CN108549239B - Method for deducing stable conditions of electro-hydraulic position servo system - Google Patents

Method for deducing stable conditions of electro-hydraulic position servo system Download PDF

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CN108549239B
CN108549239B CN201810468712.4A CN201810468712A CN108549239B CN 108549239 B CN108549239 B CN 108549239B CN 201810468712 A CN201810468712 A CN 201810468712A CN 108549239 B CN108549239 B CN 108549239B
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朱勇
汤胜楠
李伟
蒋小平
周岭
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Fluid Engineering Equipment Technology Of Jiangsu University Zhenjiang
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Abstract

The invention provides a method for deducing stable conditions of an electro-hydraulic position servo system, which comprises the following steps: (1) deducing a relational expression I between the load displacement disturbance quantity and the servo valve core displacement disturbance quantity according to the mathematical model and the model information transfer relation of the electro-hydraulic position servo system; (2) deducing a second relational expression between the displacement disturbance quantity of the valve core of the servo valve and the load displacement disturbance quantity according to a mathematical model of the displacement feedback and control part of the electro-hydraulic position servo system; (3) establishing a transfer block diagram of the disturbance quantity of the position closed-loop system according to the transfer relations respectively deduced from the relation formula I and the relation formula II; (4) judging the absolute stability of the position in closed-loop control by utilizing a Boff frequency criterion; (5) and deducing the absolute stable condition of the electro-hydraulic position servo system according to the Boff's theorem. The method can be based on the traditional transfer function, gets rid of the dilemma of reconstructing a judgment function, and can quickly and accurately deduce the absolute stable condition of the electro-hydraulic position servo system.

Description

Method for deducing stable conditions of electro-hydraulic position servo system
Technical Field
The invention relates to the technical field of hydraulic system stability judgment, in particular to a method for deducing a stability condition of an electro-hydraulic position servo system.
Background
The electro-hydraulic position servo system is a core control system of industrial equipment and national defense equipment, and the working reliability of the electro-hydraulic position servo system is the key for ensuring the high-precision, high-speed, continuous and stable operation of the equipment. In the industrial field, the hydraulic control system is widely used for an engineering machinery actuating mechanism control system, a steel rolling machinery hydraulic pressing system, a manipulator control system and the like; in the field of national defense, the system is widely applied to an automatic control system of a missile, a tracking system of a radar, a control surface control system of an airplane, a steering device of a naval vessel, a stabilizing device of a tank artillery and the like. Once the system is unstable, the system can cause shutdown or influence the product quality, and can lead the whole production line to be paralyzed to cause huge economic loss, even disaster accidents of machine damage and human death can occur to generate serious social influence. Therefore, the method is an urgent need for national economic development by exploring the stable conditions of the electro-hydraulic position servo system and further adopting real-time effective control measures.
At present, the study of the dynamic characteristics of the electro-hydraulic servo system by scholars at home and abroad is more, and most of the scholars are used to adopt the following two methods: firstly, after modeling through a transfer function mechanism, simulating by using simulation software such as MATLAB/Simulink and the like; secondly, simulation study is carried out on the dynamic characteristics of the system by using professional hydraulic system simulation software AMESim, EASY5, DSHplus, 20-Sim, Hopsan and the like. However, theoretical derivation of the stable condition of the electro-hydraulic position servo system is relatively rare. The system stability criterion based on the Lyapunov method is only a sufficient condition for judging the system stability, has certain conservative property, and is not easy to construct a required Lyapunov function in application. However, the electro-hydraulic position servo system is a typical nonlinear closed-loop control system with more influencing parameters, the dynamic characteristics are complex and variable, the factors influencing the stability are more, and if the electro-hydraulic position servo system is unstable, the vibration characteristics of the load of the electro-hydraulic position servo system are influenced. When the system is in some working states, nonlinear vibration is possibly induced, and if the stable condition of the system cannot be effectively grasped and effectively controlled in time, a serious vibration accident of the system is likely to happen. Therefore, it is necessary to find a method for deriving stable conditions of an electro-hydraulic position servo system.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for deducing the stable condition of an electro-hydraulic position servo system, and theoretical guidance is provided for deducing the stable condition of the electro-hydraulic position servo system.
The present invention achieves the above-described object by the following technical means.
The method for deducing the stable condition of the electro-hydraulic position servo system specifically comprises the following steps:
step (I): deducing a load displacement disturbance quantity delta x and a servo valve core displacement disturbance quantity delta x according to a mathematical model of the electro-hydraulic position servo system and an information transfer relation in the mathematical modelvThe relation between the two is one;
step (II): deducing the displacement disturbance quantity delta x of the valve core of the servo valve according to the mathematical models of the displacement feedback part and the control part of the electro-hydraulic position servo systemvA second relation with the load displacement disturbance quantity delta x;
step (three): establishing a transfer block diagram of the disturbance quantity of the position closed-loop system according to transfer functions respectively derived from the relation formula I and the relation formula II;
step (IV): judging the absolute stability of the position in closed-loop control by utilizing a Boff frequency criterion;
step (V): and deducing the absolute stable condition of the electro-hydraulic position servo system according to the Boff's theorem.
Further, the load displacement disturbance quantity Δ x and the spool displacement disturbance quantity Δ x of the servo valve in the step (one)vThe relation between the two is as follows:
Figure BDA0001662785400000021
in the formula,. DELTA.xvIs a valve core displacement xvThe amount of disturbance at the working point a; Δ x is the disturbance amount of the piston rod displacement at the working point A; kqIs the flow gain; kcIs the flow-pressure coefficient; kceAs a total flow-pressure coefficient, Kce＝Cip+Kc；ApIs the effective working area of the piston; v0To control the initial volume of the chamber βeThe volume elastic modulus of the oil liquid; m is1Is the equivalent total mass of the load moving part; c. C1Is an equivalent linear damping coefficient; k is a radical of1Is an equivalent linear stiffness coefficient; s is the laplace operator.
Further, the valve core displacement disturbance quantity delta x of the servo valve in the step (II)vRelation between load displacement disturbance quantity delta xThe second step is that:
Figure BDA0001662785400000022
in the formula, KpIs the controller proportionality coefficient; t isiIs an integration time constant; t isdIs a differential time constant; kaThe amplification factor of the servo amplifier; ksvThe amplification factor of the displacement of the valve core to the input current is obtained; omegasvξ being the natural angular frequency of the servo valvesvIs the damping coefficient of the servo valve; kxThe amplification factor of the displacement sensor; t isxIs the time constant of the displacement sensor.
Further, the step (iv) is specifically:
order to
Figure BDA0001662785400000031
At transfer function G1In(s), let s be i ω, frequency characteristics are obtained:
G1(iω)＝Re1(ω)+iIm1(ω)
g is to be1Substitution of expression of(s) into G1(i ω) to obtain real frequency characteristic Re1(ω) and imaginary frequency characteristics Im1(ω)：
Figure BDA0001662785400000032
Figure BDA0001662785400000033
Defining a modified frequency characteristic
Figure BDA0001662785400000034
Expression (c):
Figure BDA0001662785400000035
X1(ω)＝Re1(ω),Y1(ω)＝ωIm1(ω)
then the real frequency characteristic Re1Omega, virtual frequency characteristics Im1(omega) and correcting frequency characteristics
Figure BDA0001662785400000036
The corrected real frequency characteristic X can be obtained1(omega) and the corrected virtual frequency characteristic Y1(ω)：
Figure BDA0001662785400000037
Figure BDA0001662785400000038
Correcting frequency characteristics according to the Bowf frequency criterion
Figure BDA0001662785400000039
The intersection point of the curve and the real axis is the critical point of the Boff frequency criterion, and the coordinate is
Figure BDA00016627854000000310
Using modified real frequency characteristic X1(omega) and the corrected virtual frequency characteristic Y1(ω) the abscissa value of the critical point can be found:
Figure BDA0001662785400000041
then, from the definition of the boff straight line, it can be known that:
Figure BDA0001662785400000042
further, the absolute stability condition of the electro-hydraulic position servo system derived in the step (five) is as follows:
Figure BDA0001662785400000043
the invention has the beneficial effects that:
(1) the method has the advantages that the relation formula I and the relation formula II are derived by relying on the traditional derivation method of the transfer function, then the absolute stability of the position in closed-loop control is judged by utilizing the Bopfer frequency criterion, finally, the absolute stability condition of the electro-hydraulic position servo system can be rapidly and accurately derived according to the Bopfer theorem, and the method has high application value in solving the problems of dynamic instability and inhibition of the electro-hydraulic position servo system from the source.
(2) The invention utilizes the Boff frequency criterion to get rid of the dilemma that the stability criterion of the position closed-loop control system needs to reconstruct the judgment function in the prior art.
Drawings
FIG. 1 is a flow chart of a method for deriving a stable condition of an electro-hydraulic position servo system according to the present invention.
FIG. 2 is a block diagram illustrating the transfer of disturbance in a position closed loop system according to an embodiment of the present invention;
FIG. 3 shows a position closed loop system nonlinear characteristic curve and a Bowfish straight line l according to an embodiment of the present invention1Wherein (a) represents an absolutely stable system and (b) represents an unstable system.
Detailed Description
The invention will be further described with reference to the following figures and specific examples, but the scope of the invention is not limited thereto.
As shown in fig. 1, the method for deriving the stable condition of the electro-hydraulic position servo system according to the present invention comprises the following specific steps:
step (I): deducing a load displacement disturbance quantity delta x and a servo valve core displacement disturbance quantity delta x according to a mathematical model of the electro-hydraulic position servo system and an information transfer relation in the mathematical modelvThe relation between the two is as follows:
Figure BDA0001662785400000044
in the formula,. DELTA.xvIs a valve core displacement xvThe amount of disturbance at the working point a; Δ x is the disturbance of the piston rod displacement at the working point A；KqIs the flow gain; kcIs the flow-pressure coefficient; kceAs a total flow-pressure coefficient, Kce＝Cip+Kc；ApIs the effective working area of the piston; v0To control the initial volume of the chamber βeThe volume elastic modulus of the oil liquid; m is1Is the equivalent total mass of the load moving part; c. C1Is an equivalent linear damping coefficient; k is a radical of1Is an equivalent linear stiffness coefficient; s is the laplace operator.
Order to
Figure BDA0001662785400000051
Further, there are:
Figure BDA0001662785400000052
in the formula, CdIs the valve port flow coefficient; w is the valve port area gradient; x is the number ofvDisplacement of the main valve core; rho is the hydraulic oil density; p is a radical ofsIs the oil supply pressure; p is a radical oftIs the return oil pressure; p is a radical ofLThe working pressure of the rodless cavity of the hydraulic cylinder is adopted.
Then, as can be seen from equations (1), (2) and (3), the load displacement disturbance Δ x and the spool displacement disturbance Δ x of the servo valvevThe information relationship between them is defined by a transfer function G1(s) and non-linear mathematical expression KqAnd (5) transferring.
Step (II): according to the mathematical models of the displacement feedback part and the control part of the electro-hydraulic position servo system, the displacement disturbance quantity delta x of the valve core of the servo valve can be deducedvAnd the load displacement disturbance amount deltax are expressed by the following relation:
Figure BDA0001662785400000053
in the formula: kpIs the controller proportionality coefficient; t isiIs an integration time constant; t isdIs a differential time constant; kaThe amplification factor of the servo amplifier; ksvIs a valve coreThe amplification factor of the displacement to the input current; omegasvξ being the natural angular frequency of the servo valvesvIs the damping coefficient of the servo valve; kxThe amplification factor of the displacement sensor; t isxIs the time constant of the displacement sensor.
Order to
Figure BDA0001662785400000061
Then, as can be seen from equations (4) and (5), the spool displacement disturbance Δ x of the servo valvevThe information relation between the load displacement disturbance quantity delta x is formed by a transfer function G2(s) transferring.
Step (three): transfer function G derived from relational expression one and relational expression two respectively1(s)、KqAnd G2(s) establishing a transfer diagram of disturbance quantity of the position closed-loop system, as shown in FIG. 2.
And judging the absolute stability of the position in closed-loop control by utilizing a Boff frequency criterion. For this purpose, the transfer function G is1In(s), let s be i ω, frequency characteristics are obtained:
G1(iω)＝Re1(ω)+iIm1(ω) (6)
g is to be1Expression (2) of(s) is substituted for expression (6), and the real-frequency characteristic and the imaginary-frequency characteristic can be obtained:
Figure BDA0001662785400000062
Figure BDA0001662785400000063
defining a modified frequency characteristic
Figure BDA0001662785400000064
Expression (c):
Figure BDA0001662785400000065
X1(ω)＝Re1(ω),Y1(ω)＝ωIm1(ω) (10)
then, from the equations (7), (8) and (10), the corrected real frequency characteristic X can be obtained1(omega) and the virtual frequency characteristic Y1(ω)：
Figure BDA0001662785400000066
Figure BDA0001662785400000071
Step (IV): correcting frequency characteristics according to the Bowf frequency criterion
Figure BDA0001662785400000072
The intersection point of the curve and the real axis is the critical point of the Boff frequency criterion, and the coordinate is
Figure BDA0001662785400000077
The abscissa value of the critical point can be obtained by using equations (11) and (12):
Figure BDA0001662785400000073
then the wave form straight line l1By definition of (a), it can be known that:
Figure BDA0001662785400000074
step (V): according to the Bov's theorem, if the position of the nonlinear characteristic function f of the closed-loop system1(Δe)＝G2(s)KqΔ e satisfies the following equation, the equilibrium point of the system is absolutely stable, namely:
Figure BDA0001662785400000075
from equation (15), it can be derived if the transfer function G is non-linear2(s)KqLocated past the originA slope of P1Straight line l of1Within the sector formed by the horizontal axis (as shown in fig. 3 a), the position closed loop system becomes globally asymptotically stable. Otherwise, if the transfer function G is non-linear2(s)KqIs beyond the straight line l1A sector shaped area with the horizontal axis (as shown in fig. 3 b), the position closed loop system is unstable, and when the system parameters change, complex nonlinear dynamic behavior is generated.
From the above analysis, the absolute stability condition of the electro-hydraulic position servo system can be deduced:
Figure BDA0001662785400000076
the present invention is not limited to the above-described embodiments, and any obvious improvements, substitutions or modifications can be made by those skilled in the art without departing from the spirit of the present invention.

Claims (1)

1. The method for deducing the stable condition of the electro-hydraulic position servo system is characterized by comprising the following steps:
step (I): deducing a load displacement disturbance quantity delta x and a servo valve core displacement disturbance quantity delta x according to a mathematical model of the electro-hydraulic position servo system and an information transfer relation in the mathematical modelvThe first relation between the first and the second relations is:
Figure FDA0002446401120000011
in the formula,. DELTA.xvIs a valve core displacement xvThe amount of disturbance at the working point a; Δ x is the disturbance amount of the piston rod displacement at the working point A; kqIs the flow gain; kcIs the flow-pressure coefficient; kceAs a total flow-pressure coefficient, Kce＝Cip+Kc；ApIs the effective working area of the piston; v0To control the initial volume of the chamber βeThe volume elastic modulus of the oil liquid; m is1Is the equivalent total mass of the load moving part; c. C1Is an equivalent linear damping coefficient; k is a radical of1Is an equivalent linear stiffness coefficient; s is a laplace operator;
step (II): deducing the displacement disturbance quantity delta x of the valve core of the servo valve according to the mathematical models of the displacement feedback part and the control part of the electro-hydraulic position servo systemvAnd the load displacement disturbance quantity delta x, wherein the second relation is as follows:
Figure FDA0002446401120000012
in the formula, KpIs the controller proportionality coefficient; t isiIs an integration time constant; t isdIs a differential time constant; kaThe amplification factor of the servo amplifier; ksvThe amplification factor of the displacement of the valve core to the input current is obtained; omegasvξ being the natural angular frequency of the servo valvesvIs the damping coefficient of the servo valve; kxThe amplification factor of the displacement sensor; t isxIs the time constant of the displacement sensor;
step (three): establishing a transfer block diagram of the disturbance quantity of the position closed-loop system according to transfer functions respectively derived from the relation formula I and the relation formula II;
step (IV): the method comprises the following steps of judging absolute stability in position closed-loop control by utilizing a Boff frequency criterion, specifically:
order to
Figure FDA0002446401120000013
At transfer function G1In(s), let s be i ω, frequency characteristics are obtained:
G1(iω)＝Re1(ω)+iIm1(ω)
g is to be1Substitution of expression of(s) into G1(i ω) to obtain real frequency characteristic Re1(ω) and imaginary frequency characteristics Im1(ω)：
Figure FDA0002446401120000021
Figure FDA0002446401120000022
Defining a modified frequency characteristic
Figure FDA0002446401120000023
Expression (c):
Figure FDA0002446401120000024
X1(ω)＝Re1(ω),Y1(ω)＝ωIm1(ω)
then the real frequency characteristic Re1Omega, virtual frequency characteristics Im1(omega) and correcting frequency characteristics
Figure FDA0002446401120000025
The corrected real frequency characteristic X can be obtained1(omega) and the corrected virtual frequency characteristic Y1(ω)：
Figure FDA0002446401120000026
Figure FDA0002446401120000027
Correcting frequency characteristics according to the Bowf frequency criterion
Figure FDA0002446401120000028
The intersection point of the curve and the real axis is the critical point of the Boff frequency criterion, and the coordinate is (-P)1 -10); using modified real frequency characteristic X1(omega) and the corrected virtual frequency characteristic Y1(ω) the abscissa value of the critical point can be found:
Figure FDA0002446401120000029
then, from the definition of the boff straight line, it can be known that:
Figure FDA00024464011200000210
step (V): according to the Boff's theorem, deriving the absolute stable condition of the electro-hydraulic position servo system, wherein the absolute stable condition is as follows:
Figure FDA0002446401120000031
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