_2}}---\left(2.5\right)$

Ignore reveal and the flow of liquid appearance caused by effect time:

Obtained by formula (2.4): $\frac{Q_1}{Q_2}=\left|\frac{{\stackrel{\&CenterDot;}{V}}_1}{-{\stackrel{\&CenterDot;}{V}}_2}\right|=\frac{A_1}{A_2}=\frac{1}{\mathrm{\&eta;}}---\left(2.6\right)$

Therefore obtained by formula (2.5), (2.6): $\mathrm{\&eta;}=\frac{A_2}{A_1}=\sqrt{\frac{P_2}{P_s-P_1}}---\left(2.7\right)$

Simultaneous formula (2.1) and (2.7) solve:

$\left\{\begin{array}{c}{P}_1=\frac{P_L+{\mathrm{\&eta;}}^3{P}_s}{1+{\mathrm{\&eta;}}^3}\\ P_2=\frac{{\mathrm{\&eta;}}^2(P_S-P_L)}{1+{\mathrm{\&eta;}}^3}\end{array}\right.---\left(2.8\right)$

By load flow definition, and bring formula (2.4) (2.8) into and abbreviation obtains:

$Q_L=Q_1=C_{tc}{P}_L+C_{ta}{P}_s+\frac{V_1}{{\mathrm{\&beta;}}_e(1+{\mathrm{\&eta;}}^3)}{\stackrel{\&CenterDot;}{P}}_L+A_1\stackrel{\&CenterDot;}{y}---\left(2.9\right)$

Wherein: ---oil cylinder always reveals coefficient, m ⁵/ (Ns)

---system reveals coefficient, m ⁵/ (Ns)

By load flow definition, and bring formula (2.3) into, the another kind obtaining load flow is expressed:

$Q_L=Q_1=C_d{\mathrm{wx}}_v\sqrt{\frac{2}{\mathrm{\&rho;}}\left(\frac{P_s-P_L}{1+{\mathrm{\&eta;}}^3}\right)}---\left(2.10\right)$

By above formula (2.10) linearization:

Q _L＝k _qx _v-k _cp _L(2.11)

Wherein: ---the flow gain of guiding valve, m ²/ s;

---the flow-pressure coefficient of guiding valve, m ⁵/ (Ns)

The stressed equation of hydraulic cylinder piston is:

$F=P_1{A}_1-P_2{A}_2=A_1{P}_L=(m+M)\stackrel{\&CenterDot;\&CenterDot;}{y}+B_c\stackrel{\&CenterDot;}{y}+ky+F_L---\left(2.12\right)$

Wherein: F---the driving force that oil hydraulic cylinder produces, N

B _c---the viscous damping coefficient of piston and load, N/ (m/s)

The spring rate of k---load, N/m

F _l---act on any outer load force on piston, N

The quality of m---piston rod, kg

The quality of M---load, kg

Formula (2.9), (2.10), (2.12) move right the fundamental equation of non-linear hour for feather oil hydraulic cylinder; In order to use classical control theory research feather cylinder device, the set of equation after linearization is adopted to set up corresponding mathematical model.Formula (2.9), (2.11), (2.12) for Basic equation group linearizing when feather oil hydraulic cylinder moves right as follows:

$\left\{\begin{array}{c}{Q}_L=Q_1=C_{tc}{P}_L+C_{ta}{P}_s+\frac{V_1}{{\mathrm{\&beta;}}_e\left(1-{\mathrm{\&eta;}}^3\right)}{\stackrel{\&CenterDot;}{P}}_L+A_1\stackrel{\&CenterDot;}{y}\\ Q_L=k_q{x}_v-k_c{p}_L\\ F=P_1{A}_1-P_2{A}_2=A_1{P}_L=\left(m+M\right)\stackrel{\&CenterDot;\&CenterDot;}{y}+B_c\stackrel{\&CenterDot;}{y}+ky+F_L\end{array}\right.$

Carry out laplace transform to set of equation to obtain:

$\left\{\begin{array}{c}{Q}_L\left(s\right)=Q_1\left(s\right)=C_{tc}{P}_L\left(s\right)+C_{ta}{P}_s+\frac{V_1}{{\mathrm{\&beta;}}_e(1+{\mathrm{\&eta;}}^3)}s{P}_L\left(s\right)+A_{1}sy\left(s\right)\\ Q_L\left(s\right)=k_q{x}_v\left(s\right)-k_c{p}_L\left(s\right)\\ F=P_1{A}_1-P_2{A}_2=A_1{P}_L\left(s\right)=(m+M)s^{2}y\left(s\right)+B_{c}sy\left(s\right)+ky\left(s\right)+F_L\end{array}\right.$

In like manner can obtain feather cylinder device and open the linearizing Basic equation group of oar process mathematical model:

$\left\{\begin{array}{c}{Q}_L=Q_3=C_{tc}^{\&prime;}{P}_L+C_{ta}^{\&prime;}{P}_s+\frac{{\mathrm{\&eta;}}^3{V}_2}{{\mathrm{\&beta;}}_e\left(1+{\mathrm{\&eta;}}^3\right)}{\stackrel{\&CenterDot;}{P}}_L+A_2\stackrel{\&CenterDot;}{y}\\ Q_L=k_q^{\&prime;}{x}_v-k_c^{\&prime;}{p}_L\\ F=P_2{A}_2-P_1{A}_1=A_2{P}_L=\left(m+M\right)\stackrel{\&CenterDot;\&CenterDot;}{y}+B_c\stackrel{\&CenterDot;}{y}+ky+F_L\end{array}\right.$

Carry out laplace transformation to above set of equation to obtain:

$\left\{\begin{array}{c}{Q}_L\left(s\right)=Q_3\left(s\right)=C_{tc}^{\&prime;}{P}_L\left(s\right)+C_{ta}^{\&prime;}{P}_s+\frac{{\mathrm{\&eta;}}^3{V}_2}{{\mathrm{\&beta;}}_e\left(1+{\mathrm{\&eta;}}^3\right)}{\mathrm{sP}}_L\left(s\right)+A_{2}sy\left(s\right)\\ Q_L\left(s\right)=k_q^{\&prime;}{x}_v\left(s\right)-k_c^{\&prime;}{p}_L\left(s\right)\\ F=P_2{A}_2-P_1{A}_1=A_2{P}_L\left(s\right)=\left(m+M\right)s^{2}y\left(s\right)+B_{c}sy\left(s\right)+ky\left(s\right)+F_L\end{array}\right.$

4) feather cylinder device mathematical model simplifies

Close oar according to feather cylinder device and open the lienarized equation group of oar process, the relation between oil hydraulic cylinder displacement y and spool travel Xv and outer load force FL can be obtained:

Close oar process:

$Y\left(s\right)=\frac{\frac{k_q}{A_1}{x}_v-C_{ta}\frac{P_s}{A_1}-\frac{k_{ce}}{A_1^2}(1+\frac{V_{1}s}{k_{ce}(1+{\mathrm{\&eta;}}^3)})F_L}{\frac{V_1{m}_e}{{A^2}_1{\mathrm{\&beta;}}_e(1+{\mathrm{\&eta;}}^3)}{s}^3+(\frac{k_{ce}{m}_e}{{A_1}^2}+\frac{V_1{B}_c}{{A_1}^2{\mathrm{\&beta;}}_e(1+{\mathrm{\&eta;}}^3)})s^2+(\frac{k_{ce}{B}_c}{{A_1}^2}+\frac{V_{1}k}{{\mathrm{\&beta;}}_e(1+{\mathrm{\&eta;}}^3)}+1)s+\frac{k_{ce}}{{A_1}^2}k}$

Wherein: k _ce=k _c+ C _tc---total flow-pressure coefficient, m ⁵/ (Ns)

M _e=m+M---gross mass, kg

Now, piston rod moves right: V ₁=V ₁₀+ A ₁y, due to V ₁₀>>A ₁y, so V ₁≈ V ₁₀.And fans load is based on inertia load, the rigidity k ≈ 0 of load, therefore obtain closing the final reduced form of oar process mathematical model:

$Y\left(s\right)=\frac{\frac{k_q}{A_1}{x}_v-C_{ta}\frac{P_s}{A_1}-\frac{k_{ce}}{A_1^2}(1+\frac{V_{10}s}{k_{ce}(1+{\mathrm{\&eta;}}^3)})F_L}{s(\frac{s^2}{w_h^2}+2\frac{{\mathrm{\&xi;}}_h}{w_h}s+1)}$

Wherein: ---frequency of the natural hydraulic mode, rad/s

${\mathrm{\&xi;}}_h=\frac{1}{2}(\frac{k_{ce}}{A_1}\sqrt{\frac{{\mathrm{\&beta;}}_e{m}_e(1+{\mathrm{\&eta;}}^3)}{V_{10}}}+\frac{B_c}{A_1}\sqrt{\frac{V_{10}}{{\mathrm{\&beta;}}_e{m}_e(1+{\mathrm{\&eta;}}^3)}})$ ---hydraulic damping ratio, zero dimension

Open oar process:

$Y\left(s\right)=\frac{\frac{{k_q}^{\&prime;}}{A_2}{x}_v-{C_{ta}}^{\&prime;}\frac{P_s}{A_2}-\frac{k_{ce}}{A_2^2}(1+\frac{V_2{\mathrm{s\&eta;}}^3}{k_{ce}(1+{\mathrm{\&eta;}}^3)})F_L}{\frac{V_2{m}_e{\mathrm{\&eta;}}^3}{{A^2}_2{\mathrm{\&beta;}}_e(1+{\mathrm{\&eta;}}^3)}{s}^3+(\frac{k_{ce}{m}_e}{{A_2}^2}+\frac{V_2{B}_c{\mathrm{\&eta;}}^3}{{A_2}^2{\mathrm{\&beta;}}_e(1+{\mathrm{\&eta;}}^3)})s^2+(\frac{k_{ce}{B}_c}{{A_2}^2}+\frac{V_2{\mathrm{k\&eta;}}^3}{{\mathrm{\&beta;}}_e(1+{\mathrm{\&eta;}}^3)}+1)s+\frac{k_{ce}}{{A_2}^2}k}$

Wherein: k _ce=k _c'+C _tc'---be total flow coefficient, m ⁵/ (Ns)

M _e=m+M---be gross mass, kg

Now, piston rod is to left movement: V ₂=V ₂₀-A ₂y is due to V ₂₀>>A ₂y, so V ₂≈ V ₂₀.And fans load is based on inertia load, the rigidity k ≈ 0 of load, obtain out the final simplified style of oar process mathematical model:

$Y\left(s\right)=\frac{\frac{{k_q}^{\&prime;}}{A_2}{x}_v-{C_{ta}}^{\&prime;}\frac{P_s}{A_2}-\frac{k_{ce}}{A_2^2}(1+\frac{V_{20}{\mathrm{s\&eta;}}^3}{k_{ce}(1+{\mathrm{\&eta;}}^3)})F_L}{s(\frac{s^2}{w_h^2}+2\frac{{\mathrm{\&xi;}}_h}{w_h}s+1)}$

Wherein: ---frequency of the natural hydraulic mode, rad/s

${\mathrm{\&xi;}}_h=\frac{1}{2}\left(\frac{k_{ce}}{A_2}\sqrt{\frac{{\mathrm{\&beta;}}_e{m}_e\left(1-{\mathrm{\&eta;}}^3\right)}{V_{20}{\mathrm{\&eta;}}^3}+}\frac{B_c}{A_2}\sqrt{\frac{V_{20}{\mathrm{\&eta;}}^3}{{\mathrm{\&beta;}}_e{m}_e\left(1+{\mathrm{\&eta;}}^3\right)}}\right)$ ---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 simplification process are all based on piston rod middle low amplitude vibrations near its equilibrium position.Describe the concept of oil hydraulic cylinder spring rate in document [10] and reach a conclusion: when piston departs from equilibrium position, oil hydraulic cylinder spring rate increases, and natural frequency increases.Therefore piston-initial-position can be obtained by its spring rate representation.

Oil hydraulic cylinder spring rate if oil hydraulic cylinder total kilometres are L, piston displacement is y, then V ₁=A ₁y, V ₂=A ₂(L-y).Then obtain the relation of oil hydraulic cylinder spring rate and its piston displacement: $k_b=\frac{{\mathrm{\&beta;}}_e{A}_1}{y}+\frac{{\mathrm{\&beta;}}_e{A}_1\mathrm{\&eta;}}{L-y}={\mathrm{\&beta;}}_e{A}_1(\frac{1}{y}+\frac{\mathrm{\&eta;}}{L-y}),$ The method of extreme value is asked by higher mathematics, when $y=\frac{L}{1+\sqrt{\mathrm{\&eta;}}}$ Time, oil hydraulic cylinder spring rate is minimum, when hydraulic cylinder piston connects inertial mass load, and natural frequency (m1 is piston and load quality reduced value) is now minimum.Then $V_{10}=\frac{A_{1}L}{1+\sqrt{\mathrm{\&eta;}}},V_{20}=\frac{A_2\sqrt{\mathrm{\&eta;}}}{1+\sqrt{\mathrm{\&eta;}}}L.$

Due to feather cylinder device oil viscosity, reveal the impact that coefficient etc. is subject to temperature.Temperature should be determined a certain during certainty annuity parameter.The present invention adopts HY-YG100 type oil hydraulic cylinder at certain temperature, and design parameter is in table 1:

Table 1 feather cylinder device parameter

Data according to table 1 can calculate:

Rodless cavity area $A_1=\mathrm{\&pi;}\frac{D^2}{4}=3.14\&times;\frac{{0.1}^2}{4}=7.85\&times;{10}^{-3}{m}^2$

Rod chamber area $A_2=A_1-\mathrm{\&pi;}\frac{d^2}{4}=7.85\&times;{10}^{-3}-3.14\&times;\frac{{0.06}^2}{4}=5.024\&times;{10}^{-3}{m}^2$

Area ratio $\mathrm{\&eta;}=\frac{A_2}{A_1}=\frac{5.024\&times;{10}^{-3}}{7.85\&times;{10}^{-3}}=0.64$

Rodless cavity initial volume $V_{10}=\frac{A_{1}L}{1+\sqrt{\mathrm{\&eta;}}}=\frac{7.85\&times;{10}^{-3}\&times;0.41}{1+\sqrt{0.64}}=4.023\&times;{10}^{-3}{m}^3$

Rod chamber initial volume $V_{20}=\frac{A_2\sqrt{\mathrm{\&eta;}}}{1+\sqrt{\mathrm{\&eta;}}}L=\frac{5.024\&times;{10}^{-3}\&times;\sqrt{0.64}}{1+\sqrt{0.64}}\&times;0.41=0.915\&times;{10}^{-3}{m}^3$

(1) oar process is closed:

The flow coefficient of valve be and induced pressure P _lrelevant, conventional zero-bit flow coefficient estimation in engineering $k_{q0}=C_{d}w\sqrt{\frac{2}{\mathrm{\&rho;}}\frac{P_S}{1+{\mathrm{\&eta;}}^3}}=0.61\&times;0.02\&times;\sqrt{\frac{2}{850}\frac{1.4\&times;{10}^7}{1+{0.64}^3}}=2.068$

The flow-pressure coefficient of valve be with induced pressure and spool travel related, often in engineering adopt new definition wherein r _cfor the radial clearance between spool and valve pocket/m, r _c=5 × 10 ^-5; μ kinetic viscosity/P _as, μ=137 × 10 ^-4therefore, $k_c=\frac{{{\mathrm{\&pi;wr}}_c}^2}{32\mathrm{\&mu;}}=\frac{3.14\&times;0.02\&times;5^2\&times;{10}^{-10}}{32\&times;137\&times;{10}^{-4}}=3.581\&times;{10}^{-10}$

Frequency of the natural hydraulic mode $w_h=\sqrt{\frac{{A_1}^2{\mathrm{\&beta;}}_e(1+{\mathrm{\&eta;}}^3)}{V_{10}{m}_e}}=\sqrt{\frac{{0.00785}^2\&times;6.85\&times;{10}^8(1+{0.64}^3)}{4.023\&times;{10}^{-3}\&times;100}}=363.91$

Hydraulic damping ratio ${\mathrm{\&xi;}}_h=\frac{1}{2}(\frac{k_{ce}}{A_1}\sqrt{\frac{{\mathrm{\&beta;}}_e{m}_e(1+{\mathrm{\&eta;}}^3)}{V_{10}}}+\frac{B_c}{A_1}\sqrt{\frac{V_{10}}{{\mathrm{\&beta;}}_e{m}_e(1+{\mathrm{\&eta;}}^3)}})=0.1266$

Pass oar process piston rod displacement and spool travel relation are:

$\frac{Y\left(s\right)}{x_v}=\frac{\frac{k_q}{A_1}}{s(\frac{s^2}{w_h^2}+2\frac{{\mathrm{\&xi;}}_h}{w_h}s+1)}=\frac{263}{s(\frac{s^2}{{363.91}^2}+\frac{2\&times;0.1266}{363.91}s+1)}$

(2) oar process is opened:

The flow coefficient of valve with induced pressure P _lrelevant, conventional zero-bit flow parameter estimation in engineering ${k_{q0}}^{\&prime;}=C_{d}w\sqrt{\frac{2}{\mathrm{\&rho;}}\frac{{\mathrm{\&eta;}}^3{P}_S}{1+{\mathrm{\&eta;}}^3}}=0.61\&times;0.02\&times;\sqrt{\frac{2}{850}\frac{{0.64}^3\&times;1.4\&times;{10}^7}{1+{0.64}^3}}=1.0588$

The flow-pressure coefficient k of valve _c' ≈ k _c=3.581 × 10 ^-10

Natural frequency $w_h=\sqrt{\frac{{A_2}^2{\mathrm{\&beta;}}_e(1+{\mathrm{\&eta;}}^3)}{V_{20}{B}_c{\mathrm{\&eta;}}^3}}=\sqrt{\frac{{5.024}^2\&times;{10}^{-6}\&times;6.85\&times;{10}^8(1+{0.64}^3)}{0.915\&times;{10}^{-3}\&times;800\&times;{0.64}^3}}=337.228$

Hydraulic damping ratio ${\mathrm{\&xi;}}_h=\frac{1}{2}\left(\frac{k_{ce}}{A_2}\sqrt{\frac{{\mathrm{\&beta;}}_e{m}_e\left(1+{\mathrm{\&eta;}}^3\right)}{V_{20}{\mathrm{\&eta;}}^3}}+\frac{B_c}{A_2}\sqrt{\frac{V_{20}{\mathrm{\&eta;}}^3}{{\mathrm{\&beta;}}_e{m}_e\left(1+{\mathrm{\&eta;}}^3\right)}}\right)=0.0721$

Open the piston rod displacement of oar process and spool travel relation is:

$\frac{Y\left(s\right)}{x_v}=\frac{\frac{{k_q}^{\&prime;}}{A_2}}{s(\frac{s^2}{w_h^2}+2\frac{{\mathrm{\&xi;}}_h}{w_h}s+1)}=\frac{210.7}{s(\frac{s^2}{{337.228}^2}+\frac{2\&times;0.0721}{337.228}s+1)}$

6) wherein servovalve drives oil hydraulic cylinder link mathematical model clearly, for the quantification of servovalve amplification, shift transmission and controller link by following data acquisition.

Relation is sent in the change of table 2 servovalve driver

System realizes usually adopting PID controller, and it has four parameters undetermined: P, I, D and infinitesimal calculus time T.The present invention introduces proportional component P at this temporarily about the analysis of system vulnerability.Therefore, controller parameter can be set as K based on system block diagram, servovalve amplifier gain is K ₁, displacement transducer gain is K ₂, then have:

$K=\frac{F_{max}-F_{\min }}{O_{\max }-O_{\min }}=\frac{(20-4)mA}{(20-4)mA}=1$

$K_1=\frac{(4-0)\&CenterDot;{10}^{-3}m}{(20-4)\&CenterDot;{10}^{-3}A}\&CenterDot;25=6.25m/A$

$K_2=\frac{(20-4)\&CenterDot;{10}^{-3}A}{(500-0)\&CenterDot;{10}^{-3}m}=0.032A/m$

Wind energy conversion system hydraulic variable-pitch system open loop transfer function and closed loop transfer function can be obtained as follows respectively:

$G\left(s\right)H\left(s\right)=\frac{K\&CenterDot;K_1\&CenterDot;K_2\&CenterDot;Y\left(s\right)}{x_v}$

$F\left(s\right)=\frac{K\&CenterDot;K_1\&CenterDot;\frac{Y\left(s\right)}{x_v}}{1+K\&CenterDot;K_1\&CenterDot;K_2\&CenterDot;\frac{Y\left(s\right)}{x_v}}=\frac{K\&CenterDot;K_1\&CenterDot;Y\left(s\right)}{K\&CenterDot;K_1\&CenterDot;K_2\&CenterDot;Y\left(s\right)+x_v}$

7) progressive die near-field amplitude versus frequency characte

Known system open loop transfer function, frequency domain analysis continuous time based on system can do preliminary analysis to the analog domain fragility of this system.Defining according to frequency domain analysis to obtain wind energy conversion system hydraulic variable-pitch and to close oar process amplitude versus frequency characte representation:

$\begin{array}{c}GH\left(j\mathrm{\&omega;}\right)=\frac{263\&CenterDot;6.25\&CenterDot;0.032}{s\left(\frac{s^2}{{363.91}^2}+\frac{2\&CenterDot;0.1266}{363.91}s+1\right)}{|}_{s=j\mathrm{\&omega;}}\\ =\frac{52.6}{j\mathrm{\&omega;}\&lsqb;\left(\frac{-{\mathrm{\&omega;}}^2}{363.91}+1\right)+j\frac{2\&CenterDot;0.1266}{363.91}\mathrm{\&omega;}\&rsqb;}\end{array}$

Amplitude expression is utilized to calculate its cross-over frequency w _chave:

$\left|GH\left(j\mathrm{\&omega;}\right)\right|=\left|\frac{52.6}{j\mathrm{\&omega;}\&lsqb;\left(\frac{-{\mathrm{\&omega;}}^2}{{363.91}^2}+1\right)+j\frac{2\&CenterDot;0.1266}{363.91}\mathrm{\&omega;}\&rsqb;}\right|=1$

Solve: ω _c=53.73rad/s, being substituted into the phase margin that system phase representation can obtain system is:

Can obtain the Bode Plot of this system based on MATLAB instrument, and draw emulation stability margin numerical value thus, it is consistent with result of calculation.Based on the calculating of above stability margin, this system known has stable system architecture at analog domain, is the prerequisite of system being carried out to digitizing and vulnerability analysis thereof.

8) system digitalized and fragility characterizes

At present direct frequency response method and Bilinear transformation method are mainly comprised to the frequency response design method of number system.Because direct frequency response method loses the simplicity of Logarithm coordinates, therefore Bilinear transformation method is adopted to realize the stability analysis of number system, by the fragility of its phase margin representative digit system herein.

Discrete domain Analysis of Magnitude-Frequency Characteristic problem can be solved by the method pulsed transfer function of z-plane being transformed to w plane.This conversion is called w conversion usually, is a kind of bilinear transformation, is defined as follows:

$z=\frac{1+(T/2)w}{1-(T/2)w}$

Wherein, T is the sampling period of studied descreted-time control system.By the given pulsed transfer function in z-plane being transformed into the rational function about w, frequency response method is expanded to descreted-time control system.Based on these mapping relations, can wind energy conversion system hydraulic system pass oar process transfer function be example, successively it be converted.The sample frequency in signal transacting field is usually higher, and the sample frequency of digital control field is usually lower.Foundation system block diagram, doses sampling switch respectively before and after its controller and zero-order holder by its digitizing, according to correlating transforms principle, can convert and w transformation results by the z of this system open loop transfer function when sampling period T=0.01s.

$\begin{array}{c}GH\left(z\right)=(1-z^{-1})Z\&lsqb;\frac{GH\left(s\right)}{s}\&rsqb;\\ =\frac{0.509Z^2+0.5339Z+0.2846}{Z^3+0.1259Z^2-0.7279z-0.398}\end{array}$

$GH\left(w\right)=\frac{-0.4772w^3-69.45w^2-6.461\&CenterDot;{10}^{4}w+1.952\&CenterDot;{10}^7}{w^3+885.1w^2+3.71\&CenterDot;{10}^{5}w+1.648\&CenterDot;{10}^{-8}}$

By s territory Analysis of Magnitude-Frequency Characteristic principle, can obtain w territory amplitude versus frequency characte relation is:

$GH\left(jv\right)=\frac{-0.4772w^3-69.45w^2-6.461\&CenterDot;{10}^{4}w+1.952\&CenterDot;{10}^7}{w^3+885.1w^2+3.71\&CenterDot;{10}^{5}w+1.648\&CenterDot;{10}^{-8}}{|}_{w=jv}$

And then when can obtain sampling period T=0.01s according to amplitude, phase place formula system discrete domain amplitude versus frequency characte as shown in Figure 6.Wherein cross-over frequency and phase margin are respectively:

v _c＝53.91rad/sγ＝72.8°

9) consistency analysis

Converted z domain mapping in w territory by w, the amplitude versus frequency characte in z territory is characterized with w territory amplitude versus frequency characte, therefore consistency analysis need be carried out to it, namely compare with the amplitude versus frequency characte under continuous time frequency domain, to guarantee that w territory amplitude versus frequency characte characterizes the validity of discrete digital Amplitude Frequency Characteristic.

-the ω of s plane _s/ 2≤ω≤ω _s/ 2 frequency bands are mapped to-∞ < v <+∞ scope, and wherein v is the virtual frequency in w plane.For the vulnerability analysis of system, Phase margin is under the jurisdiction of system Low Medium Frequency characteristic, therefore frequency characteristic after compression can meet the demand that system vulnerability is analyzed.

Once pulsed transfer function G (z) be transformed to G (w) by w conversion, just can be regarded as the transfer function about w, namely traditional frequency response method can be used for w plane, thus original frequency response design method can be applied in descreted-time control system.As mentioned above, v is a virtual frequency, by replacing w with jv, then can utilize legacy frequencies response method to draw the Bode Plot about w.W plane G (jv) is corresponding with s plane G (jw), but the frequency axis of w plane is distortion, has such as formula shown corresponding relation:

Namely bilinearity w converts z-plane unit circle internal maps to w Left half-plane.From s plane to z-plane and from z-plane to the synthetic effect of w plane transformation, be that w plane is similar with the survey region of s plane.This is because convert the distortion caused from s plane to z-plane, partly compensated by the conversion of z-plane to w plane.For the two Bode Plot in the difference of high band, may be interpreted as: first, that study is only 0≤ω≤ω _s/ 2 frequency ranges, it is corresponding with 0≤v≤+ ∞; Secondly, the v=+ ∞ of w plane and the ω=ω of s plane _s/ 2 is corresponding, i.e. the limit with corresponding, and the latter is a constant value.Need point out that these two values are normally unequal, from zero pole point angle, | G (jv) | at v=+ ∞ place for nonzero value means that G (w) comprises the zeros and poles of identical number.Relatively this system is at the amplitude-versus-frequency curve of continuous domain and discrete domain, and has ω _s/ 2=2 π f _s/ 2 > ω _c, therefore known w territory frequency characteristic is consistent with analog domain frequency characteristic, and its frequency range characterized meets discrete digital domain system vulnerability analysis demand.

10) optimum interval analysis and calculating

By known to discrete digital territory Analysis of Magnitude-Frequency Characteristic under Different sampling period, from T=0.01s to T=0.1s, system phase nargin ° trends towards 0 ° from γ=72.8.As can be seen here, the fragility impact of sampling period on number system is very large.Because the fragility of system is characterized by phase margin, and the speed of response of phase margin reflection system.Phase margin is less than normal, and system vulnerability can be caused not enough; Phase margin is bigger than normal, and system responses can be caused slow.So the optimum phase angle nargin interval of system also correspond to optimum sampling period interval.The phase margin of usual system is minimum is 45 °, and optimum phase nargin is 60 °.

Exist between the inverse logical calculated optimum sampling periodic region based on Analysis of Magnitude-Frequency Characteristic and calculate too complicated drawback; So by MATLAB instrument, adopting the false position of positive logic to travel through a larger sampling period scope, is then the method for recommending herein to obtain optimum sampling computation of Period.Wherein, MATLAB is verified in 1.3 joints for the accuracy of Amplitude Frequency Characteristic Analysis function; Larger sampling period range lower limit can be determined by sampling unit precision, and the traversal step-length of false position is also this sampling precision value, and its upper limit then can be arranged according to engineering experience, can revise flexibly in computational process.This algorithm logic is as follows:

(1) according to sampling unit precision set traversal initial value, step-length, and input system analog domain open loop transfer function and experience sampling period maximum value;

(2) conversion of z territory, w territory transforming function transformation function completion system transfer function is called successively;

(3) utilize MATLAB Analysis of Magnitude-Frequency Characteristic function to obtain phase margin value and make comparisons with the interval upper and lower of optimum angle nargin;

(4) if current phase margin value and a upper traversing result phase margin interval that value is formed do not comprise the interval upper limit of optimum phase nargin or lower limit, then continue to travel through next time, circulation performs step (2) (3), until determine optimum sampling cycle upper and lower, algorithm so far completes.Prerequisite due to number system vulnerability analysis is that system has stable analog domain amplitude versus frequency characte, so, certainly exist the optimum sampling period interval.According to above algorithm flow, MATLAB can be obtained and encapsulate function (as previously mentioned).

11) model verification

For wind energy conversion system hydraulic variable-pitch system switching oar process, seek, between its optional sampling periodic region, the correctness of the method can be verified.According to the wind energy conversion system hydraulic variable-pitch system switching oar model of foundation and the Preliminary Analysis Results of its number system, can relevant parameter be obtained as follows:

Close oar process:

num＝[52.6]；

den＝[1/363.91^2,2*0.1266/363.91,1,0]；

T ₀＝0.01s；

T _L＝0.1s；

T _step＝0.001s；

Can obtain its Output rusults based on traversal optimizing method is:

T _max＝0.026s；T _min＝0.019s；

Open oar process:

num＝[42.14]；

den＝[1/339.228^2,2*0.0721/337.228,1,0]；

T ₀＝0.01s；

T _L＝0.1s；

T _step＝0.001s；

Can obtain its Output rusults based on traversal optimizing method is:

T _max＝0.034s；T _min＝0.021s；

According to above the result, it is consistent with number system Analysis of Magnitude-Frequency Characteristic result.In addition, comprise out oar due to wind energy conversion system hydraulic variable-pitch system simultaneously and close oar two asymmetric processes, share a set of sampling unit, it is a typical combined system, so, the common factor between above two process optimum sampling periodic region is required to be between the optimum sampling periodic region corresponding to the digitizing of this combined system, also namely:

[0.019,0.026]∩[0.021,0.034]＝[0.021,0.026]

Above model verification adopts precision to be the sampling unit of 1ms, if for the sampling unit analysis of other precision, can adjust accordingly the design of number system fragility.

Above-mentioned is can understand and apply the invention for ease of those skilled in the art to the description of embodiment.Person skilled in the art obviously easily can make various amendment to these embodiments, and General Principle described herein is applied in other embodiments and need not through performing creative labour.Therefore, the invention is not restricted to embodiment here, those skilled in the art, according to announcement of the present invention, do not depart from improvement that scope makes and amendment all should within protection scope of the present invention.

Claims (10)

1. a wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection, is characterized in that: comprise the following steps:

Step (1): describe wind energy conversion system hydraulic variable-pitch servo-system mathematical relationship according to the flow equation of valve, the flow continuity equation in hydraulic cylinder works chamber and equilibrium equation, certainty annuity mechanism model;

Step (2): the model being obtained each function link of wind energy conversion system hydraulic variable-pitch servo-system by the performance parameter of displacement transducer, servoamplifier and driver, servovalve and oil hydraulic cylinder;

Step (3): each function Link Model in the mechanism model of system and step (2) in integrating step (1), obtains wind energy conversion system hydraulic variable-pitch servo closed-loop model parameter and establish final mask structure;

Step (4): according to the phase margin index definition system vulnerability model in system stability nargin;

Step (5): the system vulnerability model verification system analog domain continuous time stability that the system model obtained according to step (3) and step (4) obtain, for following digital territory stability Design provides foundation;

Step (6): on the basis of step (5), by MATLAB instrument, obtains system digitalized optimum sampling range between a frequency by optimum phase nargin interval and bilinearity w conversion.

2. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterized in that: also comprise step (7): the optimum sampling frequency range upper and lower according to obtaining in step (6) verifies number system stability Design in bilinearity w transform domain, so far the number system sample frequency completed based on fragility principle is selected, and namely determines PLC sampling unit performance index.

3. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterized in that: the Low Medium Frequency characteristic considering system, by the performance parameter that fragility designs as Low Medium Frequency stability characteristic (quality), while the system of guarantee has enough robustness, fragility system being shown as to Low Medium Frequency characteristic carries out design and study, and the sample frequency completing number system based on this is selected.

4. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 3, it is characterized in that: consider such running environment that geographical position is remote, maintenance difficulty is high or breakdown loss is large residing for wind energy conversion system hydraulic control system, the stability of corresponding raising system.

5. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterized in that: the establishment of wind energy conversion system hydraulic variable-pitch servo-system mathematical model in step (1), for the typical wind energy conversion system hydraulic variable-pitch servo-system be made up of AC variale speed mechanism, pump control power mechanism, sampling transmission mechanism and PLC control mechanism, can according to the flow equation of servovalve: Q _l=k _qx _v-k _cp _lthe continuity flow equation in hydraulic work chamber: and equilibrium equation: F=A ₁p ₁-A ₂p ₂=A ₁p _l=Ms ²y+Bsy+Ky+F ₁set up the mathematical model of asymmetry oil hydraulic cylinder; Wherein Q _lfor control valve load flow, k _qfor the flow gain of guiding valve, k _cfor the flow-pressure coefficient of guiding valve, x _vfor spool travel, P _lfor the induced pressure of system of valve controlling cylinder, C _iefor oil cylinder always reveals coefficient, C _tafor system reveals coefficient, P _sfor oil supply source pressure, V ₁for rodless cavity volume, β _efor effective volume Young's modulus, m is the quality of piston rod, and s is Laplace transformation operator, and y is hydraulic cylinder travel, and F is the driving force of system of valve controlling cylinder, A ₁for the transversal useful area area of rodless cavity, A ₂for the transversal useful area of rod chamber area, P ₁for rodless cavity pressure, P ₂for rod chamber pressure, M is the quality of load, and B is the viscous damping coefficient of piston and load, and K is the spring rate of load, F ₁for acting on any outer load force on piston, the mathematical model of wherein closing oar process is $\frac{Y\left(s\right)}{x_v}=\frac{\frac{k_q}{A_1}}{s(\frac{s^2}{w_h^2}+2\frac{{\mathrm{\&xi;}}_h}{w_h}s+1)}=\frac{263}{s(\frac{s^2}{{363.91}^2}+\frac{2\&times;0.1266}{363.91}s+1)},$ K _qfor the flow coefficient of servovalve, A ₁for the transversal useful area area of rodless cavity, w _hfor frequency of the natural hydraulic mode, ξ _hfor hydraulic damping ratio; The mathematical model opening oar process is $\frac{Y\left(s\right)}{x_v}=\frac{\frac{{k_q}^{\&prime;}}{A_2}}{s(\frac{s^2}{w_h^2}+2\frac{{\mathrm{\&xi;}}_h}{w_h}s+1)}=\frac{210.7}{s(\frac{s^2}{{337.228}^2}+\frac{2\&times;0.0721}{337.228}s+1)},$ Wherein for the flow coefficient of servovalve, A ₂for the transversal useful area of rod chamber area, w _hfor frequency of the natural hydraulic mode, ξ _hfor hydraulic damping ratio.

6. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterized in that: in step (5) by continuous time analog domain stability margin characterize the fragility of analog system, and in this, as the foundation of following digital system vulnerability analysis and design.

7. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterized in that: in step (6), introduce the conversion of bilinearity w territory, frequency response method is expanded to descreted-time control system, characterize number system amplitude versus frequency characte, and then obtain fragility quantizating index; Wherein bilinearity w converts z-plane unit circle internal maps to w Left half-plane; From s plane to z-plane and from z-plane to the synthetic effect of w plane transformation, be that w plane is similar with the survey region of s plane; Convert the distortion caused from s plane to z-plane, partly compensated by the conversion of z-plane to w plane; Even if the Bode Plot of the two exists difference at high band, also can confirm that w territory frequency characteristic is consistent with analog domain frequency characteristic, and its frequency range characterized meets discrete digital domain system vulnerability analysis demand.

8. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 1, it is characterized in that: interval by optimizer system stable phase angle nargin in step (7), by MATLAB instrument, obtain the optimum sampling range between a frequency of number system based on special algorithm.

9. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 8, is characterized in that: described algorithm steps is:

(a). according to sampling unit precision set traversal initial value, step-length, and input system analog domain open loop transfer function and experience sampling period maximum value;

(b). call the conversion of z territory, w territory transforming function transformation function completion system transfer function successively;

(c). utilize MATLAB Analysis of Magnitude-Frequency Characteristic function to obtain phase margin value and make comparisons with the interval upper and lower of optimum angle nargin;

(d). if current phase margin value and a upper traversing result phase margin interval that value is formed do not comprise the interval upper limit of optimum phase nargin or lower limit, then continue to travel through next time, circulation performs step (b), (c), until determine optimum sampling cycle upper and lower, algorithm so far completes.

10. wind energy conversion system hydraulic variable-pitch system sampling frequency system of selection as claimed in claim 9, is characterized in that: described algorithm steps (a) (b) (c) (d) is as follows based on the code of the algorithm of MATLAB function custom feature:

[T _max,T _min]＝sampling_period(num,den,T ₀,T _L,T _step)

fori＝T0:Tstep:Tmax

ifi＝＝T0Pm_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>45Tmin＝T；end

ifPm<60&&Pm_0>60Tmax＝T；end

Pm_0＝Pm；

ifTmax>0&&Tmin>0i＝T _L；endend。