CN118192225A - Electrohydraulic proportional servo valve self-learning gain position axis control method - Google Patents
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Abstract
The invention discloses a self-learning gain position axis control method of an electrohydraulic proportional servo valve, which is based on a built gain self-learning mechanism, integrates a dynamic surface control idea and designs a nonlinear robust position axis control controller with self-learning gain. Aiming at the position axis control problem of the electro-hydraulic proportional servo valve, the invention not only can realize autonomous learning of system gain and simplify the complexity of actual gain adjustment, but also can avoid the problem of differential explosion in the traditional back-step control of the electro-hydraulic proportional servo valve axis control system, reduce the influence of measurement noise on control precision and realize high-precision tracking performance.
Description
Technical Field
The invention relates to the technical field of electromechanical servo control, in particular to a self-learning gain position axis control method (ALGRC) of an electrohydraulic proportional servo valve.
Background
The electrohydraulic proportional servo valve shaft control system has the important position in the fields of robots, heavy machinery, high-performance loading test equipment and the like by virtue of the characteristics of high power density, high force/torque output, quick dynamic response and the like. The electro-hydraulic proportional servo valve control system is a typical nonlinear system and comprises a plurality of nonlinear characteristics and modeling uncertainties. The nonlinear characteristics comprise input nonlinearity such as hysteresis, saturation and the like, flow pressure nonlinearity of a proportional servo valve, friction nonlinearity and the like, and the modeling uncertainty comprises parameter uncertainty and uncertainty nonlinearity, wherein the parameter uncertainty mainly comprises load quality, viscous friction coefficient of an actuator, leakage coefficient, servo valve flow gain, hydraulic oil elastic modulus and the like, and the uncertainty nonlinearity mainly comprises unmodeled friction dynamics, system high-order dynamics, external interference, unmodeled leakage and the like. When the electro-hydraulic proportional servo valve control system is developed to high precision and high frequency response, the nonlinear characteristic presented by the system has more remarkable influence on the system performance, and the controller designed by the nominal model of the system is unstable or reduced in order due to the existence of modeling uncertainty, so that the nonlinear characteristic and the modeling uncertainty of the electro-hydraulic proportional servo valve control system are important factors for limiting the improvement of the system performance. With the continuous progress of technical level in the industrial and national defense fields, the traditional controller based on the traditional linear theory design can not meet the high performance requirement of the system, so that a more advanced nonlinear control strategy must be researched aiming at the nonlinear characteristics in the electrohydraulic proportional servo valve control system.
Aiming at the nonlinear control problem of an electrohydraulic proportional servo valve control system, a plurality of methods are sequentially proposed. The self-adaptive control method is a very effective method for processing the problem of parameter uncertainty, can obtain the steady-state performance of asymptotic tracking, but is worry about uncertainty nonlinearity such as external load interference, and the like, when the uncertainty nonlinearity is overlarge, the system can be instable, and the actual electro-hydraulic proportional servo valve shaft control system has uncertainty nonlinearity, so the self-adaptive control method cannot obtain the control performance with high precision in practical application; as a robust control method, classical sliding mode control can effectively cope with any bounded modeling uncertainty and obtain steady-state performance of asymptotic tracking, but discontinuous controllers designed by classical sliding mode control easily cause flutter problems of a sliding mode surface, thereby deteriorating tracking performance of a system; in order to solve the problems of uncertainty and uncertainty nonlinearity of parameters at the same time, an adaptive robust control method is proposed, the control method can enable a system to obtain definite transient and steady-state performances under the condition that two modeling uncertainties exist at the same time, if high-precision tracking performance is to be obtained, a feedback gain is required to be improved to reduce tracking errors, and due to the existence of measurement noise, the gain is excessively high, so that high-gain feedback is often caused to cause buffeting of control input, further the control performance is deteriorated, and even instability of the system is caused.
Disclosure of Invention
The invention aims to provide the electrohydraulic proportional servo valve position axis control method with the advantages of gain self-learning, strong anti-interference capability and high tracking performance, which not only can realize autonomous learning of system gain and simplify the complexity of actual gain adjustment, but also can avoid the problem of differential explosion in the traditional backstepping control of the electrohydraulic proportional servo valve axis control system, reduce the influence of measurement noise on control precision and realize high-precision tracking performance.
The technical solution for realizing the purpose of the invention is as follows: an electrohydraulic proportional servo valve self-learning gain position axis control method comprises the following steps:
And step 1, establishing a mathematical model of the position shaft control system of the electro-hydraulic proportional servo valve, and switching to step 2.
Step 2, designing a nonlinear robust position shaft control controller with a gain self-learning mechanism based on a mathematical model of the electrohydraulic proportional servo valve position shaft control system, and turning to step 3.
And step 3, performing stability demonstration of the nonlinear robust position axis control controller by using a Lyapunov stability theory to obtain a result of asymptotically stable system tracking error.
Compared with the prior art, the invention has the remarkable advantages that: (1) Autonomous learning of system gain is realized, and complexity of actual gain adjustment is simplified; (2) The problem of differential explosion in the traditional back-step control of the electrohydraulic proportional servo valve control system is avoided, the influence of measurement noise on control precision is reduced, high-precision tracking performance is realized, and the effectiveness of the simulation result is verified.
Drawings
FIG. 1 is a schematic diagram of the self-learning gain position axis control method of the electro-hydraulic proportional servo valve.
FIG. 2 is a schematic diagram of the electro-hydraulic proportional servo valve control system of the present invention.
FIG. 3 is a graph of the tracking process of the system output versus desired command under the influence of ALGRC controller designed in accordance with this invention.
Fig. 4 is a graph of tracking error of the system over time under the influence of ALGRC controller designed in accordance with the present invention.
FIG. 5 is a graph of tracking error versus system under the influence of ALGRC and conventional PID controllers designed in accordance with the present invention.
Fig. 6 is a graph of the control inputs of the system under the influence of ALGRC controller designed according to this invention.
Detailed Description
The invention will be described in further detail with reference to the accompanying drawings and specific examples.
Referring to fig. 1 and 2, the self-learning gain position axis control method of the electro-hydraulic proportional servo valve comprises the following steps:
Step 1, establishing a mathematical model of an electrohydraulic proportional servo valve position shaft control system, which comprises the following specific steps:
And 1-1, the position shaft control system of the electro-hydraulic proportional servo valve is applied to linear motion of large industrial heavy-duty mechanical equipment, wherein a load is fixedly connected with a piston rod on a hydraulic cylinder, and the electro-hydraulic proportional servo valve controls the piston rod on the hydraulic cylinder to move, so that the load is driven to move.
According to Newton's second law, the force balance equation of the electrohydraulic proportional servo valve position shaft control system is:
（1），
in the formula (1), m represents the mass of the load, y represents the displacement of the piston rod of the hydraulic cylinder, Representing the speed of the piston rod of the hydraulic cylinder,/>The acceleration of a piston rod of the hydraulic cylinder is represented, A represents the effective acting area of the piston of the hydraulic cylinder, P 1 represents the oil pressure of an oil inlet cavity of the hydraulic cylinder, P 2 represents the oil pressure of an oil outlet cavity of the hydraulic cylinder, B represents the viscous damping coefficient of the hydraulic cylinder,/>Representing the mechanical unmodeled disturbance of the system, t representing time.
Then formula (1) is rewritten as:
（2），
In the electrohydraulic proportional servo valve position shaft control system, the oil leakage of the oil cylinder is ignored, and then the pressure dynamic equation is as follows:
（3），
In the formula (3), the amino acid sequence of the compound, Representing the effective elastic modulus of oilThe leakage coefficient in the hydraulic cylinder is represented, and the oil pressure difference between oil inlet and outlet cavities at two sides of the oil cylinder/>Control volume of oil inlet chamber/>Control volume of oil outlet chamberV 01 represents the initial volume of the oil inlet chamber, V 02 represents the initial volume of the oil inlet chamber, Q 1 represents the flow rate of the oil inlet chamber, Q 2 represents the flow rate of the oil chamber,/>Representation/>Unembossed interference of,/>Representation/>Unembossed interference of,/>Representation/>First derivative of,/>Representation/>Is a first derivative of (a).
Q 1、Q2 has the following relation with the valve core displacement x v of the electro-hydraulic proportional servo valve respectively:
（4），
Wherein, electrohydraulic proportional servo valve coefficient ，/>Representing the flow coefficient of the electrohydraulic proportional servo valve,/>Represents the area gradient of a valve core of the electrohydraulic proportional servo valve,/>Representing oil density,/>Representing the oil supply pressure,/>Indicating the return pressure,/>Representing intermediate variables/>Is defined as:
（5），
Ignoring the dynamic state of the valve core of the electrohydraulic proportional servo valve, assuming that the control input u acting on the valve core and the valve core displacement x v are in proportional relation, namely meeting Wherein/>The expression voltage-spool displacement gain coefficient is thus rewritten as:
（6），
In formula (6), the intermediate variable Intermediate variable/>Intermediate variables。
Step 1-2, defining state variables: Wherein the intermediate variable Intermediate variable/>Intermediate variable/>Then equation (2) is converted into a state equation:
（7），
In the formula (7), the amino acid sequence of the compound, Representation/>First derivative of,/>Representation/>First derivative of,/>Representation/>First derivative of (2) system unknown dynamic/>Intermediate variable/>Intermediate variable/>Intermediate variable/>System unknown dynamic/>。
To facilitate the design of the controller, the following assumptions are made:
Suppose 1: the system expects the tracking position command x d to be second order continuous and the system expects the position command, the velocity command, and the acceleration command to be bounded.
Suppose 2: system unknown dynamicsAnd/>The method meets the following conditions:
（8），
In the formula (8), the amino acid sequence of the compound, And/>Are all unknown positive constants.
And (2) switching to step 2.
Step 2, designing a nonlinear robust position shaft control controller with a gain self-learning mechanism based on a mathematical model of an electrohydraulic proportional servo valve position shaft control system, wherein the method comprises the following specific steps of:
step 2-1, defining tracking error of the system for designing the controller ，/>The invention provides a nonlinear filter with gain self-learning for the first time, which is a system expected tracking position instruction:
（9），
filter gain (9) ，/>Representation/>Virtual control of/>Representation/>Is a filtered signal of/>Error with x 2/>，/>Filtering error/>，/>Is expressed as a constant positive function and satisfiesWherein/>Representing integral variable,/>Constant representing constant positive,/>Representation/>Is used as a first derivative of (a),Representation/>First derivative of,/>Representation/>Upper bound of/>Representation/>Is used for the estimation of the (c),
Its update lawThe method comprises the following steps:
（10），
In the formula (10), the amino acid sequence of the compound, Indicating a positive gain;
For a pair of And (5) deriving to obtain:
（11），
Designing virtual controls The method comprises the following steps:
（12），
In the formula (12), gain Then
（13）。
Step 2-2, the invention innovatively proposes a nonlinear filter with gain self-learning as follows:
（14），
In the formula (14), the filter gain ，/>Representation/>Virtual control of/>Representation/>Is included in the filtered signal of (a),And/>Error/>，/>Filtering error/>，/>Represents a constant positive function and satisfies/>Wherein/>Representing integral variable,/>Constant representing constant positive,/>Representation/>First derivative of,/>Representation/>First derivative of,/>Representation/>Upper bound of/>Representation/>Is updated by the estimated value of law/>The method comprises the following steps:
（15），
in the formula (15), the amino acid sequence of the compound, Indicating a positive gain;
For a pair of The derivation can be obtained:
（16），
The following virtual control with gain self-learning is proposed for the first time The method comprises the following steps:
（17），
In the formula (17), gain ，/>Representing model-based compensation terms,/>Representing robust items,/>Representing a linear robust term,/>Representing nonlinear robust terms,/>Is expressed as a constant positive function and satisfiesWherein/>Representing integral variable,/>Constant representing constant positive,/>Representation/>Is defined by the upper bound of (c),Representation/>Is updated by the estimated value of law/>The method comprises the following steps:
（18），
In the formula (18), the amino acid sequence of the compound, Indicating a positive gain;
Substituting formula (17) into formula (16) to obtain:
（19），
step 2-3, pair And (3) deriving:
（20），
According to equation (20), the control input of the spool, i.e. the nonlinear robust position axis control controller u with gain self-learning mechanism for the first time, is:
（21），
In the formula (21), the gain ，/>Representing model-based compensation terms,/>Representing robust items,/>Representing a linear robust term,/>Representing nonlinear robust terms,/>Represents a constant positive function and satisfies/>Wherein/>Representing integral variable,/>Constant representing constant positive,/>Representation/>Upper bound of/>Representation/>Is updated by the estimated value of law/>The method comprises the following steps:
（22），
In the formula (22), the amino acid sequence of the compound, Indicating a positive gain;
substituting formula (21) into formula (20):
（23），
And (3) switching to step 3.
The stability of the nonlinear robust position axis control controller is proved by applying the Lyapunov stability theory, and the result of asymptotically stabilizing the tracking error of the system is obtained, which is specifically as follows:
the lyapunov function is defined as follows:
（24），
Wherein the intermediate variable Intermediate variable/>Intermediate variable/>Intermediate variables；
Deriving the formula (24), and substituting the formula (9), the formula (10), the formula (13), the formula (15), the formula (16), the formula (18), the formula (19), the formula (22) and the formula (23) into the formula (1):
（25），
Taking into account that 、/>、/>And/>The expression can be obtained:
（26），
Note that （27），
Is available in the form of （28），
Substituting the formula (27) and the formula (28) into the formula (26) to obtain
（29），
Definition of intermediate variablesAnd/>The method comprises the following steps of:
（30），
（31），
formula (31), intermediate variable And/>Respectively is
（32），
By adjusting the gain k 1、k2、k3 and the filtering gain、/>Can make symmetrical matrix/>For positive definite matrix, then we can get:
（33），
Formula (33), intermediate variable 。
Respectively integrating two sides of the formula (33) to obtain:
（34），
From (34), it can be seen that Is bounded,/>Is integral bounded, and thus it can be derived that all signals of the system are bounded, therefore,/>Is consistently continuous, is available according to Barbalat's lemma, tracks error/>, when time tends to be positive infinityTending toward 0.
It follows that: by adjusting the gain k 1、k2、k3 and the filtering gain、/>The nonlinear robust position axis control controller with the gain self-learning mechanism designed for the electrohydraulic proportional servo valve position axis control system for the first time can enable the system to innovatively obtain the result that tracking errors gradually converge to 0, and the schematic diagram of the nonlinear robust position axis control controller of the electrohydraulic proportional servo valve position axis control system is shown in figure 1.
Examples
The physical parameters of the position axis control system of the electrohydraulic proportional servo valve in simulation are shown in table 1:
TABLE 1 physical parameters of the system
| Physical parameters | Numerical value | Physical parameters | Numerical value |
| A (m2) | 2×10-4 | βe(Pa) | 2×108 |
| m (kg) | 40 | B (N·s/m) | 80 |
| Ct(m5/ ( N·s) ) | 7×10-12 | ku（m/V） | 4×10-8 |
| V01 (m3) | 1×10-3 | V02（m3） | 1×10-3 |
| Ps (MPa) | 7 | Pr (MPa) | 0 |
The desired instructions for a given system arem。
The following controller comparisons were taken in the simulation:
Electro-hydraulic proportional servo valve self-learning gain position axis control controller (ALGRC): gain is taken ，/>，，/>，/>，/>，/>，/>，/>。
PID controller: the PID controller parameter selection steps are as follows: firstly, under the condition of neglecting nonlinear dynamics of an electrohydraulic proportional servo valve control system, a group of controller parameters are obtained through PID parameter self-tuning functions in Matlab, and then the obtained self-tuning parameters are subjected to fine tuning after the nonlinear dynamics of the system are added, so that the system obtains optimal tracking performance. The selected controller parameters are as follows，/>，/>。
The expected instructions of the system, ALGRC controller tracking error, ALGRC controller tracking error versus PID controller are shown in fig. 3, 4 and 5, respectively. As can be seen from FIG. 4, under the action of ALGRC controller, the position output of the proportional servo valve control system has high tracking accuracy to the command, and the amplitude of the steady tracking error is aboutM. As can be seen from the comparison of the tracking errors of the two controllers in FIG. 5, the tracking error of the ALGRC controller provided by the invention is much smaller than that of the PID controller, and the tracking performance is more excellent.
Fig. 6 is a graph showing the change of the control input of the electro-hydraulic proportional servo valve control system with time under the action of ALGRC controller, and it can be seen from the graph that the obtained control input is a low-frequency continuous signal, which is more beneficial to be implemented in practical application.
Claims (10)
1. The self-learning gain position shaft control method of the electrohydraulic proportional servo valve is characterized by comprising the following steps of:
step 1, establishing a mathematical model of an electrohydraulic proportional servo valve position shaft control system, and turning to step 2;
Step 2, designing a nonlinear robust position shaft control controller with a gain self-learning mechanism based on a mathematical model of an electrohydraulic proportional servo valve position shaft control system, and turning to step 3;
And step 3, performing stability demonstration of the nonlinear robust position axis control controller by using a Lyapunov stability theory to obtain a result of asymptotically stable system tracking error.
2. The method for controlling the position of the self-learning gain of the electro-hydraulic proportional servo valve according to claim 1, wherein in the step 1, a mathematical model of the position control system of the electro-hydraulic proportional servo valve is established, specifically as follows:
The electro-hydraulic proportional servo valve position shaft control system is applied to linear motion of large industrial heavy-duty mechanical equipment, wherein a load is fixedly connected with a piston rod on a hydraulic cylinder, the electro-hydraulic proportional servo valve controls the piston rod on the hydraulic cylinder to move, so that the load is driven to move, and a mathematical model of the electro-hydraulic proportional servo valve position shaft control system is deduced according to the dynamic characteristics of the load, the hydraulic cylinder and the electro-hydraulic proportional servo valve;
And step 1-2, defining state variables for conveniently designing a controller, and converting a derived mathematical model of the electrohydraulic proportional servo valve position shaft control system into a state space equation.
3. The self-learning gain position shaft control method of an electrohydraulic proportional servo valve according to claim 2, wherein the electrohydraulic proportional servo valve position shaft control system is applied to linear motion of large industrial heavy-duty mechanical equipment in step 1-1, wherein a load is fixedly connected with a piston rod on a hydraulic cylinder, the electrohydraulic proportional servo valve controls the piston rod on the hydraulic cylinder to move so as to drive the load to move, and a mathematical model of the electrohydraulic proportional servo valve position shaft control system is obtained according to dynamics characteristics of the load, the hydraulic cylinder and the electrohydraulic proportional servo valve, and is specifically as follows:
According to Newton's second law, the force balance equation of the electrohydraulic proportional servo valve position shaft control system is:
（1），
in the formula (1), m represents the mass of the load, y represents the displacement of the piston rod of the hydraulic cylinder, Representing the speed of the piston rod of the hydraulic cylinder,/>The acceleration of a piston rod of the hydraulic cylinder is represented, A represents the effective acting area of the piston of the hydraulic cylinder, P 1 represents the oil pressure of an oil inlet cavity of the hydraulic cylinder, P 2 represents the oil pressure of an oil outlet cavity of the hydraulic cylinder, B represents the viscous damping coefficient of the hydraulic cylinder,/>Representing system mechanical unmodeled interference, t representing time;
then formula (1) is rewritten as:
（2），
In the electrohydraulic proportional servo valve position shaft control system, the oil leakage of the oil cylinder is ignored, and then the pressure dynamic equation is as follows:
（3），
In the formula (3), the amino acid sequence of the compound, Representing the effective elastic modulus of oilThe leakage coefficient in the hydraulic cylinder is represented, and the oil pressure difference between oil inlet and outlet cavities at two sides of the oil cylinder/>Control volume of oil inlet chamber/>Control volume of oil outlet chamber/>V 01 represents the initial volume of the oil inlet chamber, V 02 represents the initial volume of the oil inlet chamber, Q 1 represents the flow rate of the oil inlet chamber, Q 2 represents the flow rate of the oil chamber,/>Representation/>Unembossed interference of,/>Representation/>Unembossed interference of,/>Representation/>First derivative of,/>Representation/>Is the first derivative of (a);
Q 1、Q2 has the following relation with the valve core displacement x v of the electro-hydraulic proportional servo valve respectively:
（4），
Wherein, electrohydraulic proportional servo valve coefficient ，/>Representing the flow coefficient of the electrohydraulic proportional servo valve,/>Represents the area gradient of a valve core of the electrohydraulic proportional servo valve,/>Representing oil density,/>Representing the oil supply pressure,/>Indicating the return pressure,/>Representing intermediate variables/>Is defined as:
（5），
Ignoring the dynamic state of the valve core of the electrohydraulic proportional servo valve, assuming that the control input u acting on the valve core and the valve core displacement x v are in proportional relation, namely meeting Wherein/>The expression voltage-spool displacement gain coefficient is thus rewritten as:
（6），
In formula (6), the intermediate variable Intermediate variable/>Intermediate variables。
4. The method for controlling the position of the self-learning gain of the electro-hydraulic proportional servo valve according to claim 3, wherein in step 1-2, in order to design the controller conveniently, a state variable is defined, and a mathematical model of a derived electro-hydraulic proportional servo valve position control system is converted into a state space equation, specifically as follows:
Defining a state variable: Wherein, the intermediate variable/> Intermediate variablesIntermediate variable/>Then the equation (2) is converted into a state space equation:
（7），
In the formula (7), the amino acid sequence of the compound, Representation/>First derivative of,/>Representation/>First derivative of,/>Representation/>First derivative of (2) system unknown dynamic/>Intermediate variable/>Intermediate variable/>Intermediate variablesSystem unknown dynamic/>。
5. The method for controlling the self-learning gain position of an electrohydraulic proportional servo valve according to claim 4, wherein in step 1, in order to design the controller, the following assumptions are made:
Suppose 1: the system expected tracking position command x d is continuous in second order, and the system expected position command, the speed command and the acceleration command are all bounded;
Suppose 2: system unknown dynamics And/>The method meets the following conditions:
（8），
In the formula (8), the amino acid sequence of the compound, And/>Are all unknown positive constants;
And (2) switching to step 2.
6. The method for controlling the position of the self-learning gain of the electro-hydraulic proportional servo valve according to claim 5, wherein in the step 2, a nonlinear robust position control controller with a gain self-learning mechanism is designed based on a mathematical model of the position control system of the electro-hydraulic proportional servo valve, and the method is specifically as follows:
step 2-1, defining tracking error of the system Wherein/>Is a system expected tracking position instruction, in order to facilitate the system state/>, under the drive of a designed controllerTracking desired location instructions/>, as accurately as possibleTracking error/>, needs to be guaranteedTrend toward 0;
Step 2-2, definition error Wherein/>Representation/>Is a filtered signal of/>Representation/>To ensure tracking error/>Trend toward 0, need to guarantee error/>Trend toward 0;
step 2-3, defining errors Wherein/>Representation/>Is a filtered signal of/>Representation/>To ensure error/>Trend toward 0, need to guarantee error/>Tending toward 0.
7. The method for controlling the self-learning gain position of an electrohydraulic proportional servo valve according to claim 6, wherein step 2-1 defines a tracking error of the systemWherein/>Is a system expected tracking position instruction, in order to facilitate the system state/>, under the drive of a designed controllerTracking desired location instructions/>, as accurately as possibleTracking error/>, needs to be guaranteedTrend toward 0, specifically as follows:
To facilitate the design of the controller, the following nonlinear filter is designed:
（9），
filter gain (9) ，/>Filtering error/>，/>Is expressed as a constant positive function and satisfiesWherein/>Representing integral variable,/>Constant representing constant positive,/>Representation/>Is used as a first derivative of (a),Representation/>First derivative of,/>Representation/>Upper bound of/>Representation/>Is a function of the estimated value of (2);
Its update law The method comprises the following steps:
（10），
In the formula (10), the amino acid sequence of the compound, Indicating a positive gain;
For a pair of And (5) deriving to obtain:
（11），
Designing virtual controls The method comprises the following steps:
（12），
In the formula (12), gain Then
（13）。
8. The method for controlling the self-learning gain position of an electrohydraulic proportional servo valve according to claim 7, wherein step 2-2, defining an errorWherein/>Representation/>Is a filtered signal of/>Representation/>To ensure tracking error/>Trend toward 0, need to guarantee error/>Trend toward 0, specifically as follows:
The following nonlinear filter is designed:
（14），
In the formula (14), the filter gain ，/>Filtering error/>，/>Represents a constant positive function and satisfies/>Wherein/>Representing integral variable,/>Constant representing constant positive,/>Representation/>First derivative of,/>Representation/>First derivative of,/>Representation/>Upper bound of/>Representation/>Is updated by the estimated value of law/>The method comprises the following steps:
（15），
in the formula (15), the amino acid sequence of the compound, Indicating a positive gain;
For a pair of The derivation can be obtained:
（16），
Designing virtual controls The method comprises the following steps:
（17），
In the formula (17), gain ，/>Representing model-based compensation terms,/>Representing robust items,/>Representing a linear robust term,/>Representing nonlinear robust terms,/>Represents a constant positive function and satisfies/>Wherein/>Representing integral variable,/>Constant representing constant positive,/>Representation/>Upper bound of/>Representation/>Is updated by the estimated value of law/>The method comprises the following steps:
（18），
In the formula (18), the amino acid sequence of the compound, Indicating a positive gain;
Substituting formula (17) into formula (16) to obtain:
（19）。
9. The method for controlling the self-learning gain position of the electro-hydraulic proportional servo valve according to claim 8, wherein the step 2-3 is to define an error Wherein/>Representation/>Is a filtered signal of/>Representation/>To ensure error/>Trend toward 0, need to guarantee error/>Trend toward 0, specifically as follows:
And (3) deriving:
（20），
According to equation (20), the control input of the spool, i.e., the nonlinear robust position axis control controller u with gain self-learning mechanism, is:
（21），
In the formula (21), the gain ，/>Representing model-based compensation terms,/>Representing robust items,/>Representing a linear robust term,/>Representing nonlinear robust terms,/>Represents a constant positive function and satisfies/>Wherein/>Representing integral variable,/>Constant representing constant positive,/>Representation/>Upper bound of/>Representation/>Is updated by the estimated value of law/>The method comprises the following steps:
（22），
In the formula (22), the amino acid sequence of the compound, Indicating a positive gain;
substituting formula (21) into formula (20):
（23），
And (3) switching to step 3.
10. The method for controlling the self-learning gain position of the electro-hydraulic proportional servo valve according to claim 9, wherein the nonlinear robust position control controller stability proof by using lyapunov stability theory in the step 3 is specifically as follows:
the lyapunov function is defined as follows:
（24），
Wherein the intermediate variable Intermediate variable/>Intermediate variable/>Intermediate variable/>；
And performing stability demonstration by using a Lyapunov stability theory to obtain a result of progressive stability of the system tracking error.
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