Sensitivity-based variable input compensation control method for hydraulic servo position control system

Abstract

The present application relates to a kind of based on sensitivity hydraulic servo position control system variable input compensation control method, it includes: S1, according to typical hydraulic servo position control system modeling, the reference trajectory of the state space equation of hydraulic servo position control system is updated by variable input control method based on model;S2, based on sensitivity obtains the mapping relationship between the output variation and the parameter variation of the state space equation of hydraulic servo position control system reference trajectory updated;S3, the real-time compensation of variable input control method parameter is realized, and by analyzing the relationship between trajectory tracking error before and after compensation, stability is verified, and the variable input compensation control of hydraulic servo position control system is completed.The control method based on sensitivity of the present application can accurately reveal the relationship between the parameter variation and the output variation of nonlinear model;Variable input compensation control method based on sensitivity, through the real-time compensation of system parameter by predicting tracking error, has good working condition adaptive capacity under time-varying discontinuous working condition.

Description

Technical Field

[0001] This invention belongs to the field of fluid transmission and control technology, and specifically relates to a variable input compensation control method for a sensitivity-based hydraulic servo position control system. Background Technology

[0002] Hydraulic servo control systems, with their advantages of high load capacity and fast response speed, are widely used in mobile equipment such as aerospace, hydraulic legged robots, and industrial production. As the adaptability requirements of mobile equipment to complex and changing environments continue to increase, hydraulic servo control systems are needed to achieve high-precision control for various trajectory tracking tasks. However, due to the strong nonlinearity, time-varying parameters, and variable loads inherent in hydraulic systems, achieving high-precision trajectory tracking control with hydraulic servo control systems is quite difficult. Furthermore, high-precision trajectory tracking control of hydraulic servo control systems also faces the problem of optimal parameter uncertainty under time-varying and discontinuous operating conditions, making it difficult to achieve high-precision trajectory tracking control under all such conditions.

[0003] Given this fact, achieving high-precision trajectory tracking control in hydraulic servo position control systems has become a research hotspot for scholars worldwide in recent years. Researchers have proposed offline compensation-based control methods to achieve high-precision trajectory tracking control in hydraulic servo position control systems. Offline compensation control methods have significant advantages in trajectory tracking accuracy; however, in practical systems, they are highly sensitive to trajectory changes because they cannot adjust optimal parameters in real time. To overcome these shortcomings, online compensation control methods have received widespread attention. While online compensation control methods offer significant advantages in adaptability, they are mostly model-based, facing implicit constraints between system nonlinear model parameters and states. This limits current control methods in the field of hydraulic servo position control for addressing the uncertainty of optimal parameters and trajectory tracking accuracy under time-varying discontinuous conditions. To overcome these limitations, researchers have proposed feedback linearization methods, eliminating nonlinear terms to obtain linear relationships. Furthermore, sensitivity analysis, which accurately reveals the mapping relationship between nonlinear model parameters and states, has also received widespread attention from researchers in recent years.

[0004] Sensitivity analysis is currently widely used in hydraulic servo systems, electromagnetics, and batteries, primarily to analyze the impact of system parameters on control performance and optimize structural parameter design. In contrast, sensitivity-based control methods have received relatively little attention in various research fields. Furthermore, research reveals that the relationship between sensitivity and hydraulic servo control has not yet been specifically investigated by researchers.

[0005] In summary, there is an urgent need for a high-precision variable input compensation control method for nonlinear models in hydraulic servo position control systems. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a sensitivity-based variable input compensation control method for hydraulic servo position control systems. The sensitivity-based control method can accurately reveal the relationship between the changes in nonlinear model parameters and the changes in output. The sensitivity-based variable input compensation control method compensates system parameters in real time by predicting tracking errors, and has good adaptability under time-varying discontinuous operating conditions.

[0007] To achieve the above objectives, the present invention discloses the following technical solution:

[0008] A sensitivity-based variable input compensation control method for a hydraulic servo position control system, comprising:

[0009] S1: Model a typical hydraulic servo position control system and update the reference trajectory of the state space equation of the hydraulic servo position control system through a model-based variable input control method;

[0010] S11: Mathematical modeling is performed using a typical hydraulic servo position control system to obtain the state-space equation of the hydraulic servo position control system.

[0011] S12: Based on the state-space equation of the hydraulic servo position control system, two disturbance terms are extended to establish the state observation equation of the extended fifth-order hydraulic servo position control system.

[0012] S13: Based on the observed values ​​of the state observation equation, the backward difference method is used to establish the discretized state space equation of the third-order hydraulic servo position control system, thereby accurately predicting the trajectory tracking error in the real-time motion process;

[0013] S14: A model-based variable input control method is used to determine the reference trajectory of the state-space equations of the hydraulic servo position control system. The updated reference trajectory of the state-space equations of the hydraulic servo position control system is as follows:

[0014]

[0015] in, The reference trajectory after the state-space equations are updated; x r The initial reference trajectory for the state-space equations; τ = [τ x τ v τ a ] T τ represents the parameter vector for a model-based variable input control method. x For positional parameters; τ v For the velocity term parameter; τ aFor acceleration parameters; This represents the coefficient vector of the compensation term in a model-based variable input control method. The first derivative of the initial reference trajectory in the state-space equation; The second derivative of the initial reference trajectory in the state-space equation;

[0016] S2: Based on sensitivity, obtain the mapping relationship between the parameter changes and output changes of the state-space equation of the hydraulic servo position control system after the reference trajectory update;

[0017] S21: Extending sensitivity to the field of hydraulic servo control, solving the implicit constraints between the nonlinear model parameters and output of the hydraulic servo position control system, and realizing real-time compensation of the parameter τ of the model-based variable input control method; the discretized state-space equation of the hydraulic servo position control system after adding the model-based variable input control method is:

[0018] H k (x(k+1),x(k),u(k),p(k),τ)=0 3×1 (2)

[0019] Among them, H k The state-space equation is discretized; x(k+1) is the sampling time (k+1)T. s The state variable at time point; x(k) is the sampling time kT s The state variable at time; u(k) is the sampling time kT s The servo valve control voltage is timed; p(k) is the sampling time kT. s Time-based system parameter vector; k is the sampling time number; T s The sampling period;

[0020] Performing a first-order Taylor expansion on the above equation, the mapping relationship between the parameter τ change and the output change in the model-based variable input control method is determined as follows:

[0021]

[0022] Where, Δx p Δτ represents the output change; Δτ represents the parameter change of the model-based variable input control method. For the model-based variable input control method, the sensitivity factor of parameter τ is given. For the position term sensitivity factor; For the velocity term sensitivity factor; For the acceleration term, the sensitivity factor is used.

[0023] S22: Set the trajectory tracking error to e(k+N), and determine the compensation term Δτ(k+N) for parameter τ. p )for:

[0024] Δτ(k+N p )=αe(k+N) (4)

[0025] Wherein, Δτ(k+N) p ) is the parameter τ during the sampling time (k+N) p )T s The compensation term at each time step forms a sensitivity-based variable input compensation control method; e(k+N) is the sampling time (k+N)T. s Time-tracking error; α = [a x a v a a ] T To compensate the gain coefficient for a sensitivity-based variable input compensation control method; a x a is the position term compensation gain coefficient; v This is the gain coefficient for velocity term compensation; a a N represents the acceleration term compensation gain coefficient; N is the system prediction time domain; N p For system control time domain;

[0026] S3: Real-time compensation of parameters of variable input control method is achieved, and the stability is verified by analyzing the relationship between trajectory tracking error before and after compensation, thus completing the variable input compensation control of hydraulic servo position control system;

[0027] S31: Transpose both sides of equation (4) obtained in step S22, and multiply both sides by the compensation term coefficient vector of the model-based variable input control method. Specifically:

[0028]

[0029] in, Sampling time (k+N) p )T s The compensation term coefficient vector of the model-based variable input control method at any given time;

[0030] Further refinement yields the compensation term Δτ(k+N) for parameter τ. p The compensation term for the reference trajectory is:

[0031]

[0032] in, The compensation term Δτ(k+N) for parameter τ p Compensation terms for the reference trajectory;

[0033] A sensitivity-based variable input compensation control method is used to perform real-time compensation of the parameter τ of the model-based variable input control method, resulting in the compensation term that ultimately compensates to the reference trajectory of the state-space equation:

[0034]

[0035] Where, Δx r (k+N p ) represents the sampling time (k+N) p )T s The compensation term for the reference trajectory in the state-space equation at any given time;

[0036] S32: Obtain the reference trajectory compensation term obtained in step S31, use it for closed-loop control of the hydraulic servo position control system, verify system stability, determine the value range of the compensation gain coefficient, and complete the variable input compensation control of the hydraulic servo position control system.

[0037] Preferably, in step S11, a typical hydraulic servo position control system is used for mathematical modeling to obtain the state-space equation of the hydraulic servo position control system, specifically:

[0038] The hydraulic servo position control system is a typical servo valve control system, with settings... Where x p This refers to the output position of the hydraulic cylinder rod. P is the moving speed of the hydraulic cylinder rod. L For load pressure, P L =P1-nP2, where n is the ratio of the cross-sectional area of ​​the rod-side chamber to the rodless chamber of the hydraulic cylinder, n = A p2 / A p1 A p1 and A p2 Let P1 and P2 be the cross-sectional areas of the rodless and rod-side chambers of the hydraulic cylinder, respectively, and let P1 and P2 be the pressures in the rodless and rod-side chambers of the hydraulic cylinder, respectively. The state-space equation of the hydraulic servo position control system is:

[0039]

[0040] Where x1 is the output position of the hydraulic cylinder rod. Its derivative; x2 is the moving speed of the hydraulic cylinder rod. Its derivative; x3 is the load pressure. Its derivative; K is the load stiffness; B p m is the viscous damping coefficient. t For equivalent mass; g1(x1) is the first constructor; g2(x1) is the second constructor; g3(x1,x3,u) is the third constructor; f x For the frictional force and external disturbance terms that are not modeled in the system; f p Modeling errors in system valve flow and internal / external leakage, as well as disturbance terms caused by changes in system parameters; k axvis the servo valve gain coefficient; u is the servo valve control voltage; n is the ratio of the cross-sectional area of ​​the rod-side chamber to the rodless chamber of the hydraulic cylinder; A p1 This refers to the cross-sectional area of ​​the rodless chamber of the hydraulic cylinder.

[0041] The first constructor is:

[0042] g1(x1)=2(1+n 2 A p1 β e / V (9)

[0043] Where, β e V is the effective bulk modulus; V is the total volume of the hydraulic cylinder.

[0044] The second constructor is:

[0045] g2(x1)=2β e [(1+n)C ip +C ep ] / V (10)

[0046] Among them, C ip C is the internal leakage coefficient; ep The external leakage coefficient;

[0047] The third constructor is:

[0048]

[0049] Where, k d For the calculated flow coefficient; P s For oil supply pressure;

[0050] The total volume of the hydraulic cylinder is:

[0051] V = V g1 +A p1 L0+A p1 x1+V g2 +A p2 (L-L0)-A p2 x1 (12)

[0052] Among them, V g1 V is the volume of the hydraulic cylinder's oil inlet passage. g2 L is the volume of the hydraulic cylinder return oil passage; L is the total stroke of the hydraulic cylinder rod; L0 is the initial position of the hydraulic cylinder rod; A p2 These are the cross-sectional areas of the rod chamber of the hydraulic cylinder.

[0053] Preferably, in step S12, the state observation equations of the extended fifth-order hydraulic servo position control system are established as follows:

[0054] To accurately observe the unknown state x2 and the disturbance term fx and f p The state-space equation (8) of the hydraulic servo position control system is extended to a fifth-order system denoted by z, i.e., z = [z1, z2, z3, z4, z5]. T =[x1,x2,x3,f x ,f p ] T ;set up This is an estimated value. To estimate the error, i.e. The state-observation equations of the extended fifth-order system are as follows:

[0055]

[0056] in, This is an estimated value for the output position of the hydraulic cylinder rod. Its derivative; This is an estimated value for the movement speed of the hydraulic cylinder rod. Its derivative; This is an estimate of the load pressure. Its derivative; For the disturbance term f x The estimated value, Its derivative; For the disturbance term f p The estimated value, Its derivative; This represents the estimation error of the hydraulic cylinder rod output position; This represents the estimation error of the load pressure; This is the first constructor for a fifth-order system; This is the second constructor for a fifth-order system; This is the third constructor for a fifth-order system; To extend the parameters of the state observer;

[0057] Set the estimation error of the i-th state Third-state estimation error Fourth state estimation error Fifth state estimation error The error vector of the input state coefficient matrix estimation of a fifth-order system That is, the state estimation error vector is ε=[ε1,ε2,ε3,ε4,ε5] T The state estimation error vector of the fifth-order system is:

[0058]

[0059] Wherein, the state estimation error vector of the ε-order fifth-order system Its derivative; A εThe coefficient matrix of the state estimation error vector; The error vector is the input state coefficient matrix estimation vector of a fifth-order system. The error vector is estimated from the disturbance term matrix of the fifth-order system. G is the input state coefficient matrix of a fifth-order system, including the estimated state; e (z,u) is the input state coefficient matrix of the fifth-order system without estimated states; h4(t) is the unmodeled friction force and external disturbance term f. x The derivative of h5(t); h5(t) is the disturbance term f caused by modeling errors of system valve flow and internal / external leakage, as well as changes in system parameters. p The derivative;

[0060] Therefore, it is only necessary to guarantee the parameters of the extended state observer. State estimation error vector coefficient matrix A ε All eigenvalues ​​have negative real parts, which can be achieved by increasing... This causes the values ​​of the latter two terms to approach infinitesimal. According to the Hurwitz criterion, the hydraulic servo position control system is asymptotically stable over continuous time.

[0061] Preferably, in step S13, the backward difference method is used to establish the discretized state-space equation of the third-order hydraulic servo position control system, thereby accurately predicting the trajectory tracking error during real-time motion. Specifically:

[0062] Set the current sampling time to kT s T s The sampling period is given; according to the backward difference method, the discretized state-space equation of the hydraulic servo position control system is:

[0063]

[0064] Where C =

[100] is the output matrix of the state-space equation of the third-order system; A k G is the coefficient matrix of the state vector of a third-order system; k Γ is the coefficient matrix of the input vector of a third-order system. k The disturbance term matrix of the third-order system; y(k) is the discretized state-space equation in kT s Predicted output at time step;

[0065] Setting the prediction time domain to N, and based on the extended state-observation equation of the fifth-order system according to equation (13), the current sampling time kT is... s Time state x2 and disturbance term f x and f p Real-time observation is performed; the change in the disturbance term is zero in the prediction time domain, i.e., Δf(k+i)=0. 2×1 (i=1,2,...,N), where Δf=[Δf xΔf p ] T Specifically:

[0066] f(k+i)=f(k)(i=1,2,...,N) (16)

[0067] Where f(k+i) is the system prediction time domain (k+i)T s The perturbation term vector at time k; f(k) is the system's current sampling time kT. s The perturbation term vector at time step; i is the system prediction time-domain index;

[0068] Substituting equation (16) into the discretized state-space equation of the hydraulic servo position control system in equation (15), and combining it with the state observation equation of the extended fifth-order system in equation (13), we obtain the state observation equation in the prediction time domain (k+N)T. s The predicted output at time t is:

[0069]

[0070] Where y(k+N) is the discretized state-space equation in (k+N)T s The predicted output at time q; q is the prediction time domain number; A k+i For a third-order system in the prediction time domain (k+i)T s The state vector coefficient matrix at time step G; k+q-1 For a third-order system in the prediction time domain (k+i)T s The coefficient matrix of the input vector at time step; To estimate the state vector; To estimate the perturbation term vector;

[0071] Therefore, at the current sampling time kT s Based on the above formula, (k+N)T is obtained. s The predicted output position at any given time is used to accurately predict the trajectory tracking error during real-time motion.

[0072] Preferably, step S14, based on the model-based variable input control method, determines the reference trajectory of the state-space equation of the hydraulic servo position control system, specifically as follows:

[0073] The model-based variable input control method uses an initial reference trajectory x r The position, velocity, and acceleration terms are used to obtain the reference trajectory compensation term Δx′. r This results in an updated reference trajectory. This data is then input into the hydraulic servo position control system, utilizing the characteristics of the feedback controller to incorporate the reference trajectory compensation term Δx′. r The output after that is closer to the initial reference trajectory x. r; After adding the model-based variable input control method to the hydraulic servo position control system, the compensation term for the reference trajectory is:

[0074]

[0075] where, Δx′ r is the compensation term for the reference trajectory by the model-based variable input control method.

[0076] Preferably, the trajectory tracking error e(k + N) is set in step S22, specifically:

[0077] Set the trajectory tracking error as e = x r -x p , and according to the prediction output equation of the third-order system in formula (17), obtain the predicted tracking error at time (k + N)T s as:

[0078] e(k + N) = x r (k + N)-x p (k + N) (19)

[0079] where, e(k + N) is the predicted tracking error at sampling time (k + N)T s ; x r (k + N) is the reference trajectory at sampling time (k + N)T s ; x p (k + N) is the predicted output position at sampling time (k + N)T s ;

[0080] Set the control time domain as N p <N, and on the basis of the original τ at sampling time (k + N p )T s add the compensation term Δτ(k + N p ), then there will also be a corresponding change amount Δx s in the predicted output position at sampling time (k + N)T p ; Combining the sensitivity factor S τ , the output position change amount Δx s (k + N) at sampling time (k + N)T p is:

[0081] Δxp(k + N) = S τ Δτ(k + N p ) (20)

[0082] Assume that the predicted tracking error is all generated by the time-variable of τ, that is, Δx p (k + N) = e(k + N), specifically:

[0083] e(k+N)=S τ Δτ(k+N p ) (twenty one)

[0084] Where e(k+N) is the sampling time (k+N)T s Predictive tracking error at any given time.

[0085] Preferably, in step S32, the reference trajectory compensation term obtained in step S31 is used for closed-loop control of the hydraulic servo position control system to verify system stability. Specifically:

[0086] The hydraulic servo position control system employs PID feedback control to ensure the initial stability of the closed-loop system; further verification is achieved by adding a compensation term Δτ(k+N) to the base τ. p After that, the stability of the hydraulic servo position control system;

[0087] Given N r Reference trajectory of reference point Without compensation term Δτ(k+Np) and with compensation term Δτ(k+Np) p The predicted output sequences after ) are respectively Specifically:

[0088]

[0089] Where R is the reference point and N is the reference point. r The reference trajectory; This is the predicted output sequence without the addition of a compensation term; The predicted output sequence after adding the compensation term; x r (k) is the reference point N r The k-th element of the reference trajectory; x r (k+1) is the reference point and N is the reference point. r The (k+1)th element of the reference trajectory; x r (k+N r -1) is the reference point N. r Reference trajectory at time (k+N) r -1) element; This is the (k+1)th element of the predicted output sequence without the addition of a compensation term; This is the (k+2)th element of the predicted output sequence without the addition of a compensation term; The predicted output sequence without compensation term, for the (k+N)th... r )element; This is the (k+1)th element of the predicted output sequence after adding the compensation term; The (k+2)th element of the predicted output sequence after adding the compensation term; For the predicted output sequence after adding the compensation term, the (k+N)th... r )element;

[0090] Set the prediction output bias without compensation. Deviation from predicted output with added compensation term for:

[0091]

[0092] in, The deviation of the predicted output without compensation; To compensate for the deviation in the predicted output;

[0093] According to equation (4), the compensation term Δτ(k+N) for parameter τ p From equation (23) above, we get:

[0094]

[0095] When condition 0 < (1-S) τ If α) < 1 holds, taking the absolute value of both sides of equation (24) and using the bounding method to bound them, we get:

[0096]

[0097] For equation (25) to hold true, the following condition must be met:

[0098] 0 < S τ α<1 (26)

[0099] Therefore, when equation (26) holds true, and The relationship between them satisfies equation (25), that is, when the compensation term Δτ(k+N) is added... p After that, the system is stable.

[0100] Compared with the prior art, the present invention has the following beneficial effects:

[0101] (1) Compared with previous methods, the sensitivity-based control method proposed in this invention can accurately reveal the mapping relationship between the changes in nonlinear model parameters and the changes in output, realize precise control based on sensitivity, and greatly improve the control accuracy.

[0102] (2) The sensitivity-based variable input compensation control method proposed in this invention compensates the parameters of the hydraulic position control system in real time by predicting the tracking error, which solves the problem that the optimal parameters of the system are difficult to determine under time-varying discontinuous working conditions, and greatly improves the system response speed and stability.

[0103] (3) This invention extends the application of sensitivity to the field of hydraulic servo control, providing a reliable method that meets the actual application requirements for the optimal parameter matching strategy under time-varying discontinuous working conditions. Attached Figure Description

[0104] Figure 1 The flowchart shows the variable input compensation control method for the sensitivity-based hydraulic servo position control system of the present invention.

[0105] Figure 2 This is a structural diagram of the hydraulic drive unit motion platform of the present invention;

[0106] Figure 3 This is a schematic diagram of the servo valve-controlled hydraulic cylinder of the hydraulic drive unit motion platform of the present invention.

[0107] Figure 4 This is a schematic diagram of the sensitivity-based variable input compensation control principle of the present invention;

[0108] Figure 5 This is a diagram of the dual-cylinder top-down performance test platform of the present invention;

[0109] Figure 6 The experimental curves for parameter compensation and trajectory tracking error under variable frequency and amplitude sinusoidal trajectories of this invention are shown.

[0110] Figure 7 The experimental curves for parameter compensation and trajectory tracking error under random trajectories are shown in the present invention. Detailed Implementation

[0111] Exemplary embodiments, features, and aspects of the present invention will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0112] This invention provides a sensitivity-based variable input compensation control method for a hydraulic servo position control system, such as... Figure 1 As shown, a typical hydraulic servo position control system is modeled. The reference trajectory of the state-space equation of the hydraulic servo position control system is updated using a model-based variable input control method. Based on sensitivity, the mapping relationship between the parameter changes and output changes of the state-space equation of the hydraulic servo position control system after the reference trajectory update is obtained, realizing real-time compensation of the parameters of the variable input control method. The stability is verified by analyzing the relationship between trajectory tracking errors before and after compensation, thus completing the variable input compensation control of the hydraulic servo position control system. This includes:

[0113] Step S1: Model a typical hydraulic servo position control system and update the reference trajectory of the state space equation of the hydraulic servo position control system using a model-based variable input control method.

[0114] A typical hydraulic servo position control system according to an embodiment of the present invention, such as Figure 2 The diagram shown is a structural diagram of the hydraulic drive unit motion platform of this invention. It is the most representative hydraulic servo position control system motion platform in industrial applications, and is mainly composed of four parts: hydraulic cylinder 2, servo valve 1, position sensor 3, and force sensor 4.

[0115] like Figure 3 This is a schematic diagram of the servo valve 1 controlling the hydraulic cylinder 2 of the hydraulic drive unit motion platform of the present invention; the load pressure at the end of the hydraulic drive unit and the cylinder rod displacement are collected in real time by the force sensor 4 and the position sensor 3 respectively, and the difference between the desired trajectory and the cylinder rod displacement collected by the position sensor 3 is used as the control signal for the opening of the servo valve 1, thereby realizing the real-time control of the hydraulic drive unit by the servo valve 1.

[0116] Figure 3 5 is comparator 5.

[0117] Step S11: Perform mathematical modeling using a typical hydraulic servo position control system to obtain the state-space equations of the hydraulic servo position control system, specifically:

[0118] The hydraulic servo position control system is a typical servo valve 1 control system, with settings... Where x p This refers to the output position of the second cylinder rod of the hydraulic cylinder. P is the moving speed of the cylinder rod of hydraulic cylinder 2. L For load pressure, P L =P1-nP2, where n is the ratio of the cross-sectional area of ​​the rod-side chamber and the rodless chamber of hydraulic cylinder 2, n = A p2 / A p1 A p1 and A p2 Let P1 and P2 be the cross-sectional areas of the rodless and rod-side chambers of hydraulic cylinder 2, respectively; and let P1 and P2 be the pressures in the rodless and rod-side chambers of hydraulic cylinder 2, respectively. The state-space equation of the hydraulic servo position control system is:

[0119]

[0120] Where x1 represents the output position of hydraulic cylinder 2 rod. Let x be its derivative; x2 is the moving speed of the cylinder rod of hydraulic cylinder 2. Its derivative; x3 is the load pressure. Its derivative; K is the load stiffness; B p m is the viscous damping coefficient. tFor equivalent mass; g1(x1) is the first constructor; g2(x1) is the second constructor; g3(x1,x3,u) is the third constructor; f x For the frictional force and external disturbance terms that are not modeled in the system; f p Modeling errors in system valve flow and internal / external leakage, as well as disturbance terms caused by changes in system parameters; k axv denoted as servo valve 1 gain coefficient; u is the control voltage of servo valve 1; n is the ratio of the cross-sectional area of ​​the rod-side chamber to the rodless chamber of hydraulic cylinder 2; A p1 Let be the cross-sectional area of ​​the rodless cavity of hydraulic cylinder 2.

[0121] The first constructor is:

[0122] g1(x1)=2(1+n 2 A p1 β e / V (2)

[0123] Where, β e V is the effective bulk modulus; V is the total volume of hydraulic cylinder 2.

[0124] The second constructor is:

[0125] g2(x1)=2β e [(1+n)C ip +C ep ] / V (3)

[0126] Among them, C ip C is the internal leakage coefficient; ep This represents the external leakage coefficient.

[0127] The third constructor is:

[0128]

[0129] Where, k d For the calculated flow coefficient; P s This refers to the oil supply pressure.

[0130] The total volume of hydraulic cylinder 2 is:

[0131]

[0132] Among them, V g1 V is the volume of the oil inlet channel of hydraulic cylinder 2; g2 L is the volume of the return oil flow channel of hydraulic cylinder 2; L is the total stroke of the cylinder rod of hydraulic cylinder 2; L0 is the initial position of the cylinder rod of hydraulic cylinder 2; A p2 These are the cross-sectional areas of the rod chamber of hydraulic cylinder 2.

[0133] Step S12: Based on the state-space equation of the hydraulic servo position control system, extend the two disturbance terms to establish the extended state observation equation of the fifth-order hydraulic servo position control system, specifically:

[0134] To accurately observe the unknown state x2 and the disturbance term f x and f p The state-space equation (1) of the hydraulic servo position control system is extended to a fifth-order system denoted by z, i.e., z = [z1, z2, z3, z4, z5]. T =[x1,x2,x3,f x ,f p ] T ;set up This is an estimated value. To estimate the error, i.e. The state-observation equations of the extended fifth-order system are as follows:

[0135]

[0136] in, This is an estimated value for the output position of the cylinder rod of hydraulic cylinder 2. Its derivative; This is an estimated value for the moving speed of the rod in hydraulic cylinder 2. Its derivative; This is an estimate of the load pressure. Its derivative; For the disturbance term f x The estimated value, Its derivative; For the disturbance term f p The estimated value, Its derivative; The estimated error is the position of the output rod of hydraulic cylinder 2. This represents the estimation error of the load pressure; This is the first constructor for a fifth-order system; This is the second constructor for a fifth-order system; This is the third constructor for a fifth-order system; To extend the parameters of the state observer.

[0137] Set the estimation error of the i-th state Third-state estimation error Fourth state estimation error Fifth state estimation error The error vector of the input state coefficient matrix estimation of a fifth-order system That is, the state estimation error vector is ε=[ε1,ε2,ε3,ε4,ε5] T The state estimation error vector of the fifth-order system is:

[0138]

[0139] Wherein, the state estimation error vector of the ε-order fifth-order system Its derivative; A ε The coefficient matrix of the state estimation error vector; The error vector is the input state coefficient matrix estimation vector of a fifth-order system. The error vector is estimated from the disturbance term matrix of the fifth-order system. G is the input state coefficient matrix of a fifth-order system, including the estimated state; e (z,u) is the input state coefficient matrix of the fifth-order system without estimated states; h4(t) is the unmodeled friction force and external disturbance term f. x The derivative of h5(t); h5(t) is the disturbance term f caused by modeling errors of system valve flow and internal / external leakage, as well as changes in system parameters. p The derivative of .

[0140] State estimation error vector coefficient matrix A ε for:

[0141]

[0142] Therefore, it is only necessary to guarantee the parameters of the extended state observer. State estimation error vector coefficient matrix A ε All eigenvalues ​​have negative real parts, which can be achieved by increasing... This causes the values ​​of the latter two terms to approach infinitesimal. According to the Hurwitz criterion, the hydraulic servo position control system is asymptotically stable over continuous time.

[0143] Step S13: Based on the observed values ​​of the state observation equation, the discretized state-space equation of the third-order hydraulic servo position control system is established using the backward difference method, thereby accurately predicting the trajectory tracking error during real-time motion. Specifically:

[0144] Set the current sampling time to kT s T s The sampling period is given; according to the backward difference method, the discretized state-space equation of the hydraulic servo position control system is:

[0145]

[0146] Where C = [1 0 0] is the output matrix of the state-space equation of the third-order system; A k G is the coefficient matrix of the state vector of a third-order system; k Γ is the coefficient matrix of the input vector of a third-order system. k The disturbance term matrix of the third-order system; y(k) is the discretized state-space equation in kT sPredicted output at time step.

[0147] A is the coefficient matrix of the state vector of a third-order system. k for:

[0148]

[0149] The input vector coefficient matrix G of the third-order system k for:

[0150] G k =[0,0,k axv g3(x1,x3,u)T s ] T (11).

[0151] The disturbance term matrix Γ of the third-order system k for:

[0152] Γ k =[0,f x T s ,f p T s ] T (12).

[0153] Setting the prediction time domain to N, and based on the extended state-observation equation of the fifth-order system according to equation (6), the current sampling time kT is... s Time state x2 and disturbance term f x and f p Real-time observation is performed; the change in the disturbance term is zero in the prediction time domain, i.e., Δf(k+i)=0. 2×1 (i=1,2,...,N), where Δf=[Δf x Δf p ] T Specifically:

[0154] f(k+i)=f(k)(i=1,2,...,N) (13)

[0155] Where f(k+i) is the system prediction time domain (k+i)T s The perturbation term vector at time k; f(k) is the system's current sampling time kT. s The perturbation term vector at time t; i is the system prediction time-domain number.

[0156] Substituting equation (13) into the discretized state-space equation of the hydraulic servo position control system in equation (9), and combining it with the extended state observation equation of the fifth-order system in equation (6), we obtain the state observation equation in the prediction time domain (k+N)T. s The predicted output at time t is:

[0157]

[0158] Where y(k+N) is the discretized state-space equation in (k+N)T s The predicted output at time q; q is the prediction time domain number; A k+i For a third-order system in the prediction time domain (k+i)T s The state vector coefficient matrix at time step G; k+q-1 For a third-order system in the prediction time domain (k+i)T s The coefficient matrix of the input vector at time step; To estimate the state vector; To estimate the perturbation term vector.

[0159] Estimating the state vector for:

[0160]

[0161] Estimating the perturbation term vector for:

[0162]

[0163] Therefore, at the current sampling time kT s Based on the above formula, (k+N)T is obtained. s The predicted output position at any given time is used to accurately predict the trajectory tracking error during real-time motion.

[0164] Step S14: Using a model-based variable input control method, determine the reference trajectory of the state-space equations of the hydraulic servo position control system, specifically as follows:

[0165] The model-based variable input control method uses an initial reference trajectory x r The position, velocity, and acceleration terms are used to obtain the reference trajectory compensation term Δx′. r This results in an updated reference trajectory. This data is then input into the hydraulic servo position control system, utilizing the characteristics of the feedback controller to incorporate the reference trajectory compensation term Δx′. r The output after that is closer to the initial reference trajectory x. r After incorporating a model-based variable input control method into the hydraulic servo position control system, its compensation term for the reference trajectory is:

[0166]

[0167] Where, Δx′ r This is the compensation term for the reference trajectory in the model-based variable input control method.

[0168] The updated state-space equation reference trajectory for the hydraulic servo position control system is as follows:

[0169]

[0170] in, The reference trajectory after the state-space equations are updated; x r The initial reference trajectory for the state-space equations; τ = [τ x τ v τ a ] T τ represents the parameter vector for a model-based variable input control method. x For positional parameters; τ v For the velocity term parameter; τ a For acceleration parameters; This represents the coefficient vector of the compensation term in a model-based variable input control method. The first derivative of the initial reference trajectory in the state-space equation; The second derivative of the initial reference trajectory in the state-space equation is given.

[0171] Step S2: Based on sensitivity, obtain the mapping relationship between the parameter changes and output changes of the state space equation of the hydraulic servo position control system after the reference trajectory update.

[0172] Step S21: Extend the sensitivity application to the field of hydraulic servo control, solve the implicit constraints between the nonlinear model parameters and output of the hydraulic servo position control system, and realize real-time compensation of the parameter τ of the model-based variable input control method; the discretized state-space equation of the hydraulic servo position control system after adding the model-based variable input control method is:

[0173] H k (x(k+1),x(k),u(k),p(k),τ)=0 3×1 (19)

[0174] Among them, H k The state-space equation is discretized; x(k+1) is the sampling time (k+1)T. s The state variable at time point; x(k) is the sampling time kT s The state variable at time; u(k) is the sampling time kT s The servo valve 1 control voltage is timed; p(k) is the sampling time kT. s Time-based system parameter vector; k is the sampling time number; T s The sampling period.

[0175] Performing a first-order Taylor expansion on the above equation, the mapping relationship between the parameter τ change and the output change in the model-based variable input control method is determined as follows:

[0176]

[0177] Where, Δxp is the output variation; Δτ is the variation of the parameters of the model-based variable input control method; is the sensitivity factor of the parameter τ of the model-based variable input control method; is the sensitivity factor of the position term; is the sensitivity factor of the velocity term; is the sensitivity factor of the acceleration term.

[0178] Step S22: Set the trajectory tracking error as e(k + N), and set the trajectory tracking error as e = x r -x p , and according to the prediction output equation of the third-order system in Equation (14), obtain the predicted tracking error at time (k + N)T s as:

[0179] e(k + N) = x r (k + N) - x p (k + N) (21)

[0180] where e(k + N) is the predicted tracking error at sampling time (k + N)T s ; x r (k + N) is the reference trajectory at sampling time (k + N)T s ; x p (k + N) is the predicted output position at sampling time (k + N)T s .

[0181] Set the control time domain as N p < N, and on the basis of the original τ at sampling time (k + N p )T s add a compensation term Δτ(k + N p ), then at sampling time (k + N)T s the predicted output position will also generate a corresponding variation Δx p (k + N); combined with the sensitivity factor S τ , the output position variation Δx s at sampling time (k + N)T p is:

[0182] Δx p (k + N) = S τ Δτ(k + N p ) (22).

[0183] Assume that the predicted tracking error is all generated by the time-varying quantity of τ, that is, Δx p (k + N) = e(k + N), specifically:

[0184] e(k + N) = Sτ Δτ(k+N p ) (twenty three)

[0185] Where e(k+N) is the sampling time (k+N)T s Predictive tracking error at any given time.

[0186] Determine the compensation term Δτ(k+N) for parameter τ. p )for:

[0187] Δτ(k+N p )=αe(k+N) (24)

[0188] Wherein, Δτ(k+N) p ) is the parameter τ during the sampling time (k+N) p )T s The compensation term at each time step forms a sensitivity-based variable input compensation control method; e(k+N) is the sampling time (k+N)T. s Time-tracking error; α = [a x a v a a ] T To compensate the gain coefficient for a sensitivity-based variable input compensation control method; a x a is the position term compensation gain coefficient; v This is the gain coefficient for velocity term compensation; a a N represents the acceleration term compensation gain coefficient; N is the system prediction time domain; N p This refers to the system control time domain.

[0189] Step S3: Realize the real-time compensation of the variable input control method parameters, and verify the stability by analyzing the relationship between trajectory tracking errors before and after compensation, thus completing the variable input compensation control of the hydraulic servo position control system.

[0190] like Figure 4 This is a schematic diagram of the sensitivity-based variable input compensation control principle of the present invention. An extended observer is used to observe the unknown state and disturbance term of the system in real time, thereby refining the prediction model and accurately predicting the trajectory tracking error in the real-time motion process. Combined with the sensitivity factor, the parameter τ of the model-based variable input control method is compensated in real time.

[0191] Step S31: Transpose both sides of equation (24) obtained in step S22, and multiply both sides by the coefficient vector of the compensation term of the model-based variable input control method. Specifically:

[0192]

[0193] in, Sampling time (k+N)p )T s The compensation term coefficient vector of the model-based variable input control method at any time.

[0194] Further refinement yields the compensation term Δτ(k+N) for parameter τ. p The compensation term for the reference trajectory is:

[0195]

[0196] in, The compensation term Δτ(k+N) for parameter τ p The compensation term for the reference trajectory.

[0197] A sensitivity-based variable input compensation control method is used to perform real-time compensation of the parameter τ of the model-based variable input control method, resulting in the compensation term that ultimately compensates to the reference trajectory of the state-space equation:

[0198]

[0199] Where, Δx r (k+N p ) represents the sampling time (k+N) p )T s The compensation term for the reference trajectory in the state-space equation at time step.

[0200] Step S32: Obtain the reference trajectory compensation term obtained in step S31, and use it for closed-loop control of the hydraulic servo position control system to verify system stability; the hydraulic servo position control system uses PID feedback control to ensure the initial stability of the closed-loop system; further verify the addition of the compensation term Δτ(k+N) to τ. p After that, the stability of the hydraulic servo position control system.

[0201] Given N r Reference trajectory of reference point No compensation term Δτ(k+N) is added p ) and add compensation term Δτ(k+N p The predicted output sequences after ) are respectively Specifically:

[0202]

[0203] Where R is the reference point and N is the reference point. r The reference trajectory; X is the predicted output sequence without compensation terms; p n is the predicted output sequence after adding the compensation term; x r (k) is the reference point N r The k-th element of the reference trajectory; x r(k+1) is the reference point and N is the reference point. r The (k+1)th element of the reference trajectory; x r (k+N r -1) is the reference point N. r Reference trajectory at time (k+N) r -1) element; This is the (k+1)th element of the predicted output sequence without the addition of a compensation term; This is the (k+2)th element of the predicted output sequence without the addition of a compensation term; The predicted output sequence without compensation term, for the (k+N)th... r )element; This is the (k+1)th element of the predicted output sequence after adding the compensation term; The (k+2)th element of the predicted output sequence after adding the compensation term; For the predicted output sequence after adding the compensation term, the (k+N)th... r )element.

[0204] At reference point N r No compensation term Δτ(k+N) is added to the sequence. p Predicted output sequence at time ) for:

[0205]

[0206] Where Λ is the coefficient matrix of the estimated state vector; To estimate the state vector; The input vector matrix; It is a vector matrix containing perturbation terms.

[0207] The estimated state vector coefficient matrix Λ is:

[0208]

[0209] Input vector matrix for:

[0210]

[0211] Including perturbation term vector matrix for:

[0212]

[0213] in, This is the disturbance vector without the addition of a compensation term.

[0214] Adding the compensation term Δτ(k+N) p The predicted output sequence after ) for:

[0215]

[0216] in, The vector is the compensation term for the reference trajectory.

[0217] Reference trajectory compensation term vector for:

[0218]

[0219] At reference point N r Add compensation term Δτ(k+N) to the sequence p The subsequent trajectory tracking error is:

[0220]

[0221] in, To add the compensation term Δτ(k+N) p The trajectory tracking error is denoted as e(k+j), where e(k+j) is the compensation term Δτ(k+N). p Forward trajectory tracking error; Δτ(k+j-1) is the prediction time domain (k+j-1)T s Time-based compensation item.

[0222] According to equation (21), the sampling time (k+N)T s The prediction tracking error at time step can be converted into the above equation (35) as follows:

[0223]

[0224] Set the prediction output bias without compensation. Deviation from predicted output with added compensation term for:

[0225]

[0226] in, The deviation of the predicted output without compensation; The prediction output bias is compensated for by adding a compensation term.

[0227] According to equation (24), the compensation term Δτ(k+N) for parameter τ p From equation (37) above, we get:

[0228]

[0229] When condition 0 < (1-S) τ If α) < 1 holds, take the absolute value of both sides of equation (38) and use the scaling method to obtain:

[0230]

[0231] For equation (39) to hold true, the following conditions must be met:

[0232] 0 < S τ α < 1 (40).

[0233] Therefore, when equation (40) holds, and The relationship between them satisfies equation (39), that is, when the compensation term Δτ(k+N) is added... p After that, the system is stable. The range of the compensation gain coefficient is determined, and the variable input compensation control of the hydraulic servo position control system is completed.

[0234] like Figure 5 This is a diagram of the dual-cylinder top-down performance testing platform of the present invention; the personal computer and the Speedgoat controller establish data transmission via Ethernet, and the Speedgoat controller processes the real-time data collected by the force sensor 4 and the position sensor 33 in real time to generate the control voltage of the servo valve 1, and uses the servo amplifier to convert the control voltage signal into a current control signal that the servo valve 1 can accept, while rectifying to ensure the stability of the control signal.

[0235] like Figure 6These are experimental curves of parameter compensation and trajectory tracking error under variable frequency and amplitude sinusoidal trajectories of the present invention; used to verify the adaptive capability of the proposed sensitivity-based variable input compensation control method under time-varying discontinuous operating conditions. In the two sets of experimental curves, curve C1 is the PID error curve; curve C2 is the PID + model-based variable input control error curve; and curve C3 is the PID + model-based variable input control + sensitivity-based variable input compensation control error curve. In the sinusoidal trajectory, the reference trajectory is a sinusoidal signal with varying frequency and amplitude. As the operating conditions change, the sensitivity-based variable input compensation control method adjusts the parameter compensation of the model-based variable input control method in real time, thereby adjusting the compensation of the reference trajectory online. If the closed-loop system only uses PID and model-based variable input control methods for control, when the control effect reaches its optimum under the baseline operating conditions, C3 is unlikely to further reduce the trajectory tracking error compared to C2. However, when the operating conditions change, the trajectory tracking error of C2 is unsatisfactory. Fortunately, C3 can still maintain a relatively low trajectory tracking error. Table 1 shows the performance indicators of the root mean square (RMS) value of trajectory tracking error for variable frequency and amplitude sinusoidal trajectories. Under the condition of incorporating a sensitivity-based variable input compensation control method, the RMS value of C3 relative to C2 decreased by 13.871% and the maximum absolute value of trajectory tracking error decreased by 32.647% under the baseline operating condition. When the operating condition changed, the reduction rate of the RMS value of C3 relative to C2 was over 52%, and the reduction rate of the maximum absolute value of trajectory tracking error was over 44%. Specific data are shown in Table 2 for the maximum absolute value performance indicators of trajectory tracking error for variable frequency and amplitude sinusoidal trajectories. Therefore, the proposed sensitivity-based variable input compensation control method achieves higher trajectory tracking accuracy and operating condition adaptability by real-time compensation of model-based variable input parameters, solving the uncertainty problem of optimal system parameters under time-varying discontinuous operating conditions.

[0236] Table 1. Performance Indicators of Tracking Error Root Mean Square Value for Variable Frequency and Amplitude Sine Trajectories

[0237]

[0238] Table 2. Performance Indicators: Maximum Absolute Value of Tracking Error for Variable Frequency and Amplitude Sine Trajectories

[0239]

[0240] like Figure 7Experimental curves for parameter compensation and trajectory tracking error under random trajectories are presented to verify the feasibility of the proposed sensitivity-based variable input compensation control method under random trajectories. A random signal is used as the reference trajectory in the random trajectory test. For random trajectories, the sensitivity-based variable input compensation control method can still accurately adjust the parameters of the model-based variable input control method in real time, thereby adjusting the compensation amount of the reference trajectory online. Furthermore, under random trajectories, C3 is still significantly better than C2, greatly reducing the trajectory tracking error. Under random trajectories, the root mean square value of C3 is reduced by 53.55% compared to C2, and the maximum absolute value of the trajectory tracking error is reduced by 50.942%. Similar to the sinusoidal trajectory experiment, the reduction rate of the root mean square value is above 52%, and the reduction rate of the maximum absolute value of the trajectory tracking error is above 44%. Specific data are shown in Table 3, which displays the root mean square value and maximum absolute value performance indicators of the trajectory tracking error for random trajectories. Therefore, experiments on sinusoidal and random trajectories together demonstrate that the proposed sensitivity-based variable input compensation control method significantly improves both trajectory tracking accuracy and adaptability to operating conditions by real-time compensation of the parameters of the model-based variable input control method. Furthermore, the feasibility of the proposed sensitivity-based variable input compensation control method under different reference trajectories is verified.

[0241] Table 3. Performance Indicators of Tracking Error Root Mean Square and Maximum Absolute Value for Random Trajectories

[0242]

[0243] The beneficial effects of this invention are as follows: This invention provides a sensitivity-based variable input compensation control method for hydraulic servo position control systems. Compared with previous methods, the sensitivity-based control method proposed in this invention can accurately reveal the mapping relationship between the changes in nonlinear model parameters and the changes in output, achieving accurate sensitivity-based control and significantly improving control precision. By extending the state observer to observe the unknown state and disturbances of the system in real time, the prediction equation is refined, thereby accurately predicting the trajectory tracking error in the real-time motion process. Combined with the predicted tracking error and the sensitivity factor, the parameters of the hydraulic position control system are compensated in real time, solving the problem that the optimal parameters of the system are difficult to determine under time-varying discontinuous working conditions, and significantly improving the system response speed and stability. The sensitivity is extended to the field of hydraulic servo control, providing a reliable method that meets the practical application requirements for the optimal parameter matching strategy under time-varying discontinuous working conditions. The relationship between the trajectory tracking error 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.

[0244] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A sensitivity-based variable input compensation control method for a hydraulic servo position control system, characterized in that, It includes: S1: Model a typical hydraulic servo position control system and update the reference trajectory of the state space equation of the hydraulic servo position control system through a model-based variable input control method; S11: Mathematical modeling is performed using a typical hydraulic servo position control system to obtain the state-space equations of the hydraulic servo position control system; S12: Based on the state-space equation of the hydraulic servo position control system, two disturbance terms are extended to establish the state observation equation of the extended fifth-order hydraulic servo position control system. S13: Based on the observed values ​​of the state observation equation, the backward difference method is used to establish the discretized state space equation of the third-order hydraulic servo position control system, thereby accurately predicting the trajectory tracking error in the real-time motion process; S14: A model-based variable input control method is used to determine the reference trajectory of the state-space equations of the hydraulic servo position control system. The updated reference trajectory of the state-space equations of the hydraulic servo position control system is as follows: (1) ； in, The reference trajectory after the state-space equations are updated; The initial reference trajectory for the state-space equations; For model-based variable input control methods, the parameter vector is used. For positional parameters; For velocity parameters; For acceleration parameters; This represents the coefficient vector of the compensation term in a model-based variable input control method. The first derivative of the initial reference trajectory in the state-space equation; The second derivative of the initial reference trajectory in the state-space equation; S2: Based on sensitivity, obtain the mapping relationship between the parameter changes and output changes of the state-space equation of the hydraulic servo position control system after the reference trajectory update; S21: Extending sensitivity to the field of hydraulic servo control, resolving the implicit constraints between nonlinear model parameters and output of hydraulic servo position control systems, and realizing parameter control of model-based variable input control methods. Real-time compensation is performed; the discretized state-space equation of the hydraulic servo position control system after incorporating a model-based variable input control method is: (2) ； in, The state-space equations are discretized. Sampling time Time-state variables; Sampling time Time-state variables; Sampling time The servo valve controls the voltage at all times. Sampling time Time-matter system parameter vector; Number the sampling time; The sampling period; Performing a first-order Taylor expansion on the above equation determines the parameters of the model-based variable input control method. The mapping relationship between the change and the output change is as follows: (3) ； in, To output the change; For model-based variable input control methods, the parameter variation is... Parameters for model-based variable input control methods Sensitivity factor; For the position term sensitivity factor; For the velocity term sensitivity factor; For the acceleration term, the sensitivity factor is used. S22: Set the trajectory tracking error to... Determine parameters Compensation items for: (4) ； in, For parameters At sampling time The compensation term at each moment forms a sensitivity-based variable input compensation control method; Sampling time Time-tracking error; To compensate the gain coefficient for a sensitivity-based variable input compensation control method; This is the gain coefficient for the position term compensation; This is the gain coefficient for velocity term compensation; This is the gain coefficient for acceleration term compensation; For system prediction in the time domain; For system control time domain; S3: Real-time compensation of parameters of variable input control method is achieved, and the stability is verified by analyzing the relationship between trajectory tracking error before and after compensation, thus completing the variable input compensation control of hydraulic servo position control system; S31: Transpose both sides of equation (4) obtained in step S22, and multiply both sides by the compensation term coefficient vector of the model-based variable input control method. Specifically: (5) ； in, Sampling time The compensation term coefficient vector of the model-based variable input control method at any given time; Further processing to obtain parameters Compensation items The compensation term for the reference trajectory is: (6) ； in, For parameters Compensation items Compensation term for the reference trajectory; A sensitivity-based variable input compensation control method is used to optimize the parameters of a model-based variable input control method. Real-time compensation is performed, and the compensation term ultimately compensated to the reference trajectory of the state-space equation is obtained as follows: (7) ； in, Sampling time The compensation term for the reference trajectory in the state-space equation at any given time; S32: Obtain the reference trajectory compensation term obtained in step S31, use it for closed-loop control of the hydraulic servo position control system, verify system stability, determine the value range of the compensation gain coefficient, and complete the variable input compensation control of the hydraulic servo position control system.

2. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 1, characterized in that: Step S11 uses a typical hydraulic servo position control system for mathematical modeling to obtain the state-space equation of the hydraulic servo position control system, specifically: The hydraulic servo position control system is a typical servo valve control system, with settings... ,in This refers to the output position of the hydraulic cylinder rod. The moving speed of the hydraulic cylinder rod. For load pressure, , This is the ratio of the cross-sectional areas of the rod-side chamber and the rodless chamber of the hydraulic cylinder. , and These are the cross-sectional areas of the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. and These represent the pressure in the rodless chamber and the pressure in the rod chamber of the hydraulic cylinder, respectively; the state-space equation of the hydraulic servo position control system is: (8) ； in, This refers to the output position of the hydraulic cylinder rod. Its derivative; The moving speed of the hydraulic cylinder rod. Its derivative; For load pressure, Its derivative; For load stiffness; It is the viscous damping coefficient; For equivalent quality; This is the first constructor; This is the second constructor; This is the third constructor; For the frictional force and external disturbance terms that are not modeled in the system; Modeling errors in system valve flow and internal / external leakage, as well as disturbance terms caused by changes in system parameters; This refers to the gain coefficient of the servo valve. For servo valve control voltage; The first constructor is: (9) ； in, Effective bulk modulus; This refers to the total volume of the hydraulic cylinder; The second constructor is: (10) ； in, This is the internal leakage coefficient; The external leakage coefficient; The third constructor is: (11) ； in, To calculate the flow coefficient; For oil supply pressure; The total volume of the hydraulic cylinder is: (12) ； in, This refers to the volume of the hydraulic cylinder's oil inlet channel; This refers to the volume of the hydraulic cylinder's return oil flow channel; This refers to the total stroke of the hydraulic cylinder rod. This is the initial position of the hydraulic cylinder rod.

3. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 2, characterized in that: In step S12, the state observation equations of the extended fifth-order hydraulic servo position control system are established, specifically as follows: To accurately observe unknown states and disturbance terms and The state-space equation (8) of the hydraulic servo position control system is extended to use... The fifth-order system is represented as follows: ;set up This is an estimated value. To estimate the error, i.e. The state-observation equations for the extended fifth-order system are: (13) ； in, This is an estimated value for the output position of the hydraulic cylinder rod. Its derivative; This is an estimated value for the movement speed of the hydraulic cylinder rod. Its derivative; This is an estimate of the load pressure. Its derivative; For disturbance terms The estimated value, Its derivative; For disturbance terms The estimated value, Its derivative; This represents the estimation error of the hydraulic cylinder rod output position; This represents the estimation error of the load pressure; This is the first constructor for a fifth-order system; This is the second constructor for a fifth-order system; This is the third constructor for a fifth-order system; To extend the parameters of the state observer; Setting the first State estimation error Third-state estimation error 4th state estimation error 5th state estimation error The error vector of the input state coefficient matrix estimation of a fifth-order system That is, the state estimation error vector is The state estimation error vector of the fifth-order system is: (14) ； in, The state estimation error vector of a fifth-order system Its derivative; The coefficient matrix of the state estimation error vector; The error vector is the input state coefficient matrix estimation vector of a fifth-order system. The error vector is estimated from the disturbance term matrix of the fifth-order system. This is the input state coefficient matrix of a fifth-order system, including the estimated state. The input state coefficient matrix of the fifth-order system does not contain the estimated state; For the friction and external disturbance terms not modeled in the system The derivative; Modeling errors in system valve flow and internal / external leakage, as well as disturbance terms caused by changes in system parameters. The derivative; Therefore, it is only necessary to guarantee the parameters of the extended state observer. State estimation error vector coefficient matrix All eigenvalues ​​have negative real parts, which can be achieved by increasing... This makes the values ​​of the latter two terms approach infinitesimal. According to the Hurwitz criterion, the hydraulic servo position control system is asymptotically stable in continuous time.

4. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 3, characterized in that: Step S13 uses the backward difference method to establish the discretized state-space equation of the third-order hydraulic servo position control system, thereby accurately predicting the trajectory tracking error during real-time motion. Specifically: Set the current sampling time as According to the backward difference method, the discretized state-space equation of the hydraulic servo position control system is as follows: (15) ； in, This is the output matrix of the state-space equations of the third-order system; The coefficient matrix of the state vector of a third-order system; The coefficient matrix is ​​the input vector of a third-order system. This is the disturbance term matrix for a third-order system; To discretize the state-space equations in Predicted output at time step; Set the prediction time domain as Based on the extended state-observation equation of the fifth-order system according to equation (13), the current sampling time is... Moment State and disturbance terms and Real-time observation is performed; the change in the disturbance term is zero in the prediction time domain, i.e. ,in Specifically: (16) ； in, For system prediction in the time domain The perturbation vector at time step; The current sampling time of the system The perturbation vector at time step; Number the system prediction time domain; Substituting equation (16) into the discretized state-space equation of the hydraulic servo position control system in equation (15), and combining it with the state observation equation of the extended fifth-order system in equation (13), we obtain the state-space equation in the prediction time domain. The predicted output at time t is: (17) ； in, To discretize the state-space equations in Predicted output at time step; For prediction time domain numbering; For the third-order system in the prediction time domain The state vector coefficient matrix at time t; For the third-order system in the prediction time domain The coefficient matrix of the input vector at time step; To estimate the state vector; To estimate the perturbation term vector; Therefore, at the current sampling time Based on the above formula, we can obtain The predicted output position at any given time is used to accurately predict the trajectory tracking error during real-time motion.

5. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 1, characterized in that: Step S14, based on the model-based variable input control method, determines the reference trajectory of the state-space equation of the hydraulic servo position control system, specifically as follows: Model-based variable input control methods, using initial reference trajectories The position, velocity, and acceleration terms are used to obtain the reference trajectory compensation term. This results in an updated reference trajectory. This data is then input into the hydraulic servo position control system, utilizing the characteristics of the feedback controller to incorporate a reference trajectory compensation term. The subsequent output is closer to the initial reference trajectory. After incorporating a model-based variable input control method into the hydraulic servo position control system, its compensation term for the reference trajectory is: (18) ； in, This is the compensation term for the reference trajectory in the model-based variable input control method.

6. The sensitivity-based variable input compensation control method for a hydraulic servo position control system according to claim 4, characterized in that: In step S22, the trajectory tracking error is set. Specifically: Set the trajectory tracking error to According to the prediction output equation of the third-order system in equation (17), we obtain The prediction tracking error at time t is: (19) ； in, Sampling time Reference trajectory at any given moment; Sampling time The predicted output position at time; Set the control time domain as During sampling time time Add compensation items to the existing ones So at the sampling time The predicted output position at any given time will also produce a corresponding change. Combined with sensitivity factor Sampling time Output position change at time for: (20) ； Assuming that the prediction tracking error is all caused by The time variable produces, that is Specifically: (21)。 7. The variable input compensation control method for a sensitivity-based hydraulic servo position control system according to claim 1, characterized in that: In step S32, the reference trajectory compensation term obtained in step S31 is acquired and used for closed-loop control of the hydraulic servo position control system to verify system stability. Specifically: The hydraulic servo position control system employs PID feedback control to ensure the initial stability of the closed-loop system; further verification is performed in... Add compensation items on the basis Afterwards, the stability of the hydraulic servo position control system; Set with Reference trajectory of reference point No compensation item included and adding compensation items The subsequent predicted output sequences are as follows , Specifically: (22) ； in, For reference point The reference trajectory; This is the predicted output sequence without the addition of a compensation term; The predicted output sequence after adding the compensation term; For reference point The reference trajectory element; For reference point The reference trajectory element; For reference point Reference trajectory at time element; The predicted output sequence without compensation term. element; The predicted output sequence without compensation term. element; The predicted output sequence without compensation term. element; The predicted output sequence after adding the compensation term is the first... element; The predicted output sequence after adding compensation terms element; The predicted output sequence after adding the compensation term is the first... element; Set the prediction output bias without compensation. Deviation from predicted output with added compensation term for: (23) ； in, The deviation of the predicted output without compensation; To compensate for the deviation in the predicted output; According to the parameters in equation (4) Compensation items Combining equation (23) above, we get: (24) ； when conditions This is true. Taking the absolute value of both sides of equation (24) and scaling them using the scaling method, we get: (25) ； For equation (25) to hold true, the following condition must be met: (26) ； Therefore, when equation (26) holds true, and The relationship between them satisfies equation (25), that is, when a compensation term is added... After that, the system is stable.

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