CN114879501A - Electro-hydraulic proportional servo valve control method considering time-varying parameter uncertainty - Google Patents
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Abstract
The invention discloses a time-varying parameter uncertainty considered electro-hydraulic proportional servo valve shaft control system self-adaptive dynamic surface control method, which is obtained by fusing time-varying parameter self-adaptive control and dynamic surface control and performing feedforward cancellation on a model. Aiming at the problem of valve control of the electro-hydraulic proportional servo valve considering uncertainty of time-varying parameters, the invention can ensure the active elimination of the uncertainty of the time-varying parameters of the system, improve the capability of the system for resisting the uncertainty of the parameters, avoid the problem of differential explosion in the traditional backstepping control of the electro-hydraulic system, reduce the influence of measurement noise on the 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 an electro-hydraulic proportional servo valve control method (ADSC) considering time-varying parameter uncertainty.
Background
The electro-hydraulic proportional servo valve shaft control system plays a very important role in the fields of robots, heavy machinery, high-performance loading test equipment and the like by virtue of the characteristics of high power density, large 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 uncertainty. The nonlinear characteristics comprise input nonlinearity such as magnetic hysteresis and saturation, flow pressure nonlinearity of a proportional servo valve, friction nonlinearity and the like, 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 towards high precision and high frequency response, the influence of the nonlinear characteristics presented by the system on the system performance is more obvious, and the existence of modeling uncertainty can cause the controller designed by a system nominal model to be unstable or reduced, so the nonlinear characteristics 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 the technical level in the industrial and defense fields, the traditional controller designed based on the traditional linear theory can not meet the high-performance requirement of the system gradually, so that a more advanced nonlinear control strategy must be researched aiming at the nonlinear characteristic in the electro-hydraulic proportional servo valve shaft control system.
Aiming at the problem of nonlinear control of an electro-hydraulic proportional servo valve control system, a plurality of methods are proposed in succession. The self-adaptive control method is an effective method for processing the uncertainty problem of parameters, and can obtain the steady-state performance of asymptotic tracking, but the uncertainty nonlinearity such as external load interference is not good at all, the system can be unstable when the uncertainty nonlinearity is too large, and the actual electro-hydraulic proportional servo valve control system has uncertainty nonlinearity, so that the self-adaptive control method cannot obtain the high-precision control performance in practical application; as a robust control method, classical sliding mode control can effectively process any bounded modeling uncertainty and obtain steady-state performance of asymptotic tracking, but a discontinuous controller designed by classical sliding mode control easily causes the flutter problem of a sliding mode surface, so that the tracking performance of a system is deteriorated; in order to solve the problems of parameter uncertainty and uncertainty nonlinearity simultaneously, an adaptive robust control method is provided, the control method can enable a system to obtain determined transient and steady-state performances under the condition that two modeling uncertainties exist simultaneously, if high-precision tracking performance is obtained, a tracking error must be reduced by improving feedback gain, and due to the existence of measurement noise, the gain is excessively obtained, so that high-gain feedback is caused, the jitter of control input is caused, the control performance is further deteriorated, and even the system is unstable.
Disclosure of Invention
The invention provides an electro-hydraulic proportional servo valve shaft control method considering time-varying parameter uncertainty, which can ensure the active elimination of the time-varying parameter uncertainty of a system, improve the parameter uncertainty resistance of the system, avoid the problem of differential explosion in the traditional backstepping control of the electro-hydraulic system, reduce the influence of measurement noise on the control precision and realize high-precision tracking performance.
The technical solution for realizing the purpose of the invention is as follows: an electro-hydraulic proportional servo valve control method considering uncertainty of time-varying parameters comprises the following steps:
and 3, performing stability verification of the adaptive dynamic surface controller by using the Lyapunov stability theory in consideration of time-varying parameter uncertainty to obtain a result that the tracking error of the system is gradually stable.
Compared with the prior art, the invention has the following remarkable advantages: (1) the uncertainty of system time-varying parameters and the active compensation of unknown disturbance are realized, and the anti-interference capability is strong; (2) the problem of differential explosion in the traditional backstepping control of the electro-hydraulic system is avoided, the influence of measurement noise on the control precision is reduced, the high-precision tracking performance is realized, and the effectiveness of the simulation result is verified.
Drawings
FIG. 1 is a schematic diagram of the principle of the electro-hydraulic proportional servo valve control method considering uncertainty of time-varying parameters.
FIG. 2 is a schematic diagram of an electro-hydraulic proportional servo valve control system according to the present invention.
FIG. 3 is a graph of the trace process of the system output to the desired command under the action of the ADSC controller designed by the present invention.
FIG. 4 is a graph showing the tracking error of the ADSC controller system over time.
FIG. 5 is a graph comparing tracking error of the ADSC controller and a conventional PID controller.
FIG. 6 is a control input graph of the system under the action of the ADSC controller designed by the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
With reference to fig. 1 and 2, the electro-hydraulic proportional servo valve control method considering uncertainty of time-varying parameters of the invention comprises the following steps:
Step 1-1, the electro-hydraulic proportional servo valve position shaft control system is applied to linear motion of large-scale industrial heavy-load mechanical equipment, wherein a load is fixedly connected with a piston rod on a hydraulic oil cylinder, and the electro-hydraulic proportional servo valve controls the piston rod on the hydraulic oil cylinder to move so as to drive the load to move.
According to Newton's second law, the force balance equation of the electro-hydraulic proportional servo valve position shaft control system is as follows:
formula (1), m represents the mass of the load, y represents the displacement of the piston rod of the hydraulic oil cylinder,
the speed of a piston rod of the hydraulic oil cylinder is shown,
representing the acceleration of the piston rod of the hydraulic cylinder, A representing the effective active area of the piston of the hydraulic cylinder, P 1 Indicating the oil pressure in the inlet chamber of the hydraulic cylinder, P 2 Representing the oil pressure of an oil outlet cavity of the hydraulic oil cylinder, B representing the viscous damping coefficient of the hydraulic cylinder, A f The coulomb friction amplitude of the hydraulic cylinder is shown,
representing the approximate shape function of the Coulomb friction of the hydraulic cylinder, d 1 (t) represents unmodeled disturbance of the system machinery, and t represents time.
Then equation (1) is rewritten as:
in the position shaft control system of the electro-hydraulic proportional servo valve, if oil leakage of an oil cylinder is ignored, the pressure dynamic equation is as follows:
in the formula (3), beta e Representing the effective modulus of elasticity, C, of the oil t The oil pressure difference P of oil inlet and outlet chambers at two sides of the oil cylinder is expressed by the leakage coefficient in the hydraulic cylinder L ＝P 1 -P 2 Control volume V of oil inlet chamber 1 ＝V 01 + Ay, control volume V of oil outlet chamber 2 ＝V 02 -Ay，V 01 Indicates the initial volume of the oil inlet chamber, V 02 Showing the initial volume, Q, of the oil chamber 1 Indicating the flow of the inlet chamber, Q 2 Shows the flow of the oil chamber, q 1 Represents P 1 Unmodeled interference of q 2 Represents P 2 Is measured in a non-modeled interference of (c),
represents P 1 The first derivative of (a) is,
represents P 2 The first derivative of (a).
Q 1 、Q 2 Respectively proportional to the displacement x of the spool of the electrohydraulic servo valve v The following relationships exist:
wherein, the valve coefficient of the electro-hydraulic proportional servo valve
C d Indicating the flow coefficient, w, of an electro-hydraulic proportional servo valve 0 Showing the area gradient of a valve core of the electro-hydraulic proportional servo valve, wherein rho shows the density of oil liquid and P s Indicating the supply pressure, P r Represents the return pressure, s (-) represents a function of the intermediate variable, defined as:
neglecting the dynamic of the valve core of the electro-hydraulic proportional servo valve, assuming the control input u acting on the valve core and the valve core displacement x v Proportional relationship, i.e. satisfying x v ＝k i u, wherein k i Since the voltage-spool displacement gain coefficient is expressed, equation (4) is rewritten as:
formula (6), intermediate variable k u ＝k q k i Intermediate variables
Intermediate variables
Step 1-2, defining a state variable:
wherein the intermediate variable x 1 Y, intermediate variables
Intermediate variable x 3 ＝(AP 1 -AP 2 ) /m, system unknown time-varying parameter Θ 1 ＝[θ 1 ,θ 2 ,θ 3 ] T ＝[B,A f ,D 1 ] T Wherein the intermediate variable θ 1 B, intermediate variable θ 2 ＝A f Intermediate variable θ 3 ＝D 1 The system unknown time-varying parameter Θ 2 ＝D 2 Then, equation (2) is converted into an equation of state:
the compound of the formula (7),
denotes x 1 The first derivative of (a) is,
denotes x 2 The first derivative of (a) is,
denotes x 3 First derivative, intermediate variable of
Intermediate variables
Intermediate variable D 1 ＝d 1 (t)/m, intermediate variable
Intermediate variables
Intermediate variables
Intermediate variables
To facilitate the design of the controller and unknown dynamic observer, the following assumptions are made:
assume that 1: system expected tracking position instruction x d Is second order continuous and the system expects that the position command, velocity command, and acceleration command are bounded.
Assume 2: system unknown time varying parameter theta 1 And theta 2 Satisfies the following conditions:
||Θ 1 ||≤δ 1 ,||Θ 2 ||≤δ 2 (8)
formula (8), δ 1 And delta 2 Are all unknown positive constants.
And (5) transferring to the step 2.
step 2-1, defining the tracking error z of the system for designing the controller 1 ＝x 1 -x d ，x d Is a system expected tracking position instruction, and the following nonlinear filter is designed:
equation (9), filter gain τ 1 ＞0，α 1 Denotes x 2 Virtual control of alpha 1f Denotes alpha 1 Of the filtered signal, alpha 1f And x 2 Error z of 2 ＝x 2 -α 1f ，α 1 Filter error e 1 ＝α 1f -α 1 Gain l 1 > 0 represents
Upper bound of (a) 1 (t) represents a constant positive function, and satisfies
Wherein, v represents an integral variable,
a constant that is constant and positive is represented,
denotes alpha 1 The first derivative of (a) is,
denotes alpha 1f The first derivative of (a).
To z 1 And (5) obtaining a derivative:
designing virtual control alpha 1 Comprises the following steps:
wherein,
denotes x d First derivative, gain k 1 If greater than 0, then
Step 2-2, for z 2 And (5) obtaining a derivative:
the following nonlinear filter is designed:
equation (14), filter gain τ 2 ＞0，α 2 Denotes x 3 Virtual control of，α 2f Denotes alpha 2 Of the filtered signal, alpha 2f And x 3 Error z of 3 ＝x 3 -α 2f ，α 2 Filter error e 2 ＝α 2f -α 2 Gain l 2 > 0 represents
Upper bound of (a) ("σ 2 (t) represents a constant positive function, and satisfies
Wherein, v represents an integral variable,
a constant that is constant and positive is represented,
denotes alpha 2 The first derivative of (a) is,
denotes alpha 2f The first derivative of (a).
Defining intermediate variables
Designing virtual control alpha 2 Comprises the following steps:
formula (15), χ 1 The intermediate variable is represented by a number of variables,
to represent
Estimate of (2), gain k 2 > 0, intermediate variable
Law of update of
Is composed of
Formula (16), gain μ 1 ＞0。
Substituting formula (15) for formula (13) to obtain:
step 2-3, for z 3 And (5) obtaining a derivative:
defining intermediate variables
According to equation (18), the control input of the spool, i.e., the adaptive dynamic surface controller u designed to take into account the uncertainty of the time-varying parameters, is:
formula (19), gain k 3 > 0, intermediate variable
χ 2 The intermediate variable is represented by a number of variables,
to represent
Is determined by the estimated value of (c),
law of update
Is composed of
Formula (20), gain μ 2 ＞0。
Substituting formula (19) into formula (18):
and (5) turning to the step 3.
Step 3, the stability of the adaptive dynamic surface controller is proved by using the Lyapunov stability theory and considering the uncertainty of the time-varying parameters, and a result that the tracking error of the system is gradually stable is obtained, which is concretely as follows:
the lyapunov function is defined as follows:
wherein the intermediate variable
Intermediate variables
Derivation of equation (22) and substitution of equations (9), (12), (14), (16), (17), (20), and (21) can result:
in view of
And
the expression can be obtained:
it is noted that
Can obtain the product
By substituting formula (24) with formula (25) and formula (26), the compound can be obtained
Defining the intermediate variables z and Λ as:
z＝[z 1 ；z 2 ；z 3 ；ε 1 ；ε 2 ] (28)
equation (29), intermediate variable Λ 1 And Λ 2 Are respectively as
By adjusting the gain k 1 、k 2 、k 3 And a filter gain τ 1 、τ 2 If the symmetric matrix Λ is a positive definite matrix, then:
formula (31), intermediate variable Φ ═ z T Λz。
Integrating the two sides of equation (31) to obtain:
from equation (32), V is bounded and Φ is bounded by an integral. It follows that all signals of the system are bounded. Thus, Φ is consistently continuous. According to the Barbalt theorem, the tracking error z is obtained when the time tends to be infinite 1 Tending towards 0.
It is therefore concluded that: by adjusting the gain k 1 、k 2 、k 3 And a filter gain τ 1 、τ 2 The adaptive dynamic surface controller designed for the electro-hydraulic proportional servo valve position shaft control system and considering time-varying parameter uncertainty can enable the system to obtain a result that a tracking error gradually converges to 0, and the schematic diagram of the principle of the adaptive dynamic surface controller of the electro-hydraulic proportional servo valve position shaft control system and considering the time-varying parameter uncertainty is shown in fig. 1.
Examples
In order to examine the performance of the designed controller, the physical parameters of the electro-hydraulic proportional servo valve position shaft control system in the simulation are shown in table 1:
TABLE 1 physical parameters of the System
| Physical parameters | Numerical value | Physical parameters | Numerical value |
| A(m 2 ) | 2×10 -4 | β e (Pa) | 2×10 8 |
| m(kg) | 40 | B(N·s/m) | 80 |
| C t (m 5 /(N·s)) | 7×10 -12 | k u (m/V) | 4×10 -8 |
| V 01 (m 3 ) | 1×10 -3 | V 02 (m 3 ) | 1×10 -3 |
| P s (MPa) | 7 | P r (MPa) | 0 |
| A f (N·s/m) | 10 |
The expected instruction for a given system is
Coulomb friction shape function of S f (x 2 )＝2arctan(1000x 2 )/π。
The following controller comparisons were taken in the simulation:
electro-hydraulic proportional servo valve position shaft controller (UDORC) taking into account unknown dynamic compensation of the system: gain k is taken 1 ＝10，k 2 ＝1，k 3 ＝1，μ 1 ＝20，μ 2 ＝20，τ 1 ＝100，τ 2 ＝1000，l 1 ＝l 2 ＝1。
A PID controller: the PID controller parameter selection steps are as follows: firstly, a set of controller parameters is obtained through a PID parameter self-tuning function in Matlab under the condition of neglecting the nonlinear dynamics of an electro-hydraulic proportional servo valve shaft control system, and then the obtained self-tuning parameters are subjected to fine tuning after the nonlinear dynamics of the system is added, so that the system obtains the optimal tracking performance. The selected controller parameter is k P ＝10，k I ＝1，k D ＝1。
The expected command of the system, the ADSC controller tracking error compared to the PID controller tracking error are shown in FIGS. 3, 4 and 5, respectively. As can be seen from FIG. 4, under the action of the ADSC controller, the position output of the proportional servo valve axis control system has high tracking precision to the command, and the amplitude of the steady-state tracking error is about 5 × 10 -4 And m is selected. It can be seen from the comparison of the tracking errors of the two controllers in fig. 5 that the tracking error of the ADSC controller proposed by the present invention is much smaller than that of the PID controller, and the tracking performance is more excellent.
FIG. 6 is a graph of the control input of the electro-hydraulic proportional servo valve control system changing with time under the action of the ADSC controller, and it can be seen from the graph that the obtained control input is a continuous signal, which is more beneficial to be implemented in practical application.
Claims (4)
1. An electro-hydraulic proportional servo valve control method considering uncertainty of time-varying parameters is characterized by comprising the following steps of:
step 1, establishing a mathematical model of an electro-hydraulic proportional servo valve position shaft control system, and turning to step 2;
step 2, designing a self-adaptive dynamic surface controller considering uncertainty of time-varying parameters based on a mathematical model of an electro-hydraulic proportional servo valve position shaft control system, and turning to step 3;
and 3, performing stability verification of the adaptive dynamic surface controller by using the Lyapunov stability theory in consideration of time-varying parameter uncertainty to obtain a result that the tracking error of the system is gradually stable.
2. The electro-hydraulic proportional servo valve shaft control method considering uncertainty of time-varying parameters as claimed in claim 1, wherein in step 1, a mathematical model of an electro-hydraulic proportional servo valve position shaft control system is established, specifically as follows:
step 1-1, the electro-hydraulic proportional servo valve position shaft control system is applied to linear motion of large-scale industrial heavy-load mechanical equipment, wherein a load is fixedly connected with a piston rod on a hydraulic oil cylinder, and the electro-hydraulic proportional servo valve controls the piston rod on the hydraulic oil cylinder to move so as to drive the load to move;
according to Newton's second law, the force balance equation of the electro-hydraulic proportional servo valve position shaft control system is as follows:
formula (1), m represents the mass of the load, y represents the displacement of the piston rod of the hydraulic oil cylinder,
the speed of a piston rod of the hydraulic oil cylinder is shown,
representing the acceleration of the piston rod of the hydraulic cylinder, A representing the effective active area of the piston of the hydraulic cylinder, P 1 Indicating the oil pressure in the inlet chamber of the hydraulic cylinder, P 2 Representing the oil pressure of an oil outlet cavity of the hydraulic oil cylinder, B representing the viscous damping coefficient of the hydraulic cylinder, A f The coulomb friction amplitude of the hydraulic cylinder is shown,
representing the approximate shape function of the Coulomb friction of the cylinder, d 1 (t) represents unmodeled disturbance of the system machinery, t represents time;
then equation (1) is rewritten as:
in the position shaft control system of the electro-hydraulic proportional servo valve, if oil leakage of an oil cylinder is ignored, the pressure dynamic equation is as follows:
in the formula (3), beta e Representing the effective modulus of elasticity, C, of the oil t The oil pressure difference P of oil inlet and outlet chambers at two sides of the oil cylinder is expressed by the leakage coefficient in the hydraulic cylinder L ＝P 1 -P 2 Control volume V of oil inlet chamber 1 ＝V 01 + Ay, control volume V of oil outlet chamber 2 ＝V 02 -Ay，V 01 Indicates the initial volume of the oil inlet chamber, V 02 Showing the initial volume, Q, of the oil chamber 1 Indicating the flow of the inlet chamber, Q 2 Shows the flow of the oil chamber, q 1 Represents P 1 Unmodeled interference of q 2 Represents P 2 Is measured in a non-modeled interference of (c),
represents P 1 The first derivative of (a) is,
represents P 2 The first derivative of (a);
Q 1 、Q 2 respectively proportional to the displacement x of the spool of the electrohydraulic servo valve v The following relationships exist:
wherein, the valve coefficient of the electro-hydraulic proportional servo valve
C d Indicating the flow coefficient, w, of an electro-hydraulic proportional servo valve 0 Showing the area gradient of a valve core of the electro-hydraulic proportional servo valve, wherein rho shows the density of oil liquid and P s Indicating the supply pressure, P r Represents the return pressure, s (-) represents a function of the intermediate variable, defined as:
neglecting the dynamic of the valve core of the electro-hydraulic proportional servo valve, assuming the control input u acting on the valve core and the valve core displacement x v Proportional relationship, i.e. satisfying x v ＝k i u, wherein k i Since the voltage-spool displacement gain coefficient is expressed, equation (4) is rewritten as:
formula (6), intermediate variable k u ＝k q k i Intermediate variables
Intermediate variables
Step 1-2, defining a state variable:
wherein the intermediate variable x 1 Y, intermediate variables
Intermediate variable x 3 ＝(AP 1 -AP 2 ) /m, system unknown time-varying parameter Θ 1 ＝[θ 1 ,θ 2 ,θ 3 ] T ＝[B,A f ,D 1 ] T Wherein the intermediate variable θ 1 B, intermediate variable θ 2 ＝A f Intermediate variable θ 3 ＝D 1 The system unknown time-varying parameter Θ 2 ＝D 2 Then, equation (2) is converted into an equation of state:
in the formula (7),
denotes x 1 The first derivative of (a) is,
denotes x 2 The first derivative of (a) is,
denotes x 3 First derivative, intermediate variable of
Intermediate variables
Intermediate variable D 1 ＝d 1 (t)/m, intermediate variable
Intermediate variables
Intermediate variables
Intermediate variables
To facilitate the design of the controller and unknown dynamic observer, the following assumptions are made:
assume that 1: system expected tracking position instruction x d Is second order continuous and the system expects that the position command, the speed command and the acceleration command are bounded;
assume 2: system unknown time varying parameter theta 1 And theta 2 Satisfies the following conditions:
||Θ 1 ||≤δ 1 ,||Θ 2 ||≤δ 2 (8)
formula (8), δ 1 And delta 2 Are all unknown positive constants;
and (5) transferring to the step 2.
3. The electro-hydraulic proportional servo valve shaft control method considering the uncertainty of the time-varying parameter as claimed in claim 2, wherein in step 2, an adaptive dynamic surface controller considering the uncertainty of the time-varying parameter is designed based on a mathematical model of an electro-hydraulic proportional servo valve position shaft control system, and the specific steps are as follows:
step 2-1, defining the tracking error z of the system for designing the controller 1 ＝x 1 -x d ，x d Is a system expected tracking position instruction, and the following nonlinear filter is designed:
equation (9), filter gain τ 1 ＞0，α 1 Denotes x 2 Virtual control of alpha 1f Denotes alpha 1 Of the filtered signal, alpha 1f And x 2 Error z of 2 ＝x 2 -α 1f ，α 1 Filter error e 1 ＝α 1f -α 1 Gain l 1 > 0 represents
Upper bound of (a) 1 (t) represents a constant positive function, and satisfies
Wherein, v represents an integral variable,
a constant that is constant and positive is represented,
denotes alpha 1 The first derivative of (a) is,
denotes alpha 1f The first derivative of (a);
to z 1 And (5) obtaining a derivative:
designing virtual control alpha 1 Comprises the following steps:
wherein,
denotes x d First derivative, gain k 1 If greater than 0, then
Step 2-2, for z 2 And (5) obtaining a derivative:
the following nonlinear filter is designed:
equation (14), filter gain τ 2 ＞0，α 2 Denotes x 3 Virtual control of alpha 2f Denotes alpha 2 Of the filtered signal, alpha 2f And x 3 Error z of 3 ＝x 3 -α 2f ，α 2 Filter error e 2 ＝α 2f -α 2 Gain l 2 > 0 represents
Upper bound of (a) 2 (t) represents a constant positive function, and satisfies
Wherein, v represents an integral variable,
a constant that is constant and positive is represented,
denotes alpha 2 The first derivative of (a) is,
denotes alpha 2f The first derivative of (a);
defining intermediate variables
Designing virtual control alpha 2 Comprises the following steps:
formula (15), χ 1 The intermediate variable is represented by a number of variables,
to represent
Estimate of (2), gain k 2 > 0, intermediate variable
Law of update of
Is composed of
Formula (16), gain μ 1 ＞0；
Substituting formula (15) for formula (13) to obtain:
step 2-3, for z 3 Obtaining a derivative:
defining intermediate variables
According to equation (18), the control input of the spool, i.e., the adaptive dynamic surface controller u designed to take into account the uncertainty of the time-varying parameters, is:
formula (19), gain k 3 > 0, intermediate variables
χ 2 The intermediate variable is represented by a number of variables,
to represent
Is determined by the estimated value of (c),
law of update
Is composed of
Formula (20), gain μ 2 ＞0；
Substituting formula (19) into formula (18):
and (5) turning to the step 3.
4. The electro-hydraulic proportional servo valve shaft control method considering the uncertainty of the time-varying parameter as claimed in claim 3, wherein the stability of the adaptive dynamic surface controller considering the uncertainty of the time-varying parameter is proved by applying the Lyapunov stability theory in step 3, so as to obtain a result that the tracking error of the system is gradually stabilized, specifically as follows:
the lyapunov function is defined as follows:
wherein the intermediate variable
Intermediate variables
And (3) carrying out stability verification by using the Lyapunov stability theory to obtain a result of gradual stabilization of the tracking error of the system.
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| CN118068714A (en) * | 2024-03-04 | 2024-05-24 | 南京理工大学 | Intelligent valve core displacement control method considering unknown hydrodynamic force compensation |
| CN118192225A (en) * | 2024-02-26 | 2024-06-14 | 南京理工大学 | Electrohydraulic proportional servo valve self-learning gain position axis control method |
| CN118295246A (en) * | 2024-03-15 | 2024-07-05 | 南京理工大学 | Pilot-operated electro-hydraulic proportional servo valve output feedback control method based on instruction filtering |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN118192225A (en) * | 2024-02-26 | 2024-06-14 | 南京理工大学 | Electrohydraulic proportional servo valve self-learning gain position axis control method |
| CN118068714A (en) * | 2024-03-04 | 2024-05-24 | 南京理工大学 | Intelligent valve core displacement control method considering unknown hydrodynamic force compensation |
| CN118068714B (en) * | 2024-03-04 | 2024-08-09 | 南京理工大学 | Intelligent valve core displacement control method considering unknown hydrodynamic force compensation |
| CN118295246A (en) * | 2024-03-15 | 2024-07-05 | 南京理工大学 | Pilot-operated electro-hydraulic proportional servo valve output feedback control method based on instruction filtering |
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