CN117970797A

CN117970797A - Variable input compensation control method for hydraulic servo position control system based on sensitivity

Info

Publication number: CN117970797A
Application number: CN202311861342.8A
Authority: CN
Inventors: 佘进波; 巴凯先; 何小龙; 李欣荣; 王源; 刘宁; 马国梁; 俞滨; 袁立鹏
Original assignee: Yanshan University
Current assignee: Yanshan University
Priority date: 2023-12-29
Filing date: 2023-12-29
Publication date: 2024-05-03

Abstract

The invention relates to a variable input compensation control method of a hydraulic servo position control system based on sensitivity, which comprises the following steps of S1, modeling according to a typical hydraulic servo position control system, and updating a reference track of a state space equation of the hydraulic servo position control system through a variable input control method based on a model; s2, obtaining a mapping relation between the state space equation parameter variable quantity and the output variable quantity of the hydraulic servo position control system after the reference track is updated based on the sensitivity; and S3, realizing real-time compensation of parameters of the variable input control method, verifying stability by analyzing the relation between track tracking errors before and after compensation, and completing variable input compensation control of the hydraulic servo position control system. The control method based on the sensitivity can accurately reveal the relation between the nonlinear model parameter variation and the output variation; the variable input compensation control method based on sensitivity compensates system parameters in real time by predicting tracking errors, and has good working condition self-adaption capability under time-varying discontinuous working conditions.

Description

Variable input compensation control method for hydraulic servo position control system based on sensitivity

Technical Field

The invention belongs to the technical field of fluid transmission and control, and particularly relates to a variable input compensation control method of a hydraulic servo position control system based on sensitivity.

Background

The hydraulic servo position control system has the advantages of strong load capacity, high response speed and the like, and is widely applied to mobile equipment such as aerospace, hydraulic foot robots, industrial production and the like. With the continuous increase of the adaptive demands of mobile equipment on complex and changeable environments, a hydraulic servo position control system is required to realize high-precision control of various track tracking tasks. However, due to the influence of factors such as strong nonlinearity, parameter time variability, load variability and the like of the hydraulic system, the realization of high-precision track tracking control of the hydraulic servo position control system is difficult. In addition, the high-precision track tracking control of the hydraulic servo position control system also faces the problem of uncertainty of optimal parameters under a time-varying discontinuous working condition, so that the high-precision track tracking control is difficult to achieve under the time-varying discontinuous working condition.

In view of this fact, how to realize high-precision trajectory tracking control of a hydraulic servo position control system has become a research hotspot for various nationists in recent years. Researchers have proposed a control method based on off-line compensation to realize high-precision track tracking control of a hydraulic servo position control system. The off-line compensation control method has great advantages in track tracking accuracy, however, in an actual system, the off-line compensation control method cannot adjust optimal parameters in real time, so that the off-line compensation control method is sensitive to track changes. In order to make up for the above shortcomings of the off-line compensation control method, the on-line compensation control method has received extensive attention from researchers. Although the online compensation control method has great advantages in the aspect of self-adaptability, most of the online compensation control methods are model-based control methods, face implicit constraint between system nonlinear model parameters and states, so that the problems of uncertainty of optimal parameters and track tracking precision under time-varying discontinuous working conditions in the field of hydraulic servo position control at present are solved, and the existing control methods still have certain limitations. To overcome the above limitations, researchers have proposed feedback linearization methods to obtain linear relationships by eliminating the nonlinear terms. In addition, since sensitivity analysis can accurately reveal the mapping relationship between nonlinear model parameters and states, extensive attention has been paid to researchers in recent years.

At present, sensitivity analysis is widely applied to the fields of hydraulic servo, electromagnetism, batteries and the like, and is mostly used for analyzing the influence of system parameters on control performance, optimizing structural parameter design and the like. Compared to sensitivity analysis, sensitivity-based control methods have received little attention in various fields of research. Furthermore, through investigation, it was found that no specific investigation has been made by researchers at the present time regarding the link between sensitivity and hydraulic servo control.

In view of the foregoing, in a hydraulic servo position control system, a high-precision variable input compensation control method for a nonlinear model is highly demanded.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a variable input compensation control method of a hydraulic servo position control system based on sensitivity, and the control method based on sensitivity can accurately reveal the relation between the parameter variation of a nonlinear model and the output variation; the variable input compensation control method based on sensitivity compensates system parameters in real time by predicting tracking errors, and has good working condition self-adaption capability under time-varying discontinuous working conditions.

In order to achieve the above purpose, the invention discloses the following technical scheme:

a sensitivity-based variable input compensation control method for a hydraulic servo position control system comprises the following steps:

S1: modeling is carried out according to a typical hydraulic servo position control system, and a reference track of a state space equation of the hydraulic servo position control system is updated through a variable input control method based on the model;

s11: carrying out mathematical modeling by using a typical hydraulic servo position control system to obtain a state space equation of the hydraulic servo position control system;

s12: based on a state space equation of the hydraulic servo position control system, expanding two disturbance terms, and establishing a state observation equation of the expanded five-order hydraulic servo position control system;

s13: based on the observation value of the state observation equation, a backward difference method is used for establishing a discretization state space equation of a third-order hydraulic servo position control system, so that the track tracking error in the real-time motion process is accurately predicted;

S14: the variable input control method based on the model determines a reference track of a state space equation of the hydraulic servo position control system, and the updated reference track of the state space equation of the hydraulic servo position control system is as follows:

Wherein, A reference track updated by a state space equation; x _r is the initial reference trajectory of the state space equation; τ= [ τ _x τ_v τ_a]^T ] is a model-based variable input control method parameter vector; τ _x is the position item parameter; τ _v is a speed term parameter; τ _a is the acceleration term parameter; /(I)Compensating term coefficient vectors for a model-based variable input control method; /(I)A first derivative of an initial reference track of a state space equation; /(I)The second derivative of the initial reference track is the state space equation;

S2: obtaining a mapping relation between the state space equation parameter variable quantity and the output variable quantity of the hydraulic servo position control system after the reference track is updated based on the sensitivity;

S21: the sensitivity expansion is applied to the field of hydraulic servo control, so that the implicit constraint between the nonlinear model parameters and the output of the hydraulic servo position control system is solved, and the real-time compensation of the parameter tau of a variable input control method based on a model is realized; the discretized state space equation of the hydraulic servo position control system after the model-based variable input control method is added is as follows:

H_k(x(k+1),x(k),u(k),p(k),τ)＝0_3×1 (2)

Wherein H _k is a discretized state space equation; x (k+1) is a state variable at time point T _s of the sampling time (k+1); x (k) is a state variable at the moment of sampling time kT _s; u (k) is the servo valve control voltage at the moment of sampling time kT _s; p (k) is a system parameter vector at the moment of sampling time kT _s; k is the sampling time number; t _s is the sampling period;

Carrying out first-order Taylor expansion on the above formula, and determining the mapping relation between the variable input control method parameter tau variable quantity and the output variable quantity based on the model as follows:

Wherein Δx _p is the output variation; delta tau is the variable quantity of parameters of a variable input control method based on a model; a sensitivity factor of a control method parameter tau is input for model-based variables; /(I) Is a position item sensitivity factor; /(I)Is a speed term sensitivity factor; /(I)Is an acceleration term sensitivity factor;

S22: setting the track tracking error as e (k+n), and determining the compensation term delta tau (k+n _p) of the parameter tau as:

Δτ(k+N_p)＝αe(k+N) (4)

Wherein Deltaτ (k+N _p) is a compensation term of the parameter tau at the sampling time (k+N _p)T_s) to form a variable input compensation control method based on sensitivity, e (k+N) is a track tracking error at the sampling time (k+N) T _s, alpha= [ a _x a_v a_a]^T ] is a compensation gain coefficient of the variable input compensation control method based on sensitivity, a _x is a position term compensation gain coefficient, a _v is a speed term compensation gain coefficient, a _a is an acceleration term compensation gain coefficient, N is a system prediction time domain, and N _p is a system control time domain;

S3: real-time compensation of parameters of a variable input control method is realized, stability is verified by analyzing the relation between track tracking errors before and after compensation, and variable input compensation control of a hydraulic servo position control system is completed;

S31: simultaneously transpose the two ends of the formula (4) obtained in the step S22, and compensating the term coefficient vector by the variable input control method based on the model by multiplying the two ends The method comprises the following steps:

Wherein, Compensating term coefficient vectors for a variable input control method based on a model at a sampling time (k+N _p)T_s;

Further finishing, the compensation term of the reference track by the compensation term delta tau (k+N _p) of the parameter tau is obtained as follows:

Wherein, A compensation term for the reference trajectory for the compensation term Δτ (k+n _p) for the parameter τ;

the variable input compensation control method based on sensitivity is adopted to realize real-time compensation of the variable input control method parameter tau based on a model, and the compensation term for obtaining the final compensation to the state space equation reference track is as follows:

Wherein Δx _r(k+N_p) is a compensation term of the state space equation reference trajectory at the time of sampling (k+n _p)T_s;

S32: and (3) acquiring the reference track compensation item obtained in the step (S31) for closed-loop control of the hydraulic servo position control system, verifying the stability of the system, determining the value range of the compensation gain coefficient, and completing variable input compensation control of the hydraulic servo position control system.

Preferably, in step S11, mathematical modeling is performed using a typical hydraulic servo position control system to obtain a state space equation of the hydraulic servo position control system, specifically:

The hydraulic servo position control system is a typical servo valve control system and is set Wherein x _p is the output position of the cylinder rod of the hydraulic cylinder,/>The hydraulic cylinder rod moving speed is the hydraulic cylinder rod moving speed, P _L is the load pressure, P _L＝P₁-nP₂, n are the ratio of the cross sectional areas of the rod cavity and the rod cavity of the hydraulic cylinder, n=A _p2/A_p1,A_p1 and A _p2 are the cross sectional areas of the rod cavity and the rod cavity of the hydraulic cylinder respectively, and P ₁ and P ₂ are the pressure of the rod cavity and the pressure of the rod cavity of the hydraulic cylinder respectively; the state space equation of the hydraulic servo position control system is as follows:

Wherein x ₁ is the output position of the cylinder rod of the hydraulic cylinder, Is a derivative thereof; x ₂ is the moving speed of the cylinder rod of the hydraulic cylinder,/>Is a derivative thereof; x ₃ is the load pressure,/>Is a derivative thereof; k is load stiffness; b _p is the viscous damping coefficient; m _t is equivalent mass; g ₁(x₁) is a first constructor; g ₂(x₁) is a second constructor; g ₃(x₁,x₃, u) is a third constructor; f _x is the friction force and external disturbance term of the system which is not modeled; f _p is a disturbance term caused by modeling errors of the flow of the system valve and internal and external leakage and system parameter changes; k _axv is the servo valve gain factor; u is the servo valve control voltage; n is the ratio of the cross sectional areas of a rod cavity and a rodless cavity of the hydraulic cylinder; a _p1 is the cross section area of a rodless cavity of the hydraulic cylinder;

The first constructor is:

g₁(x₁)＝2(1+n²)A_p1β_e/V (9)

Wherein β _e is the effective bulk modulus; v is the total volume of the hydraulic cylinder;

The second constructor is:

g₂(x₁)＝2β_e[(1+n)C_ip+C_ep]/V (10)

wherein C _ip is the internal leakage coefficient; c _ep is the leakage coefficient;

The third constructor is:

Wherein k _d is a reduced flow coefficient; p _s is the oil supply pressure;

The total volume of the hydraulic cylinder is as follows:

V＝V_g1+A_p1L₀+A_p1x₁+V_g2+A_p2(L-L₀)-A_p2x₁ (12)

Wherein V _g1 is the volume of an oil inlet flow passage of the hydraulic cylinder; v _g2 is the volume of an oil return flow passage of the hydraulic cylinder; l is the total stroke of a hydraulic cylinder rod; l ₀ is the initial position of a hydraulic cylinder rod; a _p2 is the cross-sectional area of the rod cavity of the hydraulic cylinder respectively.

Preferably, in step S12, a state observation equation of the extended fifth-order hydraulic servo position control system is established, specifically:

To accurately observe the unknown state x ₂ and disturbance terms f _x and f _p, the state space equation (8) of the hydraulic servo position control system is expanded to a five-order system expressed by z, namely z＝[z₁,z₂,z₃,z₄,z₅]^T＝[x₁,x₂,x₃,f_x,f_p]^T; is set For the estimated value,/>To estimate errors, i.e. >The state observation equation of the extended fifth-order system is obtained as follows:

Wherein, For the estimated value of the output position of the cylinder rod of the hydraulic cylinder,/>Is a derivative thereof; /(I)Is the estimated value of the moving speed of the cylinder rod of the hydraulic cylinder,/>Is a derivative thereof; /(I)Is an estimate of load pressure,/>Is a derivative thereof; /(I)Is the estimated value of disturbance term f _x,/>Is a derivative thereof; /(I)Is the estimated value of disturbance term f _p,/>Is a derivative thereof; /(I)An estimation error of the output position of the cylinder rod of the hydraulic cylinder; /(I)An estimated error for the load pressure; /(I)A first constructor which is a five-order system; /(I)A second constructor which is a fifth-order system; a third constructor which is a fifth order system; /(I) Is an extended state observer parameter;

Setting an i-th state estimation error State 3 estimation error/>State 4 estimation error/>State 5 estimation error/>Input state coefficient matrix estimation error vector of five-order systemNamely, the state estimation error vector is epsilon= [ epsilon ₁,ε₂,ε₃,ε₄,ε₅]^T, and the state estimation error vector of the five-order system is:

Wherein, the state of the epsilon fifth-order system estimates an error vector, Is a derivative thereof; a _ε is a state estimation error vector coefficient matrix; /(I)Estimating an error vector for an input state coefficient matrix of a five-order system; Estimating an error vector for a disturbance term matrix of a fifth-order system; /(I) An input state coefficient matrix containing an estimated state for a five-order system; g _e (z, u) is an input state coefficient matrix of the five-order system without estimated states; h ₄ (t) is the derivative of the system-unmodeled friction with the external disturbance term f _x; h ₅ (t) is the derivative of disturbance term f _p caused by modeling errors of the flow of the system valve and internal and external leakage and the change of system parameters;

Therefore, only the extended state observer parameters need to be guaranteed All eigenvalues of the state estimation error vector coefficient matrix a _ε have negative real parts by increasing/>The values of the latter two terms are made to approach infinity, and the hydraulic servo position control system is asymptotically stable in continuous time according to the Hurwitz criterion.

Preferably, in step S13, a backward difference method is used to establish a discretized state space equation of the third-order hydraulic servo position control system, so as to accurately predict a track tracking error in a real-time motion process, specifically:

Setting the current sampling time as kT _s,T_s as a sampling period; according to a backward difference method, a discretization state space equation of the hydraulic servo position control system is obtained as follows:

Wherein, C= [100] is the output matrix of the third-order system state space equation; a _k is a third-order system state vector coefficient matrix; g _k is a three-order system input vector coefficient matrix; Γ _k is a third-order system disturbance term matrix; y (k) is the predicted output of the discretized state space equation at the time of kT _s;

Setting a prediction time domain as N, and observing the state x ₂ and disturbance terms f _x and f _p at the moment of the current sampling time kT _s in real time according to a state observation equation of a fifth-order system after expansion of a formula (13); the amount of change of the disturbance term in the prediction time domain is zero, i.e., Δf (k+i) =0 _2×1 (i=1, 2,.., N), where Δf= [ Δf _xΔf_p]^T, specifically:

f(k+i)＝f(k)(i＝1,2,...,N) (16)

Wherein f (k+i) is a disturbance term vector of a system prediction time domain (k+i) T _s moment; f (k) is a disturbance term vector at the moment of the current sampling time kT _s of the system; i is the system prediction time domain number;

The hydraulic servo position control system discretization state space equation of the formula (15) is brought into the formula (16), and the state observation equation of the five-order system after the expansion of the formula (13) is combined, so that the predicted output at the time of a predicted time domain (k+N) T _s is obtained as follows:

Wherein y (k+N) is the predicted output of the discretized state space equation at the time (k+N) T _s; q is the predicted time domain number; a _k+i is a state vector coefficient matrix of the third-order system at the time of the prediction time domain (k+i) T _s; g _k+q-1 is an input vector coefficient matrix of the third-order system at the time of the prediction time domain (k+i) T _s; to estimate a state vector; /(I) Estimating disturbance term vectors;

Therefore, at the current sampling time kT _s, the predicted output position at the time (k+n) T _s is obtained according to the above equation, so as to accurately predict the track tracking error during the real-time motion.

Preferably, step S14 is based on a variable input control method of a model, and the determining a reference track of a state space equation of a hydraulic servo position control system specifically includes:

The model-based variable input control method obtains a reference track compensation term delta x' _r through the position, the speed and the acceleration terms of an initial reference track x _r so as to form an updated reference track The output of the hydraulic servo position control system after the reference track compensation term Deltax' _r is added is more approximate to the initial reference track x _r by utilizing the characteristics of the feedback controller; after a variable input control method based on a model is added into a hydraulic servo position control system, the compensation term of the variable input control method to the reference track is as follows:

wherein Δx' _r is a compensation term of the model-based variable input control method to the reference trajectory.

It is preferable that the track following error e (k+n) is set in step S22, specifically:

Setting the track tracking error as e=x _r-x_p, and obtaining the predicted tracking error at the time (k+N) T _s according to a predicted output equation of a third-order system of the formula (17) as follows:

e(k+N)＝x_r(k+N)-x_p(k+N) (19)

Wherein e (k+N) is the sampling time (k+N) T _s, and the tracking error is predicted; x _r (k+N) is the reference trace at the time of sampling time (k+N) T _s; x _p (k+N) is the predicted output position at the time of sampling time (k+N) T _s;

Setting the control time domain as N _p < N, adding the compensation term Deltaτ (k+N _p) on the basis of the original sampling time (k+N _p)T_s) time τ, wherein the predicted output position at the sampling time (k+N) T _s also generates a corresponding variable Deltax _p (k+N), combining the sensitivity factor S _τ, and the output position variable Deltax _p (k+N) at the sampling time (k+N) T _s is as follows:

Δxp(k+N)＝S_τΔτ(k+N_p) (20)

Assuming that the predicted tracking errors are each generated by a time variable of τ, i.e., Δx _p (k+n) =e (k+n), specifically:

e(k+N)＝S_τΔτ(k+N_p) (21)

Where e (k+N) is the predicted tracking error at time T _s of the sampling time (k+N).

Preferably, the reference track compensation item obtained in step S31 is obtained in step S32, and is used for closed-loop control of a hydraulic servo position control system, and verifying the stability of the system, specifically:

The hydraulic servo position control system adopts PID to carry out feedback control, so that the initial stability of the closed loop system is ensured; further verifying the stability of the hydraulic servo position control system after adding the compensation term delta tau (k+N _p) on the basis of tau;

Reference track set with N _r reference points Predicted output sequences without addition of the compensation term Δτ (k+np) and with addition of the compensation term Δτ (k+n _p) are/>, respectivelyThe method comprises the following steps:

Wherein R is a reference track with a reference point N _r; A predicted output sequence when no compensation term is added; /(I) A predicted output sequence added with compensation items; x _r (k) is the kth element of the reference track with the reference point N _r; x _r (k+1) is the (k+1) th element of the reference track with the reference point N _r; x _r(k+N_r -1) is the (k+N _r -1) th element of the reference track when the reference point is N _r; outputting the (k+1) th element of the sequence for prediction when no compensation term is added; /(I) Outputting the (k+2) th element of the sequence for prediction when no compensation term is added; /(I)A (k+N _r) th element of the predicted output sequence when no compensation term is added; Outputting the (k+1) th element of the sequence for the prediction after adding the compensation term; /(I) Outputting the (k+2) th element of the sequence for the prediction after adding the compensation term; /(I)The (k+N _r) th element of the predicted output sequence after adding the compensation term;

Setting predicted output deviation without adding compensation term And adding a compensation term to the predicted output biasThe method comprises the following steps:

Wherein, A predicted output bias for which no compensation term is added; /(I)Predicted output bias for adding compensation term;

the compensation term Δτ (k+n _p) for parameter τ according to equation (4) and equation (23) above:

when the condition 0 < (1-S _τ α) < 1 is satisfied, taking absolute values of two sides of the formula (24) simultaneously, and performing scaling by using a scaling method to obtain the product:

When the above formula (25) is established, the condition is satisfied:

0＜S_τα＜1 (26)

therefore, when the above formula (26) is established, And/>The relationship between them satisfies equation (25), i.e., the system is stable after adding the compensation term Δτ (k+n _p).

Compared with the prior art, the invention has the following beneficial effects:

(1) Compared with the prior art, the control method based on the sensitivity can accurately reveal the mapping relation between the nonlinear model parameter variation and the output variation, realizes accurate control based on the sensitivity, and greatly improves the control precision.

(2) According to the variable input compensation control method based on sensitivity, disclosed by the invention, the hydraulic position control system parameters are compensated in real time through predicting the tracking error, the problem that the optimal parameters of the system parameters are difficult to determine under a time-varying discontinuous working condition is solved, and the response speed and stability of the system are greatly improved.

(3) The sensitivity expansion method is applied to the field of hydraulic servo control, and a reliable method capable of meeting actual application requirements is provided for an optimal parameter matching strategy under a time-varying discontinuous working condition.

Drawings

FIG. 1 is a flow chart of a sensitivity-based variable input compensation control method for a hydraulic servo position control system of the present invention;

FIG. 2 is a block diagram of a motion platform of the hydraulic drive unit of the present invention;

FIG. 3 is a schematic view of a servo valve controlled hydraulic cylinder of the hydraulic drive unit motion platform of the present invention;

FIG. 4 is a schematic diagram of a sensitivity-based variable input compensation control of the present invention;

FIG. 5 is a diagram of a dual-cylinder centering performance test platform of the present invention;

FIG. 6 is a graph of parameter compensation amount experiment and track tracking error experiment under a sinusoidal track of varying frequency and amplitude in accordance with the present invention;

Fig. 7 is a parameter compensation amount experimental curve and a track tracking error experimental curve under a random track of the present invention.

Detailed Description

Exemplary embodiments, features and aspects of the present invention will be described in detail below with reference to the attached drawings. In the drawings, like reference numbers indicate identical or functionally similar elements. Although various aspects of the embodiments are illustrated in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated.

The embodiment of the invention provides a variable input compensation control method of a hydraulic servo position control system based on sensitivity, which is shown in fig. 1, wherein modeling is carried out according to a typical hydraulic servo position control system, a reference track of a state space equation of the hydraulic servo position control system is updated through the variable input control method based on the model, a mapping relation between the parameter variation of the state space equation of the hydraulic servo position control system after the updating of the reference track and the output variation is obtained based on the sensitivity, real-time compensation of the parameter of the variable input control method is realized, and stability is verified through analyzing the relation between track tracking errors before and after compensation, so that the variable input compensation control of the hydraulic servo position control system is completed; it comprises the following steps:

Step S1: modeling is carried out according to a typical hydraulic servo position control system, and a reference track of a state space equation of the hydraulic servo position control system is updated through a variable input control method based on the model;

A typical hydraulic servo position control system of an embodiment of the present invention is shown in fig. 2; the hydraulic driving unit motion platform structure diagram is the most representative hydraulic servo position control system motion platform in industrial application, and mainly comprises a hydraulic cylinder 2, a servo valve 1, a position sensor 3 and a force sensor 4.

Fig. 3 is a schematic diagram of a servo valve 1 control hydraulic cylinder 2 of a hydraulic driving unit motion platform of the present invention; the load pressure and the cylinder rod movement displacement of the tail end of the hydraulic drive unit are respectively collected in real time through the force sensor 4 and the position sensor 3, and the difference between the expected track and the cylinder rod movement displacement collected by the position sensor 3 is used as a control signal of the opening of the servo valve 1, so that the real-time control of the servo valve 1 on the hydraulic drive unit is realized.

In fig. 3, 5 is a comparator 5.

Step S11: mathematical modeling is carried out by using a typical hydraulic servo position control system, and a state space equation of the hydraulic servo position control system is obtained, specifically:

the hydraulic servo position control system is a typical servo valve 1 control system and is set Wherein x _p is the output position of the 2 cylinder rod of the hydraulic cylinder,/>For the moving speed of the cylinder rod of the hydraulic cylinder 2, P _L is load pressure, P _L＝P₁-nP₂, n is the ratio of the cross sectional areas of the rod cavity and the rod cavity of the hydraulic cylinder 2, n=A _p2/A_p1,A_p1 and A _p2 are the cross sectional areas of the rod cavity and the rod cavity of the hydraulic cylinder 2 respectively, and P ₁ and P ₂ are the pressure of the rod cavity of the hydraulic cylinder 2 and the pressure of the rod cavity of the hydraulic cylinder 2 respectively; the state space equation of the hydraulic servo position control system is as follows:

Wherein x ₁ is the output position of the cylinder rod of the hydraulic cylinder 2, Is a derivative thereof; x ₂ is the moving speed of the 2 cylinder rod of the hydraulic cylinder,/>Is a derivative thereof; x ₃ is the load pressure,/>Is a derivative thereof; k is load stiffness; b _p is the viscous damping coefficient; m _t is equivalent mass; g ₁(x₁) is a first constructor; g ₂(x₁) is a second constructor; g ₃(x₁,x₃, u) is a third constructor; f _x is the friction force and external disturbance term of the system which is not modeled; f _p is a disturbance term caused by modeling errors of the flow of the system valve and internal and external leakage and system parameter changes; k _axv is the gain coefficient of the servo valve 1; u is the control voltage of the servo valve 1; n is the ratio of the cross sectional areas of a rod cavity and a rodless cavity of the hydraulic cylinder 2; a _p1 is the cross-sectional area of the rodless cavity of the hydraulic cylinder 2.

The first constructor is:

g₁(x₁)＝2(1+n²)A_p1β_e/V (2)

Wherein β _e is the effective bulk modulus; v is the total volume of the hydraulic cylinder 2.

The second constructor is:

g₂(x₁)＝2β_e[(1+n)C_ip+C_ep]/V (3)

Wherein C _ip is the internal leakage coefficient; c _ep is the leakage coefficient.

The third constructor is:

wherein k _d is a reduced flow coefficient; p _s is the oil supply pressure.

The total volume of the hydraulic cylinder 2 is as follows:

Wherein V _g1 is the volume of an oil inlet flow passage of the hydraulic cylinder 2; v _g2 is the volume of an oil return flow passage of the hydraulic cylinder 2; l is the total stroke of a cylinder rod of the hydraulic cylinder 2; l ₀ is the initial position of a cylinder rod of the hydraulic cylinder 2; a _p2 is the cross-sectional area of the rod cavity of the hydraulic cylinder 2.

Step S12: based on a state space equation of the hydraulic servo position control system, two disturbance terms are expanded, and a state observation equation of the expanded five-order hydraulic servo position control system is established, specifically comprising the following steps:

To accurately observe the unknown state x ₂ and disturbance terms f _x and f _p, the state space equation (1) of the hydraulic servo position control system is expanded to a five-order system expressed by z, namely z＝[z₁,z₂,z₃,z₄,z₅]^T＝[x₁,x₂,x₃,f_x,f_p]^T; is set For the estimated value,/>To estimate errors, i.e. >The state observation equation of the extended fifth-order system is obtained as follows:

Wherein, Output position estimation value for hydraulic cylinder 2 cylinder rod,/>Is a derivative thereof; /(I)Is the estimated value of the moving speed of the cylinder rod of the hydraulic cylinder 2,/>Is a derivative thereof; /(I)Is an estimate of load pressure,/>Is a derivative thereof; /(I)Is the estimated value of disturbance term f _x,/>Is a derivative thereof; /(I)Is the estimated value of disturbance term f _p,/>Is a derivative thereof; /(I)An estimation error of the output position of the cylinder rod of the hydraulic cylinder 2; /(I)An estimated error for the load pressure; /(I)A first constructor which is a five-order system; /(I)A second constructor which is a fifth-order system; a third constructor which is a fifth order system; /(I) Is an extended state observer parameter.

Setting an i-th state estimation errorState 3 estimation error/>State 4 estimation error/>State 5 estimation error/>Input state coefficient matrix estimation error vector of five-order systemNamely, the state estimation error vector is epsilon= [ epsilon ₁,ε₂,ε₃,ε₄,ε₅]^T, and the state estimation error vector of the five-order system is:

Wherein, the state of the epsilon fifth-order system estimates an error vector, Is a derivative thereof; a _ε is a state estimation error vector coefficient matrix; /(I)Estimating an error vector for an input state coefficient matrix of a five-order system; Estimating an error vector for a disturbance term matrix of a fifth-order system; /(I) An input state coefficient matrix containing an estimated state for a five-order system; g _e (z, u) is an input state coefficient matrix of the five-order system without estimated states; h ₄ (t) is the derivative of the system-unmodeled friction with the external disturbance term f _x; h ₅ (t) is the derivative of the disturbance term f _p caused by modeling errors of the system valve flow and internal and external leaks and changes of system parameters.

The state estimation error vector coefficient matrix a _ε is:

Step S13: based on the observed value of the state observation equation, a backward difference method is used for establishing a discretization state space equation of a third-order hydraulic servo position control system, so as to accurately predict the track tracking error in the real-time motion process, and the method specifically comprises the following steps:

Wherein, C= [10 ] is the output matrix of the state space equation of the third-order system; a _k is a third-order system state vector coefficient matrix; g _k is a three-order system input vector coefficient matrix; Γ _k is a third-order system disturbance term matrix; y (k) is the predicted output of the discretized state space equation at time kT _s.

The third-order system state vector coefficient matrix a _k is:

the third-order system input vector coefficient matrix G _k is:

G_k＝[0,0,k_axvg₃(x₁,x₃,u)T_s]^T (11)。

The third-order system perturbation term matrix Γ _k is:

Γ_k＝[0,f_xT_s,f_pT_s]^T (12)。

Setting a prediction time domain as N, and observing the state x ₂ and disturbance terms f _x and f _p at the moment of the current sampling time kT _s in real time according to a state observation equation of a fifth-order system after expansion of the formula (6); the amount of change of the disturbance term in the prediction time domain is zero, i.e., Δf (k+i) =0 _2×1 (i=1, 2,.., N), where Δf= [ Δf _xΔf_p]^T, specifically:

f(k+i)＝f(k)(i＝1,2,...,N) (13)

wherein f (k+i) is a disturbance term vector of a system prediction time domain (k+i) T _s moment; f (k) is a disturbance term vector at the moment of the current sampling time kT _s of the system; i is the system prediction time domain number.

The hydraulic servo position control system discretization state space equation of the formula (9) is brought into the formula (13), and the state observation equation of the five-order system after the expansion of the formula (6) is combined, so that the predicted output at the time of a predicted time domain (k+N) T _s is obtained as follows:

Wherein y (k+N) is the predicted output of the discretized state space equation at the time (k+N) T _s; q is the predicted time domain number; a _k+i is a state vector coefficient matrix of the third-order system at the time of the prediction time domain (k+i) T _s; g _k+q-1 is an input vector coefficient matrix of the third-order system at the time of the prediction time domain (k+i) T _s; to estimate a state vector; /(I) To estimate the disturbance term vector.

Estimating a state vectorThe method comprises the following steps:

Estimating disturbance term vector The method comprises the following steps:

Step S14: the variable input control method based on the model determines a reference track of a state space equation of a hydraulic servo position control system, and specifically comprises the following steps:

The updated state space equation reference track of the hydraulic servo position control system is as follows:

Wherein, A reference track updated by a state space equation; x _r is the initial reference trajectory of the state space equation; τ= [ τ _x τ_v τ_a]^T ] is a model-based variable input control method parameter vector; τ _x is the position item parameter; τ _v is a speed term parameter; τ _a is the acceleration term parameter; /(I)Compensating term coefficient vectors for a model-based variable input control method; /(I)A first derivative of an initial reference track of a state space equation; /(I)And initializing a reference track second derivative for the state space equation.

Step S2: and obtaining the mapping relation between the state space equation parameter variable quantity and the output variable quantity of the hydraulic servo position control system after the reference track is updated based on the sensitivity.

Step S21: the sensitivity expansion is applied to the field of hydraulic servo control, so that the implicit constraint between the nonlinear model parameters and the output of the hydraulic servo position control system is solved, and the real-time compensation of the parameter tau of a variable input control method based on a model is realized; the discretized state space equation of the hydraulic servo position control system after the model-based variable input control method is added is as follows:

H_k(x(k+1),x(k),u(k),p(k),τ)＝0_3×1 (19)

Wherein H _k is a discretized state space equation; x (k+1) is a state variable at time point T _s of the sampling time (k+1); x (k) is a state variable at the moment of sampling time kT _s; u (k) is the control voltage of the servo valve 1 at the moment of sampling time kT _s; p (k) is a system parameter vector at the moment of sampling time kT _s; k is the sampling time number; t _s is the sampling period.

Wherein Δx _p is the output variation; delta tau is the variable quantity of parameters of a variable input control method based on a model; a sensitivity factor of a control method parameter tau is input for model-based variables; /(I) Is a position item sensitivity factor; /(I)Is a speed term sensitivity factor; /(I)Is the acceleration term sensitivity factor.

Step S22: setting a track tracking error as e (k+n), setting the track tracking error as e=x _r-x_p, and obtaining a predicted tracking error at the time (k+n) T _s according to a predicted output equation of a third-order system of formula (14) as follows:

e(k+N)＝x_r(k+N)-x_p(k+N) (21)

Wherein e (k+N) is the sampling time (k+N) T _s, and the tracking error is predicted; x _r (k+N) is the reference trace at the time of sampling time (k+N) T _s; x _p (k+n) is the predicted output position at time T _s of the sample time (k+n).

Δx_p(k+N)＝S_τΔτ(k+N_p) (22)。

e(k+N)＝S_τΔτ(k+N_p) (23)

The compensation term Δτ (k+n _p) for the determined parameter τ is:

Δτ(k+N_p)＝αe(k+N) (24)

The method comprises the steps of forming a variable input compensation control method based on sensitivity by taking Deltaτ (k+N _p) as a compensation term of a parameter tau at sampling time (k+N _p)T_s), taking e (k+N) as a track tracking error at sampling time (k+N) T _s, taking alpha= [ a _x a_v a_a]^T ] as a compensation gain coefficient of the variable input compensation control method based on sensitivity, taking a _x as a position term compensation gain coefficient, taking a _v as a speed term compensation gain coefficient, taking a _a as an acceleration term compensation gain coefficient, taking N as a system prediction time domain and taking N _p as a system control time domain.

Step S3: real-time compensation of parameters of the variable input control method is realized, stability is verified by analyzing the relation between track tracking errors before and after compensation, and variable input compensation control of the hydraulic servo position control system is completed.

FIG. 4 is a schematic diagram of a sensitivity-based variable input compensation control of the present invention; and (3) carrying out real-time observation on the unknown state and disturbance item of the system by adopting an extended observer, thereby accurately predicting a model, further accurately predicting the track tracking error in the real-time motion process, and carrying out real-time compensation on the parameter tau of the variable input control method based on the model by combining the sensitivity factor.

Step S31: simultaneously transpose the two ends of the formula (24) obtained in the step S22, and compensating the term coefficient vector by the variable input control method based on the model by multiplying the two endsThe method comprises the following steps:

Wherein, The term coefficient vector is compensated for the model-based variable input control method at time (k+N _p)T_s).

Wherein, The compensation term for the reference trajectory is a compensation term for the parameter τ, Δτ (k+n _p).

wherein Δx _r(k+N_p) is the compensation term for the state space equation reference trajectory at the time of sampling (k+n _p)T_s).

Step S32: the reference track compensation item obtained in the step S31 is obtained and used for closed-loop control of a hydraulic servo position control system, and system stability is verified; the hydraulic servo position control system adopts PID to carry out feedback control, so that the initial stability of the closed loop system is ensured; further verifying the stability of the hydraulic servo position control system after adding the compensation term delta tau (k+N _p) on the basis of tau.

Reference track set with N _r reference pointsPredicted output sequences without addition of the compensation term Δτ (k+n _p) and with addition of the compensation term Δτ (k+n _p) are/>, respectivelyThe method comprises the following steps: /(I)

Wherein R is a reference track with a reference point N _r; A predicted output sequence when no compensation term is added; x _p n is the predicted output sequence after adding the compensation term; x _r (k) is the kth element of the reference track with the reference point N _r; x _r (k+1) is the (k+1) th element of the reference track with the reference point N _r; x _r(k+N_r -1) is the (k+N _r -1) th element of the reference track when the reference point is N _r; outputting the (k+1) th element of the sequence for prediction when no compensation term is added; /(I) Outputting the (k+2) th element of the sequence for prediction when no compensation term is added; /(I)A (k+N _r) th element of the predicted output sequence when no compensation term is added; Outputting the (k+1) th element of the sequence for the prediction after adding the compensation term; /(I) Outputting the (k+2) th element of the sequence for the prediction after adding the compensation term; /(I)The (k+N _r) th element of the predicted output sequence after adding the compensation term.

Predicted output sequence without addition of compensation term Deltaτ (k+N _p) within the sequence of reference point N _r The method comprises the following steps:

Wherein Λ is an estimated state vector coefficient matrix; to estimate a state vector; /(I) Is an input vector matrix; /(I)To include a disturbance term vector matrix.

The estimated state vector coefficient matrix Λ is:

input vector matrix The method comprises the following steps:

Comprising a matrix of disturbance term vectors The method comprises the following steps:

Wherein, The disturbance vector when the compensation term is not added.

Predicted output sequence after adding compensation term Deltaτ (k+N _p)The method comprises the following steps:

Wherein, The term vector is compensated for the reference trajectory.

Reference trajectory compensation term vectorThe method comprises the following steps: /(I)

The track tracking error after adding the compensation term delta tau (k+n _p) in the sequence of the reference point N _r is:

Wherein, Track tracking error after adding the compensation term delta tau (k+N _p); e (k+j) is the track tracking error before adding the compensation term Δτ (k+n _p); Δτ (k+j-1) is the prediction time domain (k+j-1) T _s time instant compensation term.

Based on the predictive tracking error at the time (k+n) T _s of the sampling time of equation (21), the above equation (35) is converted into:

Wherein, A predicted output bias for which no compensation term is added; /(I)Predicted output bias for adding compensation term.

The compensation term Δτ (k+n _p) for parameter τ according to equation (24) and equation (37) above:

when the condition 0 < (1-S _τ α) < 1 is satisfied, taking absolute values of two sides of the formula (38) simultaneously, and performing scaling by using a scaling method to obtain the product:

When the above formula (39) is satisfied, the condition is satisfied:

0＜S_τα＜1 (40)。

Therefore, when the above formula (40) is established, And/>The relation between the two values satisfies the formula (39), namely after the compensation term delta tau (k+N _p) is added, the system is stable, the value range of the compensation gain coefficient is determined, and the variable input compensation control of the hydraulic servo position control system is completed.

FIG. 5 is a diagram of a dual-cylinder centering performance test platform of the present invention; the personal computer and Speedgoat controller establish data transmission through Ethernet, and adopt Speedgoat controller real-time processing force sensor 4 and position sensor 33's real-time acquisition data, generate servo valve 1 control voltage, and utilize servo amplifier to convert control voltage signal into servo valve 1 acceptable current control signal, carry out the rectification simultaneously, guarantee control signal's stability.

FIG. 6 is a graph showing the parameter compensation amount experiment curve and the track tracking error experiment curve under the sine track with variable frequency and amplitude according to the invention; the method is used for verifying the working condition self-adaption capability of the sensitivity-based variable input compensation control method under the time-varying discontinuous working condition. In the two groups of experimental curves, the C1 curve is a PID error curve; c2 curve is PID+based on model variable input control error curve; the C3 curve is pid+model-based variable input control+sensitivity-based variable input compensation control error curve. Among sinusoidal tracks, the reference track is a sinusoidal signal of varying frequency and amplitude. Along with the change of working conditions, the variable input compensation control method based on the sensitivity can adjust the parameter compensation quantity of the variable input control method based on the model in real time, so that the compensation quantity of the reference track is adjusted on line. If the closed loop system is controlled by using only PID and a variable input control method based on a model, when the control effect reaches the optimum under the reference working condition, the track tracking error of C3 is difficult to be further reduced relative to C2, however, when the track tracking error of C2 is unsatisfactory after the working condition is changed, fortunately, the track tracking error of C3 can still be kept relatively low. As shown in Table 1, the root mean square value performance index of the track tracking error of the sinusoidal track with variable frequency and amplitude is reduced by 13.871% compared with the root mean square value index of C2 under the reference working condition under the condition of adding the variable input compensation control method based on sensitivity, and the maximum absolute value index of the track tracking error is reduced by 32.647%. When the working condition is changed, the reduction rate of the root mean square value index of C3 relative to C2 is more than 52%, the reduction rate of the track tracking error maximum absolute value index is more than 44%, and specific data are shown as the track tracking error maximum absolute value performance index of the frequency and amplitude variable sine track shown in table 2. Therefore, the variable input compensation control method based on the sensitivity realizes higher track tracking precision and working condition self-adaption capability by compensating the variable input parameters based on the model in real time, and solves the problem of uncertainty of the optimal parameters of the system in the time-varying discontinuous working condition.

TABLE 1 root mean square value Performance index for track tracking error for sinusoidal tracks of varying frequency and amplitude

TABLE 2 maximum absolute value Performance index of track tracking error for variable frequency and amplitude sinusoidal tracks

FIG. 7 is a graph showing the parameter compensation amount experiment curve and the track tracking error experiment curve under the random track of the present invention; the feasibility of the provided variable input compensation control method based on sensitivity under a random track is verified. In the random track, a random signal is used as a reference track. For random tracks, the variable input compensation control method based on sensitivity can still accurately adjust parameters of the variable input control method based on the model in real time, so that the compensation quantity of the reference track can be adjusted online. In addition, under the random track, C3 is still superior to C2 to a great extent, and the track tracking error is greatly reduced. The root mean square value index of C3 relative to C2 is reduced by 53.55% under the random track, the maximum absolute value index of track tracking error is reduced by 50.942%, similar to a sinusoidal track experiment, the reduction rate of the root mean square value index is above 52%, the reduction rate of the maximum absolute value index of track tracking error is above 44%, and specific data are shown as the root mean square value and the maximum absolute value performance index of track tracking error of the random track in table 3. Therefore, the sine track and random track experiments jointly show that the sensitivity-based variable input compensation control method compensates parameters of the model-based variable input control method in real time, so that the track tracking precision and the self-adaptive capacity to working conditions are greatly improved, and the feasibility of the sensitivity-based variable input compensation control method under different reference tracks is verified.

TABLE 3 track following error root mean square value and maximum absolute value Performance index for random tracks

The invention has the beneficial effects that: compared with the prior art, the sensitivity-based control method provided by the embodiment of the invention can accurately reveal the mapping relation between the nonlinear model parameter variation and the output variation, realizes accurate control based on sensitivity and greatly improves the control precision; the unknown state and disturbance of the system are observed in real time through the extended state observer, so that a prediction equation is accurately predicted, the track tracking error in the real-time motion process is accurately predicted, the hydraulic position control system parameters are compensated in real time by combining the prediction tracking error and the sensitivity factor, the problem that the optimal parameters of the system parameters are difficult to determine under the time-varying discontinuous working condition is solved, and the response speed and the stability of the system are greatly improved; the sensitivity expansion is applied to the field of hydraulic servo control, and a reliable method capable of meeting actual application requirements is provided for an optimal parameter matching strategy under a time-varying discontinuous working condition; the relation between the track tracking errors before and after the compensation term obtained by adding the sensitivity-based control method theoretically verifies the stability of the system and determines the value range of the compensation gain coefficient.

The above examples are only illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the scope of protection defined by the claims of the present invention without departing from the spirit of the present invention.

Claims

1. The variable input compensation control method of the hydraulic servo position control system based on the sensitivity is characterized by comprising the following steps of:

Wherein, A reference track updated by a state space equation; x _r is the initial reference trajectory of the state space equation; τ= [ τ _xτ_v τ_a]^T ] is a model-based variable input control method parameter vector; τ _x is the position item parameter; τ _v is a speed term parameter; τ _a is the acceleration term parameter; /(I)Compensating term coefficient vectors for a model-based variable input control method; /(I)A first derivative of an initial reference track of a state space equation; /(I)The second derivative of the initial reference track is the state space equation;

H_k(x(k+1),x(k),u(k),p(k),τ)＝0_3×1 (2)

Δτ(k+N_p)＝αe(k+N) (4)

2. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 1, characterized by: in step S11, mathematical modeling is performed by using a typical hydraulic servo position control system to obtain a state space equation of the hydraulic servo position control system, which specifically includes:

The first constructor is:

g₁(x₁)＝2(1+n²)A_p1β_e/V (9)

The second constructor is:

g₂(x₁)＝2β_e[(1+n)C_ip+C_ep]/V (10)

The third constructor is:

Wherein k _d is a reduced flow coefficient; p _s is the oil supply pressure;

The total volume of the hydraulic cylinder is as follows:

3. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 1, characterized by: in step S12, a state observation equation of the extended fifth-order hydraulic servo position control system is established, which specifically includes:

Setting an i-th state estimation error State 3 estimation error/>State 4 estimation errorState 5 estimation error/>Input state coefficient matrix estimation error vector of five-order systemNamely, the state estimation error vector is epsilon= [ epsilon ₁,ε₂,ε₃,ε₄,ε₅]^T, and the state estimation error vector of the five-order system is:

Wherein, the state of the epsilon fifth-order system estimates an error vector, Is a derivative thereof; a _ε is a state estimation error vector coefficient matrix; estimating an error vector for an input state coefficient matrix of a five-order system; Estimating an error vector for a disturbance term matrix of a fifth-order system; /(I) An input state coefficient matrix containing an estimated state for a five-order system; g _e (z, u) is an input state coefficient matrix of the five-order system without estimated states; h ₄ (t) is the derivative of the system-unmodeled friction with the external disturbance term f _x; h ₅ (t) is the derivative of disturbance term f _p caused by modeling errors of the flow of the system valve and internal and external leakage and the change of system parameters;

4. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 1, characterized by: in the step S13, a backward difference method is used for establishing a discretization state space equation of a third-order hydraulic servo position control system, so as to accurately predict the track tracking error in the real-time motion process, specifically:

Wherein, C= [ 10 ] is the output matrix of the state space equation of the third-order system; a _k is a third-order system state vector coefficient matrix; g _k is a three-order system input vector coefficient matrix; Γ _k is a third-order system disturbance term matrix; y (k) is the predicted output of the discretized state space equation at the time of kT _s;

Setting a prediction time domain as N, and observing the state x ₂ and disturbance terms f _x and f _p at the moment of the current sampling time kT _s in real time according to a state observation equation of a fifth-order system after expansion of a formula (13); the amount of change of the disturbance term in the prediction time domain is zero, i.e., Δf (k+i) =0 _2×1 (i=1, 2,.., N), where Δf= [ Δf _x Δf_p]^T, specifically:

f(k+i)＝f(k)(i＝1,2,...,N) (16)

5. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 1, characterized by: step S14 is based on a variable input control method of a model, and a reference track of a state space equation of a hydraulic servo position control system is determined, specifically:

6. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 1, characterized by: in step S22, a trajectory tracking error e (k+n) is set, specifically:

e(k+N)＝x_r(k+N)-x_p(k+N) (19)

Δx_p(k+N)＝S_τΔτ(k+N_p) (20)

e(k+N)＝S_τΔτ(k+N_p) (21)

7. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 1, characterized by: in step S32, the reference track compensation term obtained in step S31 is obtained, and is used for closed-loop control of a hydraulic servo position control system, and system stability is verified, specifically:

Wherein R is a reference track with a reference point N _r; A predicted output sequence when no compensation term is added; /(I) A predicted output sequence added with compensation items; x _r (k) is the kth element of the reference track with the reference point N _r; x _r (k+1) is the (k+1) th element of the reference track with the reference point N _r; x _r(k+N_r -1) is the (k+N _r -1) th element of the reference track when the reference point is N _r; /(I)Outputting the (k+1) th element of the sequence for prediction when no compensation term is added; /(I)Outputting the (k+2) th element of the sequence for prediction when no compensation term is added; /(I)A (k+N _r) th element of the predicted output sequence when no compensation term is added; /(I)Outputting the (k+1) th element of the sequence for the prediction after adding the compensation term; /(I)Outputting the (k+2) th element of the sequence for the prediction after adding the compensation term; /(I)The (k+N _r) th element of the predicted output sequence after adding the compensation term;

Setting predicted output deviation without adding compensation term And predicted output bias/>, incorporating compensation termThe method comprises the following steps:

When the above formula (25) is established, the condition is satisfied:

0＜S_τα＜1 (26)