CN108549239A - Electro-hydraulic position servo system stable condition derivation method - Google Patents

Electro-hydraulic position servo system stable condition derivation method Download PDF

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CN108549239A
CN108549239A CN201810468712.4A CN201810468712A CN108549239A CN 108549239 A CN108549239 A CN 108549239A CN 201810468712 A CN201810468712 A CN 201810468712A CN 108549239 A CN108549239 A CN 108549239A
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electro
servo system
hydraulic position
relational expression
position servo
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CN108549239B (en
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朱勇
汤胜楠
李伟
蒋小平
周岭
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Jiangsu University
Zhenjiang Fluid Engineering Equipment Technology Research Institute of Jiangsu University
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Jiangsu University
Zhenjiang Fluid Engineering Equipment Technology Research Institute of Jiangsu University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The present invention provides electro-hydraulic position servo system stable condition derivation method, content includes：(1) according to electro-hydraulic position servo system mathematical model and model information transitive relation, the relational expression one between load displacement disturbance quantity and valve core of servo valve shift perturbation amount is derived；(2) it according to the mathematical model of electro-hydraulic position servo system Displacement Feedback and control section, derives valve core of servo valve shift perturbation amount and loads the relational expression two between displacement disturbance quantity；(3) transitive relation derived respectively according to relational expression one and relational expression two establishes the transmission block diagram of position loop system disturbance quantity；(4) Popov frequency criterion is utilized, judges absolute when position-force control；(5) according to Popov theorem, the absolute stability condition of electro-hydraulic position servo system is derived.The present invention can be to rely on traditional transmission function, broken away from the predicament for reconfiguring decision function, can quick and precisely derive the absolute stability condition of electro-hydraulic position servo system.

Description

Electro-hydraulic position servo system stable condition derivation method
Technical field
The present invention relates to hydraulic system judgement of stability technical field more particularly to electro-hydraulic position servo system stable conditions Derivation method.
Background technology
Electro-hydraulic position servo system is the core control system of industrial equipment and defence equipment, and the reliability of work is to protect Demonstrate,prove equipment high-precision, high speed, the key of continuous and steady operation.In industrial circle, it is widely used in engineering machinery actuating mechanism controls System, rolling machinery hydraulic press down system, manipulator control system etc.；In national defence, it is widely used in automatically controlling for guided missile The stabilising arrangement etc. of system, the tracking system of radar, the rudder surface control system of aircraft, the steering gear of naval vessels and tank gun. Unstability once occurs for the system, gently then causes to shut down or influence product quality, heavy then the entire production line will be made to paralyse, and causes huge Big economic loss, or even the disaster accident of fatal crass occurs, generate serious social influence.Thus, electro-hydraulic position is watched Dress system stable condition is explored, and then takes real-time effective control measure, is the urgent need of the national economic development.
Currently, domestic and foreign scholars are also more to the research of electrohydraulic servo system dynamic characteristic, and majority get used to using with Lower two methods：First, after transmission function modelling by mechanism, emulated with simulation softwares such as MATLAB/Simulink；The Two, it is special to system dynamic using Hydraulic System Simulation software AMESim, EASY5, DSHplus, 20-Sim, Hopsan of profession etc. Property carry out simulation study.But the theory deduction about electro-hydraulic position servo system stable condition is also more rarely seen.Based on Li Ya The system stability criterion of Pu Nuofu methods, the only adequate condition of judgement system stability have certain conservative, and It is not easy to construct required Lyapunov functions in.However, electro-hydraulic position servo system is that a kind of affecting parameters are more Typical non linear closed-loop control system, dynamic characteristic is complicated and changeable, and the factor for influencing its stability is more, must if unstability It will influence the vibration characteristics of its load.Non-Linear Vibration can be very likely induced when system is in certain working conditions, such as Fruit cannot effectively grasp its stable condition and effectively be controlled in time, will be likely to result in system and great shake occurs Dynamic accident.Therefore, there is an urgent need for explore a kind of electro-hydraulic position servo system stable condition derivation method.
Invention content
In response to the deficiencies in the existing technology, the present invention provides a kind of electro-hydraulic position servo system stable condition derivation sides Method, the derivation for electro-hydraulic position servo system stable condition provide theoretical direction.
The present invention achieves the above technical objects by the following technical means.
Electro-hydraulic position servo system stable condition derivation method, specifically comprises the following steps：
Step (1)：According to the information transfering relation in electro-hydraulic position servo system mathematical model and the mathematical model, Derive load displacement disturbance quantity Δ x and valve core of servo valve shift perturbation amount Δ xvBetween relational expression one；
Step (2)：According to the mathematical model of electro-hydraulic position servo system Displacement Feedback part and control section, derive Valve core of servo valve shift perturbation amount Δ xvWith the relational expression two between load displacement disturbance quantity Δ x；
Step (3)：According to the transmission function that relational expression one and relational expression two derive respectively, establishes position loop system and disturb The transmission block diagram of momentum；
Step (4)：Using Popov frequency criterion, absolute when position-force control is judged；
Step (5)：According to Popov theorem, the absolute stability condition of electro-hydraulic position servo system is derived.
Further, displacement disturbance quantity Δ x and valve core of servo valve shift perturbation amount Δ x is loaded described in step (1)vBetween Relational expression one be：
In formula, Δ xvFor spool displacement xvDisturbance quantity at the A of operating point；Δ x is piston rod displacement at the A of operating point Disturbance quantity；KqFor flow gain；KcFor flow-pressure coefficient；KceFor total flow-pressure coefficient, Kce=Cip+Kc；ApFor work It is plugged with effect work area；V0Chamber original volume in order to control；βeFor the bulk modulus of fluid；m1For load movement component etc. Imitate gross mass；c1For equivalent linear damping coefficient；k1For equivalent linear stiffness coefficient；S is Laplace operator.
Further, the amount Δ of valve core of servo valve shift perturbation described in step (2) xvBetween load displacement disturbance quantity Δ x Relational expression two be：
In formula, KpDevice proportionality coefficient in order to control；TiFor integration time constant；TdFor derivative time constant；KaAmplify for servo Device amplification coefficient；KsvIt is spool displacement to the amplification coefficient of input current；ωsvFor the natural angular frequency of servo valve；ξsvFor servo The damped coefficient of valve；KxFor the amplification coefficient of displacement sensor；TxFor the time constant of displacement sensor.
Further, the step (4) is specially：
It enables
In transmission function G1(s) in, s=i ω is enabled, frequency characteristic is obtained：
G1(i ω)=Re1(ω)+iIm1(ω)
By G1(s) expression formula substitutes into G1In (i ω), real frequency characteristic Re is obtained1(ω) and imaginary frequency characteristic Im1(ω)：
Define frequency of amendment characteristicExpression formula：
X1(ω)=Re1(ω),Y1(ω)=ω Im1(ω)
Then by real frequency characteristic Re1(ω), imaginary frequency characteristic Im1(ω) and frequency of amendment characteristicIt can obtain correcting real frequency Characteristic X1(ω) and correct imaginary frequency characteristic Y1(ω)：
According to Popov frequency criterion, frequency of amendment characteristicThe intersection point of curve and real axis is Popov frequency criterion Critical point, enable its coordinate beUtilize the real frequency characteristic X of amendment1(ω) and correct imaginary frequency characteristic Y1(ω), which can be acquired, to be faced The abscissa value of boundary's point：
Then by the definition of Popov straight line, it is known that：
Further, the absolute stability condition for the electro-hydraulic position servo system derived in the step (5) is：
The beneficial effects of the invention are as follows：
(1) present invention is to rely on to be deduced relational expression one and relational expression two with the derivation method of traditional transmission function, Then Popov frequency criterion is utilized, absolute when judging position-force control can be fast finally according to Popov theorem The fast absolute stability condition for accurately deriving electro-hydraulic position servo system, to solving electro-hydraulic position servo system power from source Learning unstability and inhibition problem has higher application value.
(2) present invention utilizes Popov frequency criterion, has broken away from position-force control system stability in the prior art and has sentenced According to the predicament for needing to reconfigure decision function.
Description of the drawings
Fig. 1 is the flow chart of electro-hydraulic position servo system stable condition derivation method of the present invention.
Fig. 2 is the transmission block diagram of the position loop system disturbance quantity of the embodiment of the present invention；
Fig. 3 is the position loop system Nonlinear Characteristic Curve and Popov straight line l of the embodiment of the present invention1Relationship, In (a) indicate absolute stability system, (b) indicate time-dependent system.
Specific implementation mode
Below in conjunction with the accompanying drawings and specific embodiment the present invention is further illustrated, but protection scope of the present invention is simultaneously It is without being limited thereto.
As shown in Figure 1, electro-hydraulic position servo system stable condition derivation method of the present invention, specific implementation step is such as Under：
Step (1)：According to the information transfering relation in electro-hydraulic position servo system mathematical model and the mathematical model, Derive load displacement disturbance quantity Δ x and valve core of servo valve shift perturbation amount Δ xvBetween relational expression one：
In formula, Δ xvFor spool displacement xvDisturbance quantity at the A of operating point；Δ x is piston rod displacement at the A of operating point Disturbance quantity；KqFor flow gain；KcFor flow-pressure coefficient；KceFor total flow-pressure coefficient, Kce=Cip+Kc；ApFor work It is plugged with effect work area；V0Chamber original volume in order to control；βeFor the bulk modulus of fluid；m1For load movement component etc. Imitate gross mass；c1For equivalent linear damping coefficient；k1For equivalent linear stiffness coefficient；S is Laplace operator.
It enables
Also, have：
In formula, CdFor valve port flow coefficient；W is valve port area gradient；xvFor main spool displacement；ρ is hydraulic oil density；ps For charge oil pressure；ptFor return pressure；pLFor hydraulic cylinder rodless cavity operating pressure.
Displacement disturbance quantity Δ x and valve core of servo valve shift perturbation are then loaded it can be seen from formula (1), formula (2) and formula (3) Measure Δ xvBetween information relationship by transmission function G1(s) and nonlinear mathematics expression formula KqIt transmits.
Step (2)：According to the mathematical model of electro-hydraulic position servo system Displacement Feedback part and control section, can derive Go out valve core of servo valve shift perturbation amount Δ xvWith the relational expression two between load displacement disturbance quantity Δ x：
In formula：KpDevice proportionality coefficient in order to control；TiFor integration time constant；TdFor derivative time constant；KaAmplify for servo Device amplification coefficient；KsvIt is spool displacement to the amplification coefficient of input current；ωsvFor the natural angular frequency of servo valve；ξsvFor servo The damped coefficient of valve；KxFor the amplification coefficient of displacement sensor；TxFor the time constant of displacement sensor.
It enables
The then valve core of servo valve shift perturbation amount Δ x it can be seen from formula (4) and formula (5)vWith load displacement disturbance quantity Δ x Between information relationship by transmission function G2(s) it transmits.
Step (3)：The transmission function G derived respectively according to relational expression one and relational expression two1(s)、KqAnd G2(s), it establishes The transmission block diagram of position loop system disturbance quantity, as shown in Figure 2.
Using Popov frequency criterion, absolute when position-force control is judged.For this purpose, in transmission function G1 (s) in, s=i ω is enabled, frequency characteristic is obtained：
G1(i ω)=Re1(ω)+iIm1(ω) (6)
By G1(s) expression formula (2) substitutes into formula (6), can obtain real frequency characteristic and imaginary frequency characteristic：
Define frequency of amendment characteristicExpression formula：
X1(ω)=Re1(ω),Y1(ω)=ω Im1(ω) (10)
Then by formula (7), formula (8) and formula (10), can obtain correcting real frequency characteristic X1(ω) and imaginary frequency characteristic Y1(ω)：
Step (4)：According to Popov frequency criterion, frequency of amendment characteristicThe intersection point of curve and real axis is wave wave The critical point of husband's frequency criterion, enables its coordinate beThe abscissa of critical point can be acquired using formula (11) and formula (12) Value：
Then by Popov straight line l1Definition, it is known that：
Step (5)：By Popov theorem it is found that if the nonlinear characteristic function f of position loop system1(Δ e)=G2 (s)KqΔ e meets following formula, then the equalization point absolute stability of system, that is, have：
It can be obtained by formula (15), if nonlinear transfer function G2(s)KqCharacteristic curve be located at origin slope be P1 Straight line l1In the sector region constituted with horizontal axis (as shown in Figure 3a), then position loop system asymptotically stable in the large.If conversely, Nonlinear transfer function G2(s)KqCharacteristic curve exceed straight line l1The sector region (as shown in Figure 3b) constituted with horizontal axis, then position It is unstable to set closed-loop system, at this time when system parameter variations, will produce complicated Nonlinear dynamic behaviors.
From the above analysis, the absolute stability condition of electro-hydraulic position servo system can be derived：
The embodiment is the preferred embodiments of the present invention, but present invention is not limited to the embodiments described above, not Away from the present invention substantive content in the case of, those skilled in the art can make it is any it is conspicuously improved, replace Or modification all belongs to the scope of protection of the present invention.

Claims (5)

1. electro-hydraulic position servo system stable condition derivation method, which is characterized in that specifically comprise the following steps：
Step (1)：According to the information transfering relation in electro-hydraulic position servo system mathematical model and the mathematical model, derive Go out to load displacement disturbance quantity Δ x and valve core of servo valve shift perturbation amount Δ xvBetween relational expression one；
Step (2)：According to the mathematical model of electro-hydraulic position servo system Displacement Feedback part and control section, servo is derived Valve core shift perturbation amount Δ xvWith the relational expression two between load displacement disturbance quantity Δ x；
Step (3)：According to the transmission function that relational expression one and relational expression two derive respectively, position loop system disturbance quantity is established Transmission block diagram；
Step (4)：Using Popov frequency criterion, absolute when position-force control is judged；
Step (5)：According to Popov theorem, the absolute stability condition of electro-hydraulic position servo system is derived.
2. electro-hydraulic position servo system stable condition derivation method according to claim 1, which is characterized in that step (1) Described in load displacement disturbance quantity Δ x and valve core of servo valve shift perturbation amount Δ xvBetween relational expression one be：
In formula, Δ xvFor spool displacement xvDisturbance quantity at the A of operating point；Δ x is disturbance of the piston rod displacement at the A of operating point Amount；KqFor flow gain；KcFor flow-pressure coefficient；KceFor total flow-pressure coefficient, Kce=Cip+Kc；ApHave for piston Imitate work area；V0Chamber original volume in order to control；βeFor the bulk modulus of fluid；m1For the equivalent total of load movement component Quality；c1For equivalent linear damping coefficient；k1For equivalent linear stiffness coefficient；S is Laplace operator.
3. electro-hydraulic position servo system stable condition derivation method according to claim 1, which is characterized in that step (2) Described in valve core of servo valve shift perturbation amount Δ xvIt is the relational expression two loaded between displacement disturbance quantity Δ x：
In formula, KpDevice proportionality coefficient in order to control；TiFor integration time constant；TdFor derivative time constant；KaIt is put for servo amplifier Big coefficient；KsvIt is spool displacement to the amplification coefficient of input current；ωsvFor the natural angular frequency of servo valve；ξsvFor servo valve Damped coefficient；KxFor the amplification coefficient of displacement sensor；TxFor the time constant of displacement sensor.
4. electro-hydraulic position servo system stable condition derivation method according to claim 1, which is characterized in that the step (4) it is specially：
It enables
In transmission function G1(s) in, s=i ω is enabled, frequency characteristic is obtained：
G1(i ω)=Re1(ω)+iIm1(ω)
By G1(s) expression formula substitutes into G1In (i ω), real frequency characteristic Re is obtained1(ω) and imaginary frequency characteristic Im1(ω)：
Define frequency of amendment characteristicExpression formula：
X1(ω)=Re1(ω),Y1(ω)=ω Im1(ω)
Then by real frequency characteristic Re1(ω), imaginary frequency characteristic Im1(ω) and frequency of amendment characteristicIt can obtain correcting real frequency characteristic X1(ω) and correct imaginary frequency characteristic Y1(ω)：
According to Popov frequency criterion, frequency of amendment characteristicThe intersection point of curve and real axis is facing for Popov frequency criterion Boundary's point, it is (- P to enable its coordinate1 -1,0)；Utilize the real frequency characteristic X of amendment1(ω) and correct imaginary frequency characteristic Y1(ω) can acquire critical point Abscissa value：
Then by the definition of Popov straight line, it is known that：
5. electro-hydraulic position servo system stable condition derivation method according to claim 1, which is characterized in that the step (5) the absolute stability condition for the electro-hydraulic position servo system derived in is：
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CN112213947A (en) * 2020-10-20 2021-01-12 西安工程大学 Modeling method based on LS-SVM electro-hydraulic position servo system
CN114483324A (en) * 2022-01-10 2022-05-13 江苏大学 Binary coding digital valve array regulated and controlled fuel metering valve and control method thereof

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CN111852992A (en) * 2020-07-24 2020-10-30 华北电力大学 Output feedback self-adaptive control method for hydraulic servo system
CN112213947A (en) * 2020-10-20 2021-01-12 西安工程大学 Modeling method based on LS-SVM electro-hydraulic position servo system
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