CN112096696A - Self-adaptive inversion control method for pump-controlled asymmetric hydraulic position system - Google Patents

Self-adaptive inversion control method for pump-controlled asymmetric hydraulic position system Download PDF

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CN112096696A
CN112096696A CN202011068850.7A CN202011068850A CN112096696A CN 112096696 A CN112096696 A CN 112096696A CN 202011068850 A CN202011068850 A CN 202011068850A CN 112096696 A CN112096696 A CN 112096696A
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pump
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许文斌
曾乐
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Changsha Aeronautical Vocational and Technical College
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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Abstract

The invention discloses a self-adaptive inversion control method of a pump-controlled asymmetric hydraulic position system, which comprises the following steps: s1, establishing a system mathematical model of the pump control asymmetric hydraulic position system, and generating a system state space model; s2, for each state of the state space model
Figure DDA0002711515570000011
Respectively constructing Lyapunov functions, and respectively obtaining differential values corresponding to the Lyapunov functions by an inversion algorithm
Figure DDA0002711515570000012
S3, constructing Lyapunov function V for system uncertainty parametersλAccording to said
Figure DDA0002711515570000013
To obtain
Figure DDA0002711515570000014
Selecting a self-adaptive control law to obtain a boundary condition; and S4, when the system meets the boundary condition, the system position tracking precision is relatively higher. The invention aims at the uncertain parameters and the load disturbance of the system, utilizes the self-adaptive control to compensate the influence of the uncertain parameters on the system performance, and processes the load disturbance through the robust control, thereby improving the robustness of the system, and effectively improving the tracking precision of the system position under the load disturbance of different working conditions.

Description

Self-adaptive inversion control method for pump-controlled asymmetric hydraulic position system
Technical Field
The invention relates to the technical field of hydraulic control, in particular to a self-adaptive inversion control method for a pump control asymmetric hydraulic position system.
Background
The asymmetric hydraulic cylinder system has the advantages of large power-to-volume ratio, strong bearing capacity and the like, so the asymmetric hydraulic cylinder system is widely applied to industry, but higher requirements are provided for the stability and reliability control of the system due to strong nonlinearity of the system, uncertainty of parameters and change of load force under different working conditions. In order to solve the problems and improve the control precision and robustness of the system, scholars at home and abroad carry out a great deal of research and provide a plurality of control algorithms and control strategies: for example, in order to ensure that the system is bounded and reduce the tracking error of the system, adaptive control is proposed at present; in order to improve the control precision and robustness of the system, the robust control is researched; the model predictive control can effectively solve the overshoot problem of the pump control asymmetric hydraulic system and realize high-precision position control under multiple constraint conditions; aiming at the problem that the tracking error of the motion track and the pressure precision of a hydraulic drive piston is large, the fuzzy sliding mode control of a neural network is designed; the variable structure control can improve the position control precision of the system aiming at strong nonlinearity of the system; the sliding mode control can improve the robustness of the system to mismatching disturbance and uncertain parameters and improve the position tracking precision of the electro-hydraulic system. The control improves the system operation performance and the control precision to a certain extent, but lacks the consideration of uncertain parameters of the system, and the designed control algorithm is verified through the experiment of single working condition load, so that the position tracking precision of the hydraulic position system is to be further improved.
Disclosure of Invention
Technical problem to be solved
Based on the problems, the invention provides a self-adaptive inversion control method for a pump-controlled asymmetric hydraulic position system, which aims at system uncertainty parameters and load disturbance, utilizes self-adaptive control to compensate the influence of the uncertainty parameters on the system performance, processes the load disturbance through robust control, and improves the system robustness, thereby effectively improving the system position tracking precision under the load disturbance of different working conditions.
(II) technical scheme
Based on the technical problem, the invention provides a self-adaptive inversion control method for a pump-controlled asymmetric hydraulic position system, which comprises the following steps:
s1, establishing a system mathematical model of the pump control asymmetric hydraulic position system, and generating a system state space model:
Figure BDA0002711515550000021
wherein the content of the first and second substances,
Figure BDA0002711515550000022
β＝A1βe，
Figure BDA0002711515550000023
D＝ηKnDpeta is hydraulic pump efficiency, KnAs a motor speed gain factor, DpIs the volume displacement of the hydraulic pump, u is the control voltage, betaeIs the equivalent elastic modulus of oil, CiIs the coefficient of leakage in the cylinder, V01、V02The volumes of a rodless cavity and a rod cavity of the hydraulic cylinder when the hydraulic rod is positioned at the middle position are respectively A1、A2Areas of rodless and rod chambers, P, of the hydraulic cylinder1、P2Respectively the pressure of a rodless cavity and a rod cavity of the hydraulic cylinder, wherein m is equivalent mass, F is equivalent external load, and y is hydraulic rod displacement;
s2, for each subsystem of the state space model
Figure BDA0002711515550000031
Respectively constructing Lyapunov functions, respectively acquiring a virtual control signal of each subsystem through an inversion algorithm, and taking the virtual control signal as a tracking target of the next subsystem to obtain a differential value corresponding to the Lyapunov functions
Figure BDA0002711515550000032
S3, constructing Lyapunov function V for system uncertainty parametersλAccording to said
Figure BDA0002711515550000033
To obtain
Figure BDA0002711515550000034
Selecting a self-adaptive control law to obtain a boundary condition;
and S4, when the system meets the boundary condition, the system position tracking precision is relatively higher.
Further, the step S2 includes the following steps:
s2.1, for the first subsystem
Figure BDA0002711515550000035
Construction of Lyapuloff function V1Obtained by an inversion algorithm
Figure BDA0002711515550000036
Acquiring a virtual control signal of a first subsystem;
s2.2, for the second subsystem
Figure BDA0002711515550000037
Construction of Lyapuloff function V2The virtual control signal of the first subsystem is used as the tracking target of the second subsystem, and the tracking target is obtained by an inversion algorithm
Figure BDA0002711515550000038
Acquiring a virtual control signal of a second subsystem;
s2.3, because h (x) is more than or equal to 0,
Figure BDA0002711515550000039
for the third subsystem
Figure BDA00027115155500000310
Construction of Lyapuloff function V3The virtual control signal of the second subsystem is used as the heel of the third subsystemThe trace object is obtained by inversion algorithm
Figure BDA00027115155500000311
And acquiring a system control signal.
Further, the inversion algorithm in steps S2.1 and S2.2 is obtained according to a state error and a virtual control signal, where the state error includes:
e1＝x1-x1d，e2＝x2-x2d，e3＝x3-x3d；
the virtual control signal includes:
Figure BDA0002711515550000041
Figure BDA0002711515550000042
wherein x is1d、x2d、x3dAre respectively x1、x2、x3H ═ d |, > 0 is e2The boundary value of (1).
Further, in the step S2
Figure BDA0002711515550000043
Figure BDA0002711515550000044
Further, the step S2.3 is
Figure BDA0002711515550000045
Wherein the content of the first and second substances,
Figure BDA0002711515550000046
uncertainty parameter lambda1＝(V01+kAV02)·β，λ2＝(V02+kAV01)·βCi，
λ3＝(A1V02+kAV01A2)·β，λ4＝βA2·(A1-A2)，
λ5＝V01V02，λ6＝V02A1-V01A2。
Further, u is:
Figure BDA0002711515550000051
wherein u is1Adaptive control signals to compensate for system uncertainty parameters; u. of2Robust control signals for processing system load interference signals d (t); sign (·) is a sign function; k is a radical of3，k4Normal number, and k3>1，k4＞1，
Figure BDA0002711515550000052
Are each alphaf，αg，αhAn estimated value of.
Further, in the step S2
Figure BDA0002711515550000053
Wherein the content of the first and second substances,
Figure BDA0002711515550000054
respectively, corresponding errors.
Further, the step of S3
Figure BDA0002711515550000055
Wherein, Tf，Tg，ThA constant diagonal matrix is positively fixed.
Further, the adaptive control law in step S3 is
Figure BDA0002711515550000056
Wherein, Tf，Tg，ThA constant diagonal matrix is positively fixed.
Further, the boundary conditions in step S3 are:
if it is not
Figure BDA0002711515550000061
Then
Figure BDA0002711515550000062
If it is not
Figure BDA0002711515550000063
Then
Figure BDA0002711515550000064
Wherein alpha ishmin，αfminIs a system
Figure BDA0002711515550000065
Minimum boundary value, alpha, presenthmin，αfminIs greater than 0, and alphaf＞αfmin，αh＞αhmin。
(III) advantageous effects
The technical scheme of the invention has the following advantages:
(1) the invention combines an improved inversion algorithm with a special self-adaptive law to compensate the parameter uncertainty and load disturbance existing in the pump control asymmetric hydraulic position; an improved inversion control is designed by establishing a mathematical model of a pump control asymmetric hydraulic position system, and a virtual control signal of a previous subsystem is used as a tracking target of a next subsystem; adapting to uncertainties in the hydraulic system using a special Lyapunov function for the uncertainty parameter;
(2) the input signal of the system controller in the invention consists of an adaptive control signal for compensating the uncertainty parameter of the system and a simple robust control signal, and the robustness of load disturbance is ensured by selecting a proper adaptive control law and boundary conditions, so that the system position tracking precision is effectively improved under the load disturbance of different working conditions.
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The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are illustrative and not to be construed as limiting the invention in any way, and in which:
FIG. 1 is a schematic flow chart of an adaptive inversion control method for a pump-controlled asymmetric hydraulic position system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a pump-controlled electro-hydraulic system according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a test of a pump-controlled electro-hydraulic system according to an embodiment of the present invention;
fig. 4 is a displacement response graph of the system when the load force F is 0kN according to the embodiment of the present invention;
FIG. 5 is an adaptive inversion controller input signal u for an embodiment of the present invention with a load force F of 0 kN;
fig. 6 is a simulated load signal for a load force F of 10kN according to an embodiment of the present invention;
FIG. 7 is a graph of the displacement response of the system at a load force F of 10kN according to an embodiment of the present invention;
FIG. 8 is a diagram of an adaptive inversion controller input signal u for a system with a load force F of 10kN according to an embodiment of the present invention;
FIG. 9 is a simulated load signal for a variable load condition in accordance with an embodiment of the present invention;
FIG. 10 is a displacement response of the system under varying load conditions in accordance with an embodiment of the present invention;
in the figure: 1: a controller; 2: a server; 3: a servo motor; 4: a quantitative hydraulic pump; 5: an overflow valve; 6: a proportional directional valve; 7: a rod cavity pressure sensor; 8: a rodless cavity pressure sensor; 9: a hydraulic lever; 10: and a hydraulic rod displacement sensor.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
The embodiment of the invention provides a self-adaptive inversion control method of a pump-controlled asymmetric hydraulic position system, which comprises the following steps as shown in figure 1:
s1, establishing a system mathematical model of the pump control asymmetric hydraulic position system, and generating a system state space model;
the pump control electro-hydraulic system schematic diagram is shown in fig. 2, and comprises a quantitative hydraulic pump 4 and an overflow valve 5 which are communicated with an oil tank, wherein an oil inlet of a proportional reversing valve 6 is connected with an oil inlet of a rodless cavity of a hydraulic cylinder, the oil tank is connected with an oil return port of a rod cavity of the hydraulic cylinder through an oil return port of the proportional reversing valve 6, the quantitative hydraulic pump 4 is sequentially connected with a servo motor 3 and a servo 2, a hydraulic rod 9 is displaced under the action of hydraulic pushing and load disturbance, and a controller 1 inputs data collected by a rodless cavity pressure sensor 8, a rod cavity pressure sensor 7 and a hydraulic rod displacement sensor 10 and outputs and controls the servo 2 and the proportional reversing valve 6. In the figure A1、A2Areas of rodless and rod chambers, P, of the hydraulic cylinder1、P2Pressure, V, of rodless and rodless chambers of the hydraulic cylinder, respectively1、V2Respectively, the volume of the rodless cavity and the rod cavity of the hydraulic cylinder, Q1、Q2Respectively the rodless cavity oil inlet flow and the rod cavity oil inlet flow of the hydraulic cylinder, Q is the output flow of the hydraulic pump, PsFor delivery of pressure, P, from a hydraulic pumptThe equivalent mass of m, the equivalent external load of F and the displacement of y hydraulic rod are the return pressure of the system.
Neglecting the elastic deformation of the system and the change of the oil compression volume, the force balance equation of the hydraulic rod is
Figure BDA0002711515550000081
Neglecting the leakage of the hydraulic cylinder, the continuous flow equation of the hydraulic cylinder is
Figure BDA0002711515550000082
Figure BDA0002711515550000083
In the formula: v01、V02The volumes of a rodless cavity and a rod cavity of the hydraulic cylinder are respectively when the hydraulic rod is positioned at the middle position; beta is aeThe equivalent elastic modulus of oil liquid; ciCoefficient of leakage in the hydraulic cylinder.
Assuming no pressure loss in the operation process of the system, in order to simplify the calculation, the oil inlet quantity Q of two cavities of the hydraulic cylinder is taken when the piston rod extends out and retracts1＝Q2Q, wherein Q is the output flow of the hydraulic pump, the system load flow equation is
Q1＝Q2＝Q＝ηKnDpu (4)
In the formula: η hydraulic pump efficiency; knMotor speed gain factor; dpThe volume displacement of the hydraulic pump; u controls the voltage.
When the initial working point is selected at the middle position of the hydraulic cylinder, selecting a state variable x, and defining:
Figure BDA0002711515550000091
the scheme emphasizes the consideration of implementing control on the influence of external load change on the system position, and selects x to simplify system analysis1Indicating hydraulic rod displacement, x2Indicating the speed of movement of the hydraulic ram, x3Representing the hydraulic action acceleration of the hydraulic rod;
the system state space model obtained from equations (1) - (5) is
Figure BDA0002711515550000092
In the formula:
Figure BDA0002711515550000093
β＝A1βe；
Figure BDA0002711515550000094
D＝ηKnDp。
in order to improve the tracking precision and robustness of the system position, a self-adaptive inversion control strategy is designed. Let x1d、x2d、x3dAre respectively x1、x2、x3The adaptive inversion control strategy firstly uses an inversion algorithm to construct a differential value of a Lyapunov function of each state of the system,
s2, for each subsystem of the state space model
Figure BDA0002711515550000095
Respectively constructing Lyapunov functions, respectively acquiring a virtual control signal of each subsystem through an inversion algorithm, and taking the virtual control signal as a tracking target of the next subsystem to obtain a differential value corresponding to the Lyapunov functions
Figure BDA0002711515550000101
S2.1, for the first subsystem
Figure BDA0002711515550000102
Construction of Lyapuloff function V1Obtained by an inversion algorithm
Figure BDA0002711515550000103
Acquiring a virtual control signal of a first subsystem;
Figure BDA0002711515550000104
defining the state error:
e1＝x1-x1d (8)
then there is
Figure BDA0002711515550000105
-taking a virtual control signal for the first subsystem (9):
Figure BDA0002711515550000106
defining the state error:
e2＝x2-x2d (11)
then, the following equations (9) to (11) can be obtained:
Figure BDA0002711515550000107
can be differentiated by equation (7)
Figure BDA0002711515550000108
From the equation (12), when the state error e2Convergence to 0, state error e1Converging to 0.
S2.2, for the second subsystem
Figure BDA0002711515550000109
Construction of Lyapuloff function V2The virtual control signal of the first subsystem is used as the tracking target of the second subsystem, and the tracking target is obtained by an inversion algorithm
Figure BDA00027115155500001010
Acquiring a virtual control signal of a second subsystem;
Figure BDA00027115155500001011
by differentiating the equation (11) and using the virtual control signal of the first subsystem as the tracking target of the second subsystem, the following can be obtained:
Figure BDA0002711515550000111
-taking a virtual control signal for the second subsystem (14):
Figure BDA0002711515550000112
in the formula: h ═ d |; > 0 is e2The boundary value of (1).
Defining the state error:
Figure BDA0002711515550000113
the differential to equation (13) can be obtained:
Figure BDA0002711515550000114
formula (17) indicates that provided e3Small enough, then e2Converging on the boundary value.
S2.3, because h (x) is more than or equal to 0,
Figure BDA0002711515550000115
for the third subsystem
Figure BDA0002711515550000116
Construction of Lyapuloff function V3The virtual control signal of the second subsystem is used as the tracking target of the third subsystem, and the tracking target is obtained by an inversion algorithm
Figure BDA0002711515550000117
Acquiring a system control signal;
Figure BDA0002711515550000118
in the formula:
Figure BDA0002711515550000119
defining:
f(x)＝(V02+kAV01)·βD
g(x)＝-(V02+kAV01)·βCi·(P1-P2)
-(A1V02+kAV01A2)·βx2
+βA2·(A1-A2)·x1x2
in formula (6)
Figure BDA0002711515550000121
Can be expressed as:
Figure BDA0002711515550000122
defining: λ ═ λ1，λ2，λ3，λ4，λ5，λ6]TIs a system uncertainty parameter vector.
Wherein:
λ1＝(V02+kAV01)·β；λ2＝(V02+kAV01)·βCi；
λ3＝(A1V02+kAV01A2)·β；λ4＝βA2·(A1-A2)；
λ5＝V01V02；λ6＝V02A1-V01A2；
then f (x), g (x), h (x) can be simplified to
Figure BDA0002711515550000123
The differential of equation (18) can be obtained:
Figure BDA0002711515550000124
in the formula
Figure BDA0002711515550000125
The differentiation of equation (15) is used to obtain the virtual control signal of the second subsystem as the tracking target of the third subsystem:
Figure BDA0002711515550000126
further simplifying the formula, define:
Figure BDA0002711515550000127
Figure BDA0002711515550000131
the following equations (22) and (23) can be obtained:
Figure BDA0002711515550000132
definition of
Figure BDA0002711515550000133
Are each alphaf，αg，αhAn estimated value of;
Figure BDA0002711515550000134
Figure BDA0002711515550000135
for the respective error, the system controller input u is designed as follows:
Figure BDA0002711515550000136
in the formula: u. of1Adaptive control signals to compensate for system uncertainty parameters; u. of2Robust control signals for processing system load interference signals d (t); sign (·) is a sign function; k is a radical of3，k4Normal number, and k3>1，k4＞1。
The following equations (21) to (25) can be obtained:
Figure BDA0002711515550000137
s3, constructing Lyapunov function V for system uncertainty parametersλAccording to said
Figure BDA0002711515550000138
To obtain
Figure BDA0002711515550000139
Selecting a self-adaptive control law to obtain a boundary condition;
Figure BDA0002711515550000141
in the formula: t isf，Tg，ThA constant diagonal matrix is positively fixed.
The differential to equation (27) can be obtained:
Figure BDA0002711515550000142
selecting an adaptive control law as
Figure BDA0002711515550000143
Equation (29) ensures that the following inequality holds:
Figure BDA0002711515550000144
there is a minimum boundary value alpha for the system (19)hmin，αfminIs greater than 0, and alphaf＞αfmin，αh＞αhmin。
For inequality (30), the boundary condition is selected:
if it is not
Figure BDA0002711515550000151
Then
Figure BDA0002711515550000152
If it is not
Figure BDA0002711515550000153
Then
Figure BDA0002711515550000154
And S4, when the system meets the boundary condition, the system position tracking precision is relatively higher.
The scheme divides the system into three subsystems, and gradually obtains the tracking target of the next subsystem from the previous subsystem through an inversion algorithm, namely the boundary condition of the last subsystem is also the boundary condition of the whole system.
The experiment was carried out as shown in the experimental schematic diagram of fig. 3, with the left hydraulic system simulating the drive system and the right hydraulic system simulating the external load, providing the load force.
The hydraulic system parameter settings are shown in table 1.
TABLE 1 Hydraulic System parameter values
Figure BDA0002711515550000155
The control parameters are set as follows:
H＝2.5，＝0.4，k1＝10，k3＝4，k4＝5，
Tf＝10-1，Tg＝diag([0 10 10-4]T)，Th＝diag([1 10-2 0]T),
assuming the expected values of the hydraulic rod displacement tracking signal are: x is the number of1d＝100sin(0.1πt)mm,
Fig. 4 and 5 show the displacement response of the system and the adaptive inversion controller input signal u when the load force F is 0kN, respectively, and it can be seen from fig. 4 that the tracking error of the system is ± 0.02 mm; it can be seen from fig. 5 that the control input signal is smooth and the system operates stably.
Fig. 6, 7, and 8 show the simulated load signal, the displacement response of the system, and the adaptive inversion controller input signal u, respectively, when the load force F is 10kN, and the load signal, i.e., the load force, as can be seen from fig. 7, the system has a tracking error of ± 0.05 mm; it can be seen from fig. 8 that the control input signal is smooth and the system operates stably.
Fig. 9 and 10 show the simulated load signal and the displacement response of the system in the case of variable load, respectively, and it can be seen from fig. 10 that the system has a tracking error of ± 0.05 mm.
Therefore, the experimental result proves that the proposed control strategy can obtain better position tracking and robustness, and the system position tracking precision reaches +/-0.05 mm under the load disturbance of different working conditions.
In summary, the self-adaptive inversion control method for the pump-controlled asymmetric hydraulic position system has the following advantages:
(1) the invention combines an improved inversion algorithm with a special self-adaptive law to compensate the parameter uncertainty and load disturbance existing in the pump control asymmetric hydraulic position; an improved inversion control is designed by establishing a mathematical model of a pump control asymmetric hydraulic position system, and a virtual control signal of a previous subsystem is used as a tracking target of a next subsystem; adapting to uncertainties in the hydraulic system using a special Lyapunov function for the uncertainty parameter;
(2) the input signal of the system controller in the invention consists of an adaptive control signal for compensating the uncertainty parameter of the system and a simple robust control signal, and the robustness of load disturbance is ensured by selecting a proper adaptive control law and boundary conditions, so that the system position tracking precision is effectively improved under the load disturbance of different working conditions.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations fall within the scope defined by the appended claims.

Claims (10)

1. A self-adaptive inversion control method for a pump-controlled asymmetric hydraulic position system is characterized by comprising the following steps:
s1, establishing a system mathematical model of the pump control asymmetric hydraulic position system, and generating a system state space model:
Figure FDA0002711515540000011
wherein the content of the first and second substances,
Figure FDA0002711515540000012
β＝A1βe，
Figure FDA0002711515540000013
D＝ηKnDpeta is hydraulic pump efficiency, KnAs a motor speed gain factor, DpIs the volume displacement of the hydraulic pump, u is the control voltage, betaeIs the equivalent elastic modulus of oil, CiIs the coefficient of leakage in the cylinder, V01、V02The volumes of a rodless cavity and a rod cavity of the hydraulic cylinder when the hydraulic rod is positioned at the middle position are respectively A1、A2Areas of rodless and rod chambers, P, of the hydraulic cylinder1、P2Respectively a rodless cavity and a rod cavity of the hydraulic cylinderPressure, m is equivalent mass, F is equivalent external load, and y is hydraulic rod displacement;
s2, for each subsystem of the state space model
Figure FDA0002711515540000014
Respectively constructing Lyapunov functions, respectively acquiring a virtual control signal of each subsystem through an inversion algorithm, and taking the virtual control signal as a tracking target of the next subsystem to obtain a differential value corresponding to the Lyapunov functions
Figure FDA0002711515540000021
S3, constructing Lyapunov function V for system uncertainty parametersλAccording to said
Figure FDA0002711515540000022
To obtain
Figure FDA0002711515540000023
Selecting a self-adaptive control law to obtain a boundary condition;
and S4, when the system meets the boundary condition, the system position tracking precision is relatively higher.
2. The adaptive inversion control method for the pump-controlled asymmetric hydraulic position system according to claim 1, wherein the step S2 comprises the following steps:
s2.1, for the first subsystem
Figure FDA0002711515540000024
Construction of Lyapuloff function V1Obtained by an inversion algorithm
Figure FDA0002711515540000025
Acquiring a virtual control signal of a first subsystem;
s2.2, for the second subsystem
Figure FDA0002711515540000026
Construction of Lyapuloff function V2The virtual control signal of the first subsystem is used as the tracking target of the second subsystem, and the tracking target is obtained by an inversion algorithm
Figure FDA0002711515540000027
Acquiring a virtual control signal of a second subsystem;
s2.3, because h (x) is more than or equal to 0,
Figure FDA0002711515540000028
for the third subsystem
Figure FDA0002711515540000029
Construction of Lyapuloff function V3The virtual control signal of the second subsystem is used as the tracking target of the third subsystem, and the tracking target is obtained by an inversion algorithm
Figure FDA00027115155400000210
And acquiring a system control signal.
3. The adaptive inversion control method of a pump-controlled asymmetric hydraulic position system according to claim 2, wherein the inversion algorithm in steps S2.1 and S2.2 is derived from a state error and a virtual control signal, the state error comprising:
e1＝x1-x1d，e2＝x2-x2d，e3＝x3-x3d；
the virtual control signal includes:
Figure FDA00027115155400000211
Figure FDA00027115155400000212
wherein x is1d、x2d、x3dAre respectively x1、x2、x3H ═ d |, > 0 is e2The boundary value of (1).
4. The adaptive inversion control method for the pump-controlled asymmetric hydraulic position system according to claim 3, wherein the step S2 is performed in step S2
Figure FDA0002711515540000031
Figure FDA0002711515540000032
5. The adaptive inversion control method for the pump-controlled asymmetric hydraulic position system according to claim 2, wherein the step S2.3 is performed by the adaptive inversion control method
Figure FDA0002711515540000033
Wherein the content of the first and second substances,
Figure FDA0002711515540000034
uncertainty parameter lambda1＝(V01+kAV02)·β，λ2＝(V02+kAV01)·βCi，
λ3＝(A1V02+kAV01A2)·β，λ4＝βA2·(A1-A2)，
λ5＝V01V02，λ6＝V02A1-V01A2。
6. The pump-controlled asymmetric hydraulic position system adaptive inversion control method according to claim 5, wherein u is:
Figure FDA0002711515540000035
wherein u is1Adaptive control signals to compensate for system uncertainty parameters; u. of2Robust control signals for processing system load interference signals d (t); sign (·) is a sign function; k is a radical of3，k4Normal number, and k3>1，k4＞1，
Figure FDA0002711515540000041
Are each alphaf，αg，αhAn estimated value of.
7. The adaptive inversion control method for the pump-controlled asymmetric hydraulic position system according to claim 6, wherein the step S2 is performed in
Figure FDA0002711515540000042
Wherein the content of the first and second substances,
Figure FDA0002711515540000043
respectively, corresponding errors.
8. The adaptive inversion control method for the pump-controlled asymmetric hydraulic position system according to claim 1, wherein the step S3 is performed in step S3
Figure FDA0002711515540000044
Wherein, Tf，Tg，ThA constant diagonal matrix is positively fixed.
9. The adaptive inversion control method for the pump-controlled asymmetric hydraulic position system according to claim 1, wherein the adaptive control law in step S3 is
Figure FDA0002711515540000045
Wherein, Tf，Tg，ThA constant diagonal matrix is positively fixed.
10. The adaptive inversion control method for the pump-controlled asymmetric hydraulic position system according to claim 1, wherein the boundary conditions in step S3 are as follows:
if it is not
Figure FDA0002711515540000046
Then
Figure FDA0002711515540000047
If it is not
Figure FDA0002711515540000051
Then
Figure FDA0002711515540000052
Wherein alpha ish min，αf minIs a system
Figure FDA0002711515540000053
Minimum boundary value, alpha, presenth min，αf minIs greater than 0, and alphaf＞αf min，αh＞αh min。
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