An adaptive compensation method for low-pressure nonlinear elastic modulus of hydraulic slewing joints

Abstract

The present invention discloses a method for adaptively compensating the low-pressure nonlinear elastic modulus of a hydraulic rotary joint. The method comprises: establishing a linear parameterized dynamic model of the rotary joint of a hydraulic manipulator based on the bulk elastic modulus in the form of a parameterized fraction, designing an adaptive robust controller, inputting the ideal joint angle of the current rotary joint into the controller, and simultaneously performing online adaptive update of the parameters, the controller outputs the ideal control flow after processing, and obtains the valve port control voltage after static mapping to control the hydraulic valve; the rotary joint outputs the actual control flow, actual driving torque and actual joint angle to the controller in real time, realizing adaptive compensation closed-loop control. The method of the present invention can realize effective compensation of the bulk elastic modulus and precise parameter adaptation in the case of changes in the bulk elastic modulus of the rotary joint of the hydraulic manipulator, thereby further improving the parameter adaptation effect while ensuring the motion control performance.

Description

Technical Field

[0001] The invention relates to a joint adaptive compensation method, in particular to a low-pressure nonlinear elastic modulus adaptive compensation method for a hydraulic rotary joint. Background Art

[0002] Intelligence and robotization are emerging trends in key application areas of hydraulic equipment, such as construction machinery. Replacing manual closed-loop control with machine-based closed-loop control is a crucial element at the equipment level. Therefore, high-performance control of hydraulic rotary joints has become an indispensable key foundational technology. Existing research primarily focuses on online adaptive and compensatory control of model parameters such as load mass, moment of inertia, dynamic friction, and external load force. However, nearly all studies treat the critical bulk modulus of hydraulic transmission systems as a known quantity or estimate it online as a lumped parameter. However, the actual bulk modulus is complex. Hydraulic system pressure fluctuates rapidly and drastically, especially under conditions such as frequent starts and stops and dynamic acceleration and deceleration. Furthermore, unlike parameters such as the friction coefficient, which can be easily and accurately obtained through system identification experiments, the specific value of the bulk modulus requires specialized equipment. Even if it can be determined, the bulk modulus used to establish cavity pressure dynamics is not equivalent to the oil value due to factors such as hydraulic oil pipe elasticity and oil gas content. Therefore, accurately accounting for changes in bulk modulus in closed-loop control has a significant impact on feedback gain tuning and feedback control. However, the key lies in the mathematical expression used to account for this mechanistic relationship. Therefore, finding a solution to accurately reflect the actual mechanism of bulk modulus changes in hydraulic rotary joints while also ensuring the feasibility of control design is an urgent issue. Summary of the Invention

[0003] In order to solve the problems existing in the background technology, the present invention provides a low-pressure nonlinear elastic modulus adaptive compensation method for a hydraulic rotary joint.

[0004] The technical solution adopted in the present invention is:

[0005] The low-pressure nonlinear elastic modulus adaptive compensation method of the hydraulic rotary joint of the present invention comprises:

[0006] In the first step, a linear parametric dynamic model of the rotary joint of the hydraulic manipulator is established based on the bulk elastic modulus in the form of a parametric fraction.

[0007] In the second step, based on the linear parameterized dynamic model of the rotary joint of the hydraulic manipulator, the backstepping method is used to design the adaptive robust controller of the rotary joint. The ideal joint angle of the current rotary joint is input into the adaptive robust controller, and the parameters of the adaptive robust controller are adaptively updated online. After processing, the adaptive robust controller outputs the ideal control flow of the rotary joint. After static mapping of the ideal control flow, the valve port control voltage is obtained to control the hydraulic valve of the rotary joint.

[0008] In the third step, the current rotary joint of the hydraulic manipulator outputs the actual control flow, actual driving torque and actual joint angle to the adaptive robust controller in real time to realize adaptive compensation closed-loop control of the rotary joint.

[0009] In the first step, the linear parameterized dynamic model of the rotary joint of the hydraulic manipulator is as follows:

[0010]

[0011] τ=μF L =μ(p1A1-p2A2)

[0012]

[0013] d1=d 1n +Δd1

[0014] d 21 =d 21n +Δd 21

[0015] d 22 =d 22n +Δd 22

[0016] Q 1d =f v1 (Δp v1 ,u v1 )

[0017] Q 2d =f v2 (Δp v2 ,u v2 )

[0018]

[0019] θ1=J L ,θ2=B f ,θ3=F f ,θ4=d 1n ,θ5=d 21n ,θ6=d 22n

[0020]

[0021] Among them, J L Represents the moment of inertia of the rotary joint of the hydraulic manipulator; and They represent the actual joint angular velocity and actual joint angular acceleration of the rotary joint respectively; τ represents the actual joint driving torque of the rotary joint; B f and F f Represent the viscous friction coefficient and the Coulomb friction coefficient respectively; S() represents the replacement of the switching function A continuous smooth function; d1 represents the centralized modeling error including external interference and unmodeled quantities; μ represents the torque coefficient obtained based on the principle of virtual work, Used to characterize the relationship between hydraulic cylinder thrust and joint torque, x L Indicates the displacement of the hydraulic cylinder; F L represents the thrust of the hydraulic cylinder of the slewing joint; p1 and p2 represent the pressure of the rodless chamber and the rod chamber of the hydraulic cylinder of the slewing joint respectively. and Represent the derivatives of the pressure in the rodless chamber and the rod chamber, respectively; A1 and A2 represent the piston areas of the rodless chamber and the rod chamber, respectively; V1 and V2 represent the volumes of the compressible chambers of the rodless chamber and the rod chamber, respectively; β e1 and β e2 represent the bulk elastic modulus of the rodless cavity and the rod cavity, respectively; Represents the derivative of the displacement of the hydraulic cylinder; Q 1d and Q 2d Represents the ideal control flow of the rodless cavity and the rod cavity respectively; d 21 and d 22 denote the first and second modeling errors of pressure dynamics, d 1n d 21n and d 22n denote the nominal values ​​of the concentrated modeling error, the first and second modeling errors of pressure dynamics, Δd1, Δd 21 and Δd 22 They represent the fast-changing error quantities of the centralized modeling error, the first and second modeling errors of pressure dynamics, respectively; f v1 () and f v2 () represent the voltage-flow mapping function of the rodless cavity and the rod cavity, Δp v1 and Δp v2 Respectively represent the valve port pressure drop of the hydraulic valve with and without rod cavity, u v1 and u v2represents the valve control voltage of the hydraulic valve with and without rod chamber respectively; α1, α2, α3, α4 represent the first, second, third and fourth polynomial fitting parameters respectively; θ1, θ2, θ3, θ4, θ5, θ6, θ7 11 ,θ 12 ,θ 13 ,θ 14 ,θ 21 ,θ 22 ,θ 23 ,θ 24 ,θ β1 and θ β2 They respectively represent the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth, thirteenth, fourteenth, fifteenth and sixteenth model parameters to be updated.

[0022] In the second step, the adaptive robust controller of the rotary joint is specifically as follows:

[0023] Q 1d =Q 1da +Q 1ds

[0024] Q 1da =Q 1da1 +Q 1da2 +Q 1da3 ,Q 1ds =Q 1ds1 +Q 1ds2

[0025]

[0026] Q 1da3 =-V1A1μz2

[0027] Q 1ds1 =-V1k 3s1 z p1 ,Q 1ds2 =-V1k 3s2 z p1

[0028] Q 2d =Q 2da +Q 2ds

[0029] Q 2da =Q 2da1 +Q 2da2 +Q 2da3 ,Q 2ds =Q 2ds1 +Q 2ds2

[0030]

[0031] Q 2da3 =-V2A2μz2

[0032] Q 2ds1 =V2k 4s1 z p2 ,Q 2ds2 =V2k 4s2 z p2

[0033]

[0034]

[0035] z1=qq d , z3=τ-τ d

[0036]

[0037] τ d =τ da +τ ds

[0038] τ da =τ da1 +τ da2 ,τ ds =τ ds1 +τ ds2

[0039]

[0040] τ ds1 =-k 2s1 z2,τ ds2 =-k 2s2 z2

[0041]

[0042] z p1 =p1-p 1d ,z p2 =p2-p 2d

[0043] Among them, Q 1d , Q 1da and Q 1ds They represent the ideal control flow of the rodless cavity and its model compensation control term and feedback control term, respectively. 1da1 , Q 1da2 , Q 1da3 , Q 1ds1 and Q1ds2 They represent the ideal control flow Q of the rodless cavity respectively 1d The feedforward model compensation term, fast dynamics compensation term, backstepping compensation term, linear stability feedback term and nonlinear robust feedback term; and denote the estimated values ​​of the fifth and fifteenth model parameters, respectively; Indicates the reference pressure p of the rodless cavity 1d The derivative of The computable part p 1dc The derivative of Indicates the reference pressure p of the rodless cavity 1d The derivative of The uncomputable part p 1di The derivative of 21 、 and denote the slow variables of the rodless cavity and their estimated values ​​and estimation errors respectively; z2 and They represent the error sliding modulus and its derivative of the rotary joint respectively; k 3s1 and k 3s2 They represent the ideal control flow Q of the rodless cavity respectively 1d The linear feedback gain and nonlinear robust feedback gain of z p1 Indicates the pressure tracking error of the rodless cavity; Q 2d , Q 2da and Q 2ds They represent the ideal control flow of the rod cavity and its model compensation control term and feedback control term, respectively. 2da1 , Q 2da2 , Q 2ds1 , Q 2ds2 and Q 2da3 They represent the ideal control flow Q of the rod cavity respectively 2d The feedforward model compensation term, fast dynamics compensation term, linear stability feedback term, nonlinear robust feedback term and backstepping compensation term; and denote the estimated values ​​of the sixth and sixteenth model parameters, respectively; Indicates the reference pressure p of the rod chamber 2d The derivative of The computable part p 2dc The derivative of Indicates the reference pressure p of the rod chamber 2d The derivative of The uncomputable part p 2di The derivative of 22 、 and are the slow variables of the rod cavity and their estimated values ​​and estimation errors; k 3s1 and k 3s2They represent the ideal control flow Q of the rod cavity respectively 2d The linear feedback gain and nonlinear robust feedback gain of z p2 represents the pressure tracking error of the rod cavity; τ and τ d Represent the actual driving torque and ideal driving torque respectively, τ da and τ ds They represent the ideal driving torque τ d The model compensation control term and feedback control term, τ da1 , τ da2 , τ ds1 and τ ds2 They represent the ideal driving torque τ d The feedforward model compensation term, fast dynamics compensation term, linear stability feedback term and nonlinear robust feedback term; D1, and denote the total slow variable and its estimated value and estimation error respectively; Represents the overall uncertain fast variable; ε1, ε 21 and ε 22 Represent the first, second and third preset parameters respectively; and Denote the uncertain fast variables of the rodless cavity and the rod cavity respectively; z1 and They represent the angle tracking error of the rotary joint and its derivative respectively; q, p d and They represent the actual joint angle and ideal joint angle of the rotary joint and their derivatives respectively; k1 represents the positive definite diagonal matrix of the sliding mode coefficient; and They represent the expected value of the joint angle q in the sliding modulus eq The derivative and second-order derivative of ; z3 represents the torque tracking error of the rotary joint; and denote the estimated values ​​of the first, second, third and fourth model parameters respectively; k 2s1 and k 2s2 They represent the ideal driving torque τ d The linear feedback gain and nonlinear robust feedback gain of p 1d and p 2d Represent the reference pressure of the rodless cavity and the rod cavity respectively; p c Indicates the preset minimum pressure of the chamber; and They represent the ideal driving torque τ d the derivatives of the computable and non-computable parts of ; represents the estimated value of the angular acceleration of the revolute joint; represents the derivative of the estimated value of the lumped parameter of the driving torque of the revolute joint; Represents the derivative of the estimate of the total slow variable.

[0044] The actual control flow output by the current rotary joint of the hydraulic manipulator in real time is used as the ideal control flow of the rodless cavity and the rod cavity in the adaptive robust controller.

[0045] In the second step, the parameters are updated online adaptively as follows:

[0046]

[0047] φ 11 =p1,φ 12 =ln(p1),

[0048] φ 21 =p2,φ 22 =ln(p2),

[0049]

[0050] Λ 21 =-[φ 11 ,φ 12 ,φ 13 ,φ 14 ,0] T

[0051] Λ 22 =-[φ 21 ,φ 22 ,φ 23 ,φ 24 ,0] T

[0052] Θ1=[θ1,θ2,θ3,θ4] T

[0053] Θ 21 =[θ 11 ,θ 12 ,θ 13 ,θ 14 ,θ5] T

[0054] Θ 22 =[θ 21 ,θ 22 ,θ 23 ,θ 24 ,θ6] T

[0055]

[0056] Among them, u1, u21 and u 22 Represent the first, second and third filter inputs respectively; φ 11 、φ 12 、φ 13 、φ 14 、φ 21 、φ 22 、φ 23 and φ 24 denote the first, second, third, fourth, fifth, sixth, seventh and eighth regressors, respectively. and denote the derivatives of the first, second, third, fourth, fifth, sixth, seventh and eighth regressors respectively; ln() denotes the logarithmic function; ζ1, ζ 21 and ζ 22 denote the first, second and third filtered linear regression matrices respectively, and denote the derivatives of the first, second and third filter linear regression matrices respectively; λ1, λ 21 and λ 22 Represent the first, second and third filter time constants respectively; Φ1, Φ 22 and Φ 22 denote the fourth, fifth and sixth filtered linear regression matrices respectively, and denote the derivatives of the fourth, fifth, and sixth filtered linear regression matrices, respectively;

[0057] F1, F 21 and F 22 Represent the first, second and third virtual filter input regression matrices respectively; y1, y 21 and y 22 Represent the output of the first, second and third filters respectively, and denote the estimated values ​​of the output of the first, second and third filters respectively, and denote the estimated deviations of the outputs of the first, second and third filters, respectively, and Respectively represent the estimated values ​​of the output of the first, second and third filters after reconstruction; Λ1, Λ 21 and Λ 22 Respectively represent the first, second and third auxiliary filter matrices; Θ1, Θ 21 and Θ 22 denote the first, second and third lumped parameter matrices respectively, and denote the estimated values ​​of the first, second and third lumped parameter matrices, respectively, and denote the estimation errors of the first, second and third lumped parameter matrices, respectively.

[0058] Perform online parameter adaptive update on the adaptive robust controller, and use the obtained first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters to update the estimated values ​​of the first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters in the adaptive robust controller.

[0059] The parameter adaptive law continuously estimates and updates the bulk elastic modulus of the hydraulic slewing joint and incorporates it into the model compensation.

[0060] In the second step, the ideal control flow Q of the rodless cavity is 1d And the ideal control flow Q of the rod cavity 2d After static mapping, the valve port control voltage u of the hydraulic valve of the rodless cavity is obtained v1 And the valve port control voltage u of the hydraulic valve with rod chamber v2 , and then control the hydraulic valve of the rotary joint. The present invention first considers the high-order characteristics such as the configuration of the hydraulic rotary joint and the strong nonlinearity unique to various hydraulic systems, considers the feasibility of model compensation and parameter adaptation, and proposes a volume elastic modulus model in the form of a parameterized fraction. Taking the rotary joint driven by the hydraulic cylinder as an example, a parameterized dynamic model of the overall system is established, and then the established high-order nonlinear dynamic model is linearly parameterized to facilitate the design of the controller and parameter adaptive law. In the controller, by designing the X-swapping mechanism, the online adaptive law of the main parameters is designed, and the parameter adaptive law based on recursive least squares is adopted to design an adaptive robust controller. Further improvement of the parameter adaptive effect is achieved while ensuring the motion control performance. It can achieve effective model compensation of the volume elastic modulus and accurate parameter adaptation when the volume elastic modulus of the hydraulic actuator changes.

[0061] The beneficial effects of the present invention are:

[0062] The method of the present invention can achieve effective compensation of the bulk elastic modulus and accurate parameter adaptation when the bulk elastic modulus of the rotary joint of the hydraulic manipulator changes, thereby further improving the parameter adaptation effect while ensuring motion control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a motion control block diagram of the method of the present invention;

[0064] Figure 2 is a schematic diagram of the motion reference trajectory of two groups of experiments of the method of the present invention, wherein, Figure 2 (a) is a schematic diagram of the S-shaped trajectory of the first set of experiments. Figure 2(b) is a schematic diagram of the sinusoidal trajectory of the second set of experiments;

[0065] Figure 3 is a comparison diagram of the S-shaped trajectory motion tracking error of the method of the present invention, wherein, Figure 3 (a) is a schematic diagram of the tracking error of controller C1 under the S-shaped trajectory. Figure 3 (b) is a schematic diagram of the tracking error of controller C2 under the S-shaped trajectory. Figure 3 (c) is a schematic diagram of the tracking error of controller C3 under the S-shaped trajectory;

[0066] Figure 4 is a comparison diagram of the sinusoidal trajectory motion tracking error of the method of the present invention, wherein, Figure 4 (a) is a schematic diagram of the tracking error of controller C1 under the sinusoidal trajectory. Figure 4 (b) is a schematic diagram of the tracking error of controller C2 under the sinusoidal trajectory. Figure 4 (c) is a schematic diagram of the tracking error of controller C3 under the sinusoidal trajectory;

[0067] Figure 5 This is a comparison diagram of the S-shaped trajectory pressure tracking error under the rod cavity of the method of the present invention, where: Figure 5 (a) is a schematic diagram of the tracking error of the rod cavity controller C1 under the S-shaped trajectory with respect to the pressure reference trajectory. Figure 5 (b) is a schematic diagram of the tracking error of the rod cavity controller C2 under the S-shaped trajectory with respect to the pressure reference trajectory. Figure 5 (c) is a schematic diagram of the tracking error of the rod cavity controller C3 under the S-shaped trajectory relative to the pressure reference trajectory;

[0068] Figure 6 This is a comparison diagram of the sinusoidal trajectory pressure tracking error under the rod cavity of the method of the present invention, where: Figure 6 (a) is a schematic diagram of the tracking error of the rod cavity controller C1 under the sine trajectory with respect to the pressure reference trajectory. Figure 6 (b) is a schematic diagram of the tracking error of the rod cavity controller C2 under the sine trajectory with respect to the pressure reference trajectory. Figure 6 (c) is a schematic diagram of the tracking error of the rod cavity controller C3 under the sinusoidal trajectory relative to the pressure reference trajectory;

[0069] Figure 7 : is a schematic diagram of the adaptive curve of the sinusoidal trajectory bulk elastic modulus of the controller C1 of the method of the present invention, wherein: Figure 7 (a) is a schematic diagram of the parameter adaptation of the controller C1 with a rod cavity under a sinusoidal trajectory. Figure 7 (b) is a schematic diagram of the parameter adaptation of the rodless cavity under the sinusoidal trajectory of controller C1;

[0070] Figure 8 : is a schematic diagram of the adaptive curve of the sinusoidal trajectory bulk elastic modulus of the controller C2 of the method of the present invention, wherein: Figure 8 (a) is a schematic diagram of the parameter adaptation of the rodless cavity under the sinusoidal trajectory of controller C2. Figure 8 (b) is a schematic diagram of the parameter adaptation of the rod cavity of controller C2 under the sinusoidal trajectory. DETAILED DESCRIPTION

[0071] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0072] like Figure 1 As shown, the low-pressure nonlinear elastic modulus adaptive compensation method of the hydraulic rotary joint of the present invention is specifically as follows:

[0073] The first step is to establish a linear parametric dynamic model of the rotary joint of the hydraulic manipulator based on the bulk elastic modulus in the form of a parameterized fraction, as follows:

[0074]

[0075] τ=μF L =μ(p1A1-p2A2)

[0076]

[0077] d1=d 1n +Δd1

[0078] d 21 =d 21n +Δd 21

[0079] d 22 =d 22n +Δd 22

[0080] Q 1d =f v1 (Δp v1 ,u v1 )

[0081] Q 2d =f v2 (Δp v2 ,u v2 )

[0082]

[0083] θ1=J L ,θ2=B f ,θ3=F f ,θ4=d 1n ,θ5=d 21n ,θ6=d 22n

[0084]

[0085] Among them, J L Represents the moment of inertia of the rotary joint of the hydraulic manipulator; and They represent the actual joint angular velocity and actual joint angular acceleration of the rotary joint respectively; τ represents the actual joint driving torque of the rotary joint; B f and F f Represent the viscous friction coefficient and the Coulomb friction coefficient respectively; S() represents the replacement of the switching function A continuous smooth function; d1 represents the centralized modeling error including external interference and unmodeled quantities; μ represents the torque coefficient obtained based on the principle of virtual work, Used to characterize the relationship between hydraulic cylinder thrust and joint torque, x L Indicates the displacement of the hydraulic cylinder; F L represents the thrust of the hydraulic cylinder of the slewing joint; p1 and p2 represent the pressure of the rodless chamber and the rod chamber of the hydraulic cylinder of the slewing joint respectively. and Represent the derivatives of the pressure in the rodless chamber and the rod chamber, respectively; A1 and A2 represent the piston areas of the rodless chamber and the rod chamber, respectively; V1 and V2 represent the volumes of the compressible chambers of the rodless chamber and the rod chamber, respectively; β e1 and β e2 represent the bulk elastic modulus of the rodless cavity and the rod cavity, respectively; Represents the derivative of the displacement of the hydraulic cylinder; Q 1d and Q 2d Represents the ideal control flow of the rodless cavity and the rod cavity respectively; d 21 and d 22 denote the first and second modeling errors of pressure dynamics, d 1n d 21n and d 22n denote the nominal values ​​of the concentrated modeling error, the first and second modeling errors of pressure dynamics, Δd1, Δd 21 and Δd 22 They represent the fast-changing error quantities of the centralized modeling error, the first and second modeling errors of pressure dynamics, respectively; f v1 () and f v2() represent the voltage-flow mapping function of the rodless cavity and the rod cavity, Δp v1 and Δp v2 Respectively represent the valve port pressure drop of the hydraulic valve with and without rod cavity, u v1 and u v2 represents the valve control voltage of the hydraulic valve with and without rod chamber respectively; α1, α2, α3, α4 represent the first, second, third and fourth polynomial fitting parameters respectively; θ1, θ2, θ3, θ4, θ5, θ6, θ7 11 ,θ 12 ,θ 13 ,θ 14 ,θ 21 ,θ 22 ,θ 23 ,θ 24 ,θ β1 and θ β2 They respectively represent the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth, thirteenth, fourteenth, fifteenth and sixteenth model parameters to be updated.

[0086] In the second step, based on the linear parameterized dynamic model of the rotary joint of the hydraulic manipulator, the backstepping method is used to design the adaptive robust controller of the rotary joint. The ideal joint angle of the current rotary joint is input into the adaptive robust controller, and the parameters of the adaptive robust controller are adaptively updated online. After processing, the adaptive robust controller outputs the ideal control flow of the rotary joint. After static mapping of the ideal control flow, the valve port control voltage is obtained to control the hydraulic valve of the rotary joint.

[0087] The adaptive robust controller of the rotary joint is as follows:

[0088] Q 1d =Q 1da +Q 1ds

[0089] Q 1da =Q 1da1 +Q 1da2 +Q 1da3 ,Q 1ds =Q 1ds1 +Q 1ds2

[0090]

[0091] Q 1da3 =-V1A1μz2

[0092] Q 1ds1 =-V1k 3s1 z p1,Q 1ds2 =-V1k 3s2 z p1

[0093] Q 2d =Q 2da +Q 2ds

[0094] Q 2da =Q 2da1 +Q 2da2 +Q 2da3 ,Q 2ds =Q 2ds1 +Q 2ds2

[0095]

[0096] Q 2da3 =-V2A2μz2

[0097] Q 2ds1 =V2k 4s1 z p2 ,Q 2ds2 =V2k 4s2 z p2

[0098]

[0099] z1=qq d , z3=τ-τ d

[0100]

[0101] t d =t da +t ds

[0102] t da =t da1 +t da2 ,t ds =t ds1 +t ds2

[0103]

[0104] t ds1 =-k 2s1 z2,t ds2 =-k 2s2 z2

[0105]

[0106]

[0107] z p1 =p1-p 1d ,z p2 =p2-p 2d

[0108] Among them, Q 1d , Q 1da and Q 1ds They represent the ideal control flow of the rodless cavity and its model compensation control term and feedback control term, respectively. 1da1 , Q 1da2 , Q 1da3 , Q 1ds1 and Q 1ds2 They represent the ideal control flow Q of the rodless cavity respectively 1d The feedforward model compensation term, fast dynamics compensation term, backstepping compensation term, linear stability feedback term and nonlinear robust feedback term; and denote the estimated values ​​of the fifth and fifteenth model parameters, respectively; Indicates the reference pressure p of the rodless cavity 1d The derivative of The computable part p 1dc The derivative of Indicates the reference pressure p of the rodless cavity 1d The derivative of The uncomputable part p 1di The derivative of 21 、 and denote the slow variables of the rodless cavity and their estimated values ​​and estimation errors respectively; z2 and They represent the error sliding modulus and its derivative of the rotary joint respectively; k 3s1 and k 3s2 They represent the ideal control flow Q of the rodless cavity respectively 1d The linear feedback gain and nonlinear robust feedback gain of z p1 Indicates the pressure tracking error of the rodless cavity; Q 2d , Q 2da and Q 2ds They represent the ideal control flow of the rod cavity and its model compensation control term and feedback control term, respectively. 2da1 , Q 2da2 , Q 2ds1 , Q 2ds2 and Q 2da3 They represent the ideal control flow Q of the rod cavity respectively 2d The feedforward model compensation term, fast dynamics compensation term, linear stability feedback term, nonlinear robust feedback term and backstepping compensation term; and denote the estimated values ​​of the sixth and sixteenth model parameters, respectively; Indicates the reference pressure p of the rod chamber 2d The derivative of The computable part p 2dc The derivative of Indicates the reference pressure p of the rod chamber 2d The derivative of The uncomputable part p 2di The derivative of 22 、 and are the slow variables of the rod cavity and their estimated values ​​and estimation errors; k 3s1 and k 3s2 They represent the ideal control flow Q of the rod cavity respectively 2d The linear feedback gain and nonlinear robust feedback gain of z p2 represents the pressure tracking error of the rod cavity; τ and τ d Represent the actual driving torque and ideal driving torque respectively, τ da and τ ds They represent the ideal driving torque τ d The model compensation control term and feedback control term, τ da1 , τ da2 , τ ds1 and τ ds2 They represent the ideal driving torque τ d The feedforward model compensation term, fast dynamics compensation term, linear stability feedback term and nonlinear robust feedback term; D1, and denote the total slow variable and its estimated value and estimation error respectively; Represents the overall uncertain fast variable; ε1, ε 21 and ε 22 Represent the first, second and third preset parameters respectively; and Denote the uncertain fast variables of the rodless cavity and the rod cavity respectively; z1 and They represent the angle tracking error of the rotary joint and its derivative respectively; q, p d and They represent the actual joint angle and ideal joint angle of the rotary joint and their derivatives respectively; k1 represents the positive definite diagonal matrix of the sliding mode coefficient; and They represent the expected value of the joint angle q in the sliding modulus eq The derivative and second-order derivative of ; z3 represents the torque tracking error of the rotary joint; and denote the estimated values ​​of the first, second, third and fourth model parameters respectively; k 2s1 and k 2s2They represent the ideal driving torque τ d The linear feedback gain and nonlinear robust feedback gain of p 1d and p 2d Represent the reference pressure of the rodless cavity and the rod cavity respectively; p c Indicates the preset minimum pressure of the chamber; and They represent the ideal driving torque τ d the derivatives of the computable and non-computable parts of ; represents the estimated value of the angular acceleration of the revolute joint; represents the derivative of the estimated value of the lumped parameter of the driving torque of the revolute joint; Represents the derivative of the estimate of the total slow variable.

[0109] The actual control flow output by the current rotary joint of the hydraulic manipulator in real time is used as the ideal control flow of the rodless cavity and the rod cavity in the adaptive robust controller.

[0110] The online adaptive update of parameters is as follows:

[0111]

[0112] φ 11 =p1,φ 12 =ln(p1),

[0113] φ 21 =p2,φ 22 =ln(p2),

[0114]

[0115]

[0116] Λ 21 =-[φ 11 ,φ 12 ,φ 13 ,φ 14 ,0] T

[0117] Λ 22 =-[φ 21 ,φ 22 ,φ 23 ,φ 24 ,0] T

[0118] Θ1=[θ1,θ2,θ3,θ4] T

[0119] Θ 21 =[θ 11 ,θ 12 ,θ 13 ,θ 14 ,θ5] T

[0120] Θ 22 =[θ 21 ,θ 22 ,θ 23 ,θ 24 ,θ6] T

[0121]

[0122] Among them, u1, u 21 and u 22 Represent the first, second and third filter inputs respectively; φ 11 、φ 12 、φ 13 、φ 14 、φ 21 、φ 22 、φ 23 and φ 24 denote the first, second, third, fourth, fifth, sixth, seventh and eighth regressors, respectively. and denote the derivatives of the first, second, third, fourth, fifth, sixth, seventh and eighth regressors respectively; ln() denotes the logarithmic function; ζ1, ζ 21 and ζ 22 denote the first, second and third filtered linear regression matrices respectively, and denote the derivatives of the first, second and third filter linear regression matrices respectively; λ1, λ 21 and λ 22 Represent the first, second and third filter time constants respectively; Φ1, Φ 22 and Φ 22 denote the fourth, fifth and sixth filtered linear regression matrices respectively, and denote the derivatives of the fourth, fifth, and sixth filtered linear regression matrices, respectively;

[0123] F1, F 21 and F 22 Represent the first, second and third virtual filter input regression matrices respectively; y1, y 21 and y 22 Represent the output of the first, second and third filters respectively, and denote the estimated values ​​of the output of the first, second and third filters respectively, and denote the estimated deviations of the outputs of the first, second and third filters, respectively, and Respectively represent the estimated values ​​of the output of the first, second and third filters after reconstruction; Λ1, Λ 21 and Λ 22 Respectively represent the first, second and third auxiliary filter matrices; Θ1, Θ 21 and Θ 22 denote the first, second and third lumped parameter matrices respectively, and denote the estimated values ​​of the first, second and third lumped parameter matrices, respectively, and denote the estimation errors of the first, second and third lumped parameter matrices, respectively.

[0124] Perform online parameter adaptive update on the adaptive robust controller, and use the obtained first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters to update the estimated values ​​of the first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters in the adaptive robust controller.

[0125] The parameter adaptive law continuously estimates and updates the bulk elastic modulus of the hydraulic slewing joint and incorporates it into the model compensation.

[0126] The ideal control flow Q of the rodless cavity 1d And the ideal control flow Q of the rod cavity 2d After static mapping, the valve port control voltage u of the hydraulic valve of the rodless cavity is obtained v1 And the valve port control voltage u of the hydraulic valve with rod chamber v2 , and then control the hydraulic valve of the slewing joint.

[0127] In the third step, the current rotary joint of the hydraulic manipulator outputs the actual control flow, actual driving torque and actual joint angle to the adaptive robust controller in real time to realize adaptive compensation closed-loop control of the rotary joint.

[0128] The goal of motion control is to achieve the actual joint angle q to the reference trajectory q d To accurately track the load, based on the adaptive robust control and backstepping control ideas, taking into account the characteristics of the load port independent control mode and the established bulk elastic modulus model, the present invention proposes a motion control system consisting of five main modules, including ideal driving torque calculation, cavity pressure update, rod cavity pressure control, rodless cavity pressure control and parameter online estimation based on X-swapping, such as Figure 1 As shown. Reference trajectory q dAs the input of the system, it is first used to calculate the ideal driving torque. This module calculates the ideal driving torque τ according to the reference trajectory. d Ideal driving torque τ d After calculation, it is passed to the cavity pressure update module, which is based on the ideal driving torque τ d The pressure demand of the system is updated and two signals are generated: the desired pressure p of the rod cavity and the 1d and the desired pressure p of the rodless chamber 2d The pressure generated by the cavity p 1d and p 2d The pressure is transmitted to the rod cavity pressure control module and the rodless cavity pressure control module respectively. These two modules control the pressure of the rod cavity and the rodless cavity respectively and output the corresponding control signal Q 1d and Q 2d At the same time, the system is also performing online parameter estimation based on X-swapping. This module runs in parallel and estimates the system parameters online through the X-swapping method, which may be used to optimize or adjust subsequent control links. Output Q of rod cavity pressure control and rodless cavity pressure control 1d and Q 2d The static mapping module for valve control signals converts these pressure control signals into the actual control signals required by the hydraulic system. Ultimately, the mapped signals are transmitted to the independent hydraulic rotary joint at the hydraulic load port, the system's actual actuator for load control and regulation. The system's execution status is transmitted back to the control system via state feedback, enabling real-time correction and optimization of control results within the closed-loop control system.

[0129] When the present invention is implemented, three methods are compared in the experiment, as follows:

[0130] Controller C1: the control method proposed by the present invention.

[0131] Controller C2: According to the existing mainstream control method, the bulk elastic modulus is regarded as a concentrated parameter for modeling and control, that is, only the bulk elastic modulus θ is considered. β , and is not expanded into the fractional parameterized form proposed in the present invention. The rest of the parts remain consistent with the controller C1. After fine parameter tuning, while ensuring control accuracy, it is possible to ensure that no obvious vibration occurs during the movement process.

[0132] Controller C3: To further verify the effect of bulk modulus on feedback control and confirm that controller C2 has basically reached its performance limit, controller C3 is consistent with controller C2 but with a slightly increased feedback gain.

[0133] Two groups of comparative experiments were carried out. The first group tracked the S-shaped acceleration and deceleration trajectory, and the second group tracked the sinusoidal trajectory. The specific reference trajectories are as follows: Figure 2(a) and Figure 2 As shown in (b).

[0134] The tracking errors of controllers C1, C2, and C3 in the two groups of comparative experiments are shown as follows: Figure 3 (a) Figure 3 (b) Figure 3 (c) Figure 4 (a) Figure 4 (b) and Figure 4 As shown in (c), the results show that controller C1 achieves the best tracking performance, has a good error peak suppression effect, and no obvious oscillation occurs during the motion tracking process; controllers C2 and C3 represent the mainstream method of modeling and controlling the bulk elastic modulus as a concentrated parameter. Among them, controller C2 has been carefully tuned and debugged, and it basically achieves good control performance in motion tracking without obvious oscillation, but the control accuracy is slightly inferior to the controller C1 proposed by the present invention. Controller C3 further improves the control gain compared to controller C2. Although the peak error is reduced, more obvious oscillation occurs, which indicates that controller C3 is already at the limit of performance. It can be confirmed that controller C2 has achieved the optimal performance that can be achieved by mainstream control methods. Therefore, the above comparison can ensure fairness. In addition, the control error was quantitatively compared, and the results are shown in Table 1, where the indicators ||e||1, ||e||2, ||e|| ∞ are the first norm, second norm and infinite norm of the peak error e, respectively. ρ is the control performance index, which is expressed as the ratio of the peak error to the maximum speed of the reference trajectory. From the numerical comparison results, the control accuracy of controller C1 is better than that of controller C2 and controller C3. Controller C3 is slightly better than controller C2 in terms of indicators, but Figure 3 and Figure 4 The tracking process of controller C3 shows significant oscillation. Therefore, combined with the motion tracking error comparison chart and the quantitative results in Table 1, by considering the nonlinearity of the bulk modulus in modeling and control, the controller C1 proposed in this invention achieves superior control performance compared to mainstream methods.

[0135] Table 1

[0136]

[0137] Further, Figure 5 (a) Figure 5 (b) Figure 5 (c) Figure 6 (a) Figure 6 (b) and Figure 6Figure (c) shows the tracking error of the rod cavity relative to the pressure reference trajectory for the three methods in two sets of experiments. It can be seen that controller C1 outperforms existing mainstream controllers C2 and C3 in terms of control accuracy and smoothness. Controller C3 also exhibits significant oscillation, confirming its performance has reached its limit. This type of pressure tracking control performance is not only crucial in the load-port independent system of interest to this invention, but also serves as a crucial foundation for electro-hydraulic servo force control systems. Therefore, the control method proposed in this invention provides valuable insights into related research on force control.

[0138] Take the data of the sinusoidal trajectory tracking experimental group as an example, Figure 7 and Figure 8 As shown in the figure, the online adaptive results of the parameters of controller C1 and controller C2 for the bulk elastic modulus are as follows: Figure 7 (a) and Figure 7 As shown in (b), it is the parameter adaptation in the fractional parameterized model of the bulk elastic modulus of controller C1. It can be seen that no matter it is a rod cavity or a rodless cavity, each parameter shows a certain convergence effect, which shows that from a mechanistic point of view, the above parameters can better fit the real model of the bulk elastic modulus; Figure 8 (a) and Figure 8 Figure (b) shows the lumped parameter adaptation of the bulk modulus of controller C2. It can be seen that the bulk moduli of both the rod-mounted and rodless cavities change significantly. The reason for this, analyzed in conjunction with the research results of the present invention, is that the bulk modulus itself is affected by pressure changes. During actuator motion, the cavity pressure changes significantly. Therefore, when describing the bulk modulus with lumped parameters, its true value is constantly changing, causing the estimated value to fluctuate accordingly, making it difficult to converge to a relatively fixed range. Therefore, method C1 proposed in the present invention can better achieve online adaptation of the bulk modulus model.

[0139] In summary, compared with mainstream control methods, the control method proposed in this paper further enhances motion tracking and pressure tracking control performance, and improves the online adaptation of the bulk modulus. Mechanistically, the bulk modulus of hydraulic transmissions is clearly linked to the operating pressure, but existing model-based control methods do not account for this. Therefore, by analyzing the mechanism of bulk modulus variation, this paper proposes a parameterized fractional bulk modulus model, balancing the accuracy of the model description with the feasibility of control design. Taking a hydraulic cylinder-driven rotary actuator as an example, a backstepping method is employed for model-based motion control design within the framework of adaptive robust control. By designing an exchange lemma mechanism, effective model compensation for the bulk modulus and online adaptation of key parameters are achieved, theoretically ensuring closed-loop system performance. A series of comparative experiments were conducted. Compared to mainstream control methods that treat the bulk modulus as a lumped parameter in both motion tracking and pressure tracking, the proposed method demonstrates improved performance and enables online adaptation of the hydraulic transmission bulk modulus model.

[0140] The above content is only the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A method for adaptively compensating the low-pressure nonlinear elastic modulus of a hydraulic rotary joint, characterized in that: include: The first step is to establish a linear parameterized dynamic model of the rotary joint of the hydraulic manipulator based on the parameterized fractional form of the bulk elastic modulus; In the second step, an adaptive robust controller for the rotary joint is designed using the backstepping method based on the linear parameterized dynamic model of the hydraulic manipulator's rotary joint. The ideal joint angle of the current rotary joint is input into the adaptive robust controller, and the parameters of the adaptive robust controller are adaptively updated online. After processing, the adaptive robust controller outputs the ideal control flow of the rotary joint. The ideal control flow is statically mapped to obtain the valve port control voltage, which is then used to control the hydraulic valve of the rotary joint. In the third step, the hydraulic manipulator's current rotary joint outputs the actual control flow, actual drive torque, and actual joint angle to the adaptive robust controller in real time, achieving adaptive compensation closed-loop control of the rotary joint. In the first step, the linear parameterized dynamic model of the rotary joint of the hydraulic manipulator is as follows: τ=μF L =μ(p1A1-p2A2) d1=d 1n +Δd1 d 21 =d 21n +Δd 21 d 22 =d 22n +Δd 22 Q 1d =f v1 (Δp v1 ,u v1 ) Q 2d =f v2 (Δp v2 ,u v2 ) θ1=J L ,θ2=B f ,θ3=F f ,θ4=d 1n ,θ5=d 21n ,θ6=d 22n Among them, J L Represents the moment of inertia of the rotary joint of the hydraulic manipulator; and They represent the actual joint angular velocity and actual joint angular acceleration of the rotary joint respectively; τ represents the actual joint driving torque of the rotary joint; B f and F f Represent the viscous friction coefficient and the Coulomb friction coefficient respectively; S( ) represents a continuous smooth function; d1 represents the centralized modeling error; μ represents the torque coefficient; F L represents the thrust of the hydraulic cylinder of the slewing joint; p1 and p2 represent the pressure of the rodless chamber and the rod chamber of the hydraulic cylinder of the slewing joint respectively. and Represent the derivatives of the pressure in the rodless chamber and the rod chamber, respectively; A1 and A2 represent the piston areas of the rodless chamber and the rod chamber, respectively; V1 and V2 represent the volumes of the compressible chambers of the rodless chamber and the rod chamber, respectively; β e1 and β e2 represent the bulk elastic modulus of the rodless cavity and the rod cavity, respectively; Represents the derivative of the displacement of the hydraulic cylinder; Q 1d and Q 2d Represents the ideal control flow of the rodless cavity and the rod cavity respectively; d 21 and d 22 denote the first and second modeling errors of pressure dynamics, d 1n d 21n and d 22n denote the nominal values ​​of the concentrated modeling error, the first and second modeling errors of pressure dynamics, Δd1, Δd 21 and Δd 22 They represent the fast-changing error quantities of the centralized modeling error, the first and second modeling errors of pressure dynamics, respectively; f v1 ( ) and f v2 ( ) represent the voltage-flow mapping function of the rodless cavity and the rod cavity, respectively, Δp v1 and Δp v2 Respectively represent the valve port pressure drop of the hydraulic valve with and without rod cavity, u v1 and u v2 represents the valve control voltage of the hydraulic valve with and without rod chamber respectively; α1, α2, α3, α4 represent the first, second, third and fourth polynomial fitting parameters respectively; θ1, θ2, θ3, θ4, θ5, θ6, θ7 11 ,θ 12 ,θ 13 ,θ 14 ,θ 21 ,θ 22 ,θ 23 ,θ 24 ,θ β1 and θ β2 Represent the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth, thirteenth, fourteenth, fifteenth and sixteenth model parameters respectively.

2. The method for adaptively compensating the low-pressure nonlinear elastic modulus of a hydraulic rotary joint according to claim 1, characterized in that: In the second step, the adaptive robust controller of the rotary joint is as follows: 1d =Q 1da +Q 1ds Q 1da =Q 1da1 +Q 1da2 +Q 1da3 ,Q 1ds =Q 1ds1 +Q 1ds2 Q 1ds1 =-V1k 3s1 z p1 ,Q 1ds2 =-V1k 3s2 z p1 Q 2d =Q 2da +Q 2ds Q 2da =Q 2da1 +Q 2da2 +Q 2da3 ,Q 2ds =Q 2ds1 +Q 2ds2 Q 2ds1 =V2k 4s1 With p2 ,Q 2ds2 =V2k 4s2 With p2 t d =t da +t ds t da =t da1 +t da2 ,t ds =t ds1 +t ds2 τ ds1 =-k 2s1 z2,τ ds2 =-k 2s2 z2 from p1 =p1-p 1d ,from p2 =p2-p 2d Among them, Q 1d , Q 1da and Q 1ds They represent the ideal control flow of the rodless cavity and its model compensation control term and feedback control term, respectively. 1da1 , Q 1da2 , Q 1da3 , Q 1ds1 and Q 1ds2 They represent the ideal control flow Q of the rodless cavity respectively 1d The feedforward model compensation term, fast dynamics compensation term, backstepping compensation term, linear stability feedback term and nonlinear robust feedback term; and denote the estimated values ​​of the fifth and fifteenth model parameters, respectively; Indicates the reference pressure p of the rodless cavity 1d The derivative of The computable part p 1dc The derivative of Indicates the reference pressure p of the rodless cavity 1d The derivative of The uncomputable part p 1di The derivative of 21 、 and denote the slow variables of the rodless cavity and their estimated values ​​and estimation errors respectively; z2 and They represent the error sliding modulus and its derivative of the rotary joint respectively; k 3s1 and k 3s2 They represent the ideal control flow Q of the rodless cavity respectively 1d The linear feedback gain and nonlinear robust feedback gain of z p1 Indicates the pressure tracking error of the rodless cavity; Q 2d , Q 2da and Q 2ds They represent the ideal control flow of the rod cavity and its model compensation control term and feedback control term, respectively. 2da1 , Q 2da2 , Q 2ds1 , Q 2ds2 and Q 2da3 They represent the ideal control flow Q of the rod cavity respectively 2d The feedforward model compensation term, fast dynamics compensation term, linear stability feedback term, nonlinear robust feedback term and backstepping compensation term; and denote the estimated values ​​of the sixth and sixteenth model parameters, respectively; Indicates the reference pressure p of the rod chamber 2d The derivative of The computable part p 2dc The derivative of Indicates the reference pressure p of the rod chamber 2d The derivative of The uncomputable part p 2di The derivative of 22 、 and are the slow variables of the rod cavity and their estimated values ​​and estimation errors; k 3s1 and k 3s2 They represent the ideal control flow Q of the rod cavity respectively 2d The linear feedback gain and nonlinear robust feedback gain of z p2 represents the pressure tracking error of the rod cavity; τ and τ d Represent the actual driving torque and ideal driving torque respectively, τ da and τ ds They represent the ideal driving torque τ d The model compensation control term and feedback control term, τ da1 , τ da2 , τ ds1 and τ ds2 They represent the ideal driving torque τ d The feedforward model compensation term, fast dynamics compensation term, linear stability feedback term and nonlinear robust feedback term; D1, and denote the total slow variable and its estimated value and estimation error respectively; Represents the overall uncertain fast variable; ε1, ε 21 and ε 22 Represent the first, second and third preset parameters respectively; and Denote the uncertain fast variables of the rodless cavity and the rod cavity respectively; z1 and They represent the angle tracking error of the rotary joint and its derivative respectively; q, p d and They represent the actual joint angle and ideal joint angle of the rotary joint and their derivatives respectively; k1 represents the positive definite diagonal matrix of the sliding mode coefficient; and They represent the expected value of the joint angle q in the sliding modulus eq The derivative and second-order derivative of ; z3 represents the torque tracking error of the rotary joint; and denote the estimated values ​​of the first, second, third and fourth model parameters respectively; k 2s1 and k 2s2 They represent the ideal driving torque τ d The linear feedback gain and nonlinear robust feedback gain of p 1d and p 2d Represent the reference pressure of the rodless cavity and the rod cavity respectively; p c Indicates the preset minimum pressure of the chamber; and They represent the ideal driving torque τ d the derivatives of the computable and non-computable parts of ; represents the estimated value of the angular acceleration of the revolute joint; represents the derivative of the estimated value of the lumped parameter of the driving torque of the revolute joint; represents the derivative of the estimated value of the total slow variable; The actual control flow output by the current rotary joint of the hydraulic manipulator in real time is used as the ideal control flow of the rodless cavity and the rod cavity in the adaptive robust controller.

3. The method for adaptively compensating the low-pressure nonlinear elastic modulus of a hydraulic rotary joint according to claim 1, characterized in that: In the second step, the parameters are updated online adaptively as follows: f 11 =p1,φ 12 =ln(p1), f 21 =p2,φ 22 =ln(p2), Θ1=[θ1,θ2,θ3,θ4] T I 21 =[θ 11 ,i 12 ,i 13 ,i 14 ,θ5] T I 22 =[θ 21 ,i 22 ,i 23 ,i 24 ,θ6] T Among them, u1, u 21 and u 22 Represent the first, second and third filter inputs respectively; φ 11 、φ 12 、φ 13 、φ 14 、φ 21 、φ 22 、φ 23 and φ 24 denote the first, second, third, fourth, fifth, sixth, seventh and eighth regressors, respectively. and denote the derivatives of the first, second, third, fourth, fifth, sixth, seventh and eighth regressors respectively; ln( ) denotes the logarithmic function; ζ1, ζ 21 and ζ 22 denote the first, second and third filtered linear regression matrices respectively, and denote the derivatives of the first, second and third filter linear regression matrices respectively; λ1, λ 21 and λ 22 Represent the first, second and third filter time constants respectively; Φ1, Φ 22 and Φ 22 denote the fourth, fifth and sixth filtered linear regression matrices respectively, and Denote the derivatives of the fourth, fifth and sixth filter linear regression matrices respectively; F1, F 21 and F 22 Represent the first, second and third virtual filter input regression matrices respectively; y1, y 21 and y 22 Represent the output of the first, second and third filters respectively, and denote the estimated values ​​of the output of the first, second and third filters respectively, and denote the estimated deviations of the outputs of the first, second and third filters, respectively, and Respectively represent the estimated values ​​of the output of the first, second and third filters after reconstruction; Λ1, Λ 21 and Λ 22 Respectively represent the first, second and third auxiliary filter matrices; Θ1, Θ 21 and Θ 22 denote the first, second and third lumped parameter matrices respectively, and denote the estimated values ​​of the first, second and third lumped parameter matrices, respectively, and denote the estimation errors of the first, second and third lumped parameter matrices respectively; Perform online parameter adaptive update on the adaptive robust controller, and use the obtained first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters to update the estimated values ​​of the first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters in the adaptive robust controller.

4. The method for adaptively compensating the low-pressure nonlinear elastic modulus of a hydraulic rotary joint according to claim 1, characterized in that: In the second step, the ideal control flow Q of the rodless cavity is 1d And the ideal control flow Q of the rod cavity 2d After static mapping, the valve port control voltage u of the hydraulic valve of the rodless cavity is obtained v1 And the valve port control voltage u of the hydraulic valve with rod chamber v2 , and then control the hydraulic valve of the slewing joint.

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