Self-adaptive compensation method for low-pressure nonlinear elastic modulus of hydraulic rotary joint

Abstract

The invention discloses a low-pressure nonlinear elastic modulus self-adaptive compensation method for a hydraulic rotary joint. The method comprises the steps that a linear parameterized kinetic model of the rotary joint of the hydraulic mechanical arm based on the volume elastic modulus in a parameterized fractional form is established, a self-adaptive robust controller is designed, the ideal joint angle of the current rotary joint is input into the controller, meanwhile, online self-adaptive parameter updating is conducted, and the optimal joint angle of the rotary joint is obtained. The controller outputs ideal control flow after processing, and valve port control voltage is obtained after static mapping to control a hydraulic valve; and the rotary joint outputs the actual control flow, the actual driving torque and the actual joint angle to the controller in real time, and self-adaptive compensation closed-loop control is achieved. According to the method, under the condition that the volume elastic modulus of the rotary joint of the hydraulic mechanical arm changes, effective compensation of the volume elastic modulus and accurate parameter self-adaption can be achieved, and the parameter self-adaption effect is further improved under the condition that the motion control performance is guaranteed.

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 swivel joint. Background Art

[0002] Intelligence and robotization are new development directions in important application fields of hydraulic equipment such as engineering machinery. Among them, machine closed loop replacing manual closed loop is an important link at the equipment level, so high-performance control of hydraulic slewing joints has become an indispensable key basic technology. Existing research mainly conducts online adaptive and compensatory control on model parameters such as load mass, moment of inertia, dynamic friction, and external load force. However, for the important bulk elastic modulus of hydraulic transmission system, almost all studies regard it as a known quantity or estimate it online in the form of concentrated parameters. However, the actual situation of bulk elastic modulus is very complicated. The pressure of hydraulic system changes rapidly and with large amplitude, especially under the condition of frequent start-stop, dynamic acceleration and deceleration. Under this influence, the bulk elastic modulus will also change significantly. In addition, unlike parameters such as friction coefficient, which are easy to obtain more accurate values ​​through system identification experiments, the specific value of bulk elastic modulus requires special equipment to measure, and even if it can be measured, due to the influence of factors such as hydraulic oil pipe elasticity and oil gas content, the bulk elastic modulus used to establish the cavity pressure dynamics is not equivalent to the oil value. Therefore, considering the change of bulk elastic modulus as accurately as possible in closed-loop control has an important impact on feedback gain setting, feedback control effect, etc. However, the key lies in what mathematical expression method is used to consider such a mechanism relationship. Therefore, how to solve the actual mechanism of the change of bulk elastic modulus of the hydraulic slewing joint more accurately during the control process and take into account the feasibility of the control design is an urgent problem to be solved. 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 swivel joint.

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

[0005] The low-pressure nonlinear elastic modulus adaptive compensation method of the hydraulic swivel 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 parameterized fractions.

[0007] In the second step, based on the linear parameterized dynamic model of the slewing joint of the hydraulic manipulator, the backstepping method is used to design an adaptive robust controller for the slewing joint. The ideal joint angle of the current slewing 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 slewing joint. After static mapping of the ideal control flow, the valve port control voltage is obtained to control the hydraulic valve of the slewing 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 is a continuous smooth function; d1 represents the concentrated 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 Respectively represent the derivatives of the pressure of the rodless chamber and the rod chamber, 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 cavity without rod and the cavity with rod, respectively; Represents the derivative of the displacement of the hydraulic cylinder; Q 1d and Q 2d Respectively represent the ideal control flow of the rodless cavity and the rod cavity; 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 the pressure dynamics, Δd1, Δd 21 and Δd 22 Respectively represent the fast-changing error of the concentrated modeling error, the first and second modeling errors of pressure dynamics; 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 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 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 rate 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 chamber 1d The derivative of The computable part p 1dc The derivative of Indicates the reference pressure p of the rodless chamber 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; 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 rate Q of the rodless cavity respectively 1d The linear feedback gain and nonlinear robust feedback gain of z p1 Represents 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 They represent the slow variables of the rod cavity and their estimated values ​​and estimation errors respectively; 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 Respectively represent the total slow variable and its estimated value and estimation error; represents the overall uncertain fast variable; ε1, ε 21 and ε 22 Respectively represent the first, second and third preset parameters; and Respectively represent the uncertain fast variables of the rodless cavity and the rod cavity; z1 and They represent the angular 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 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 Respectively represent the first, second and third filter input quantities; 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 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 Respectively represent the first, second and third filter time constants; Φ1, Φ 22 and Φ 22 denote the fourth, fifth and sixth filtering 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 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] The parameters of the adaptive robust controller are updated online adaptively, and the estimated values ​​of the first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters in the adaptive robust controller are updated using the obtained first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters.

[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 rate 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 chamber 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. The present invention first considers the high-order characteristics such as the configuration of the hydraulic slewing 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 slewing joint driven by a 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. The parameter adaptive effect is further improved while ensuring the motion control performance. It can achieve effective model compensation of the volume elastic modulus and precise 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 realize effective compensation of the bulk elastic modulus and accurate parameter adaptation when the bulk elastic modulus of the rotary joint of the hydraulic mechanical arm changes, thereby further improving the parameter adaptation effect while ensuring the 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 sinusoidal trajectory motion tracking errors of the method of the present invention, wherein: Figure 4 (a) is a schematic diagram of the tracking error of controller C1 under a sinusoidal trajectory. Figure 4 (b) is a schematic diagram of the tracking error of controller C2 under a sinusoidal trajectory. Figure 4 (c) is a schematic diagram of the tracking error of controller C3 under the sinusoidal trajectory;

[0067] Figure 5 is a comparison diagram of the S-shaped trajectory pressure tracking error under the rod cavity of the method of the present invention, wherein: 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 with respect to the pressure reference trajectory of the controller C3 under the rod cavity under the S-shaped trajectory;

[0068] Figure 6 is a comparison diagram of the sinusoidal trajectory pressure tracking error under the rod cavity of the method of the present invention, wherein: 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 with respect to the pressure reference trajectory of the controller C3 under the rod cavity under the sinusoidal trajectory;

[0069] Figure 7 : is a schematic diagram of the adaptive curve of the sine 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 of controller C1 under the sinusoidal trajectory;

[0070] Figure 8 : is a schematic diagram of the adaptive curve of the sine 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 of controller C2 under the sinusoidal trajectory. 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 purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. The specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in each embodiment of the present invention described below can 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 swivel 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 parameterized fractions, 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 is a continuous smooth function; d1 represents the concentrated 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 Respectively represent the derivatives of the pressure of the rodless chamber and the rod chamber, 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 cavity without rod and the cavity with rod, respectively; Represents the derivative of the displacement of the hydraulic cylinder; Q 1d and Q 2d Respectively represent the ideal control flow of the rodless cavity and the rod cavity; 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 the pressure dynamics, Δd1, Δd 21 and Δd 22 Respectively represent the fast-changing error of the concentrated modeling error, the first and second modeling errors of pressure dynamics; 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 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 slewing joint of the hydraulic manipulator, the backstepping method is used to design an adaptive robust controller for the slewing joint. The ideal joint angle of the current slewing 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 slewing joint. After static mapping of the ideal control flow, the valve port control voltage is obtained to control the hydraulic valve of the slewing 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 rate 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 chamber 1d The derivative of The computable part p 1dc The derivative of Indicates the reference pressure p of the rodless chamber 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; 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 rate Q of the rodless cavity respectively 1d The linear feedback gain and nonlinear robust feedback gain of z p1 Represents 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 They represent the slow variables of the rod cavity and their estimated values ​​and estimation errors respectively; 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 Respectively represent the total slow variable and its estimated value and estimation error; represents the overall uncertain fast variable; ε1, ε 21 and ε 22 Respectively represent the first, second and third preset parameters; and Respectively represent the uncertain fast variables of the rodless cavity and the rod cavity; z1 and They represent the angular 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 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 Respectively represent the first, second and third filter input quantities; 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 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 Respectively represent the first, second and third filter time constants; Φ1, Φ 22 and Φ 22 denote the fourth, fifth and sixth filtering 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 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] The parameters of the adaptive robust controller are updated online adaptively, and the estimated values ​​of the first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters in the adaptive robust controller are updated using the obtained first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters.

[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 chamber 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, considering the characteristics of the load port independent control mode and the established bulk elastic modulus model, the present invention proposes a motion control system containing 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 chamber 1d and the desired pressure p of the rodless chamber 2d The pressure generated by the cavity is 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 of the valve control signal is responsible for converting these pressure control signals into the control signals actually required by the hydraulic system. Finally, the statically mapped signal is transmitted to the independent hydraulic rotary joint at the hydraulic load port, which is the actual actuator of the system and is used to control and adjust the load. The execution status of the system will be transmitted back to the control system through state feedback so that the control effect can be corrected and optimized in real time in closed-loop control.

[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 , but not expanded into the fractional parameterized form proposed by the present invention, and the rest of the parts remain consistent with the controller C1. After fine parameter adjustment, under the premise of ensuring control accuracy, it is ensured that no obvious vibration occurs during the motion process.

[0132] Controller C3: To further verify the effect of bulk modulus on feedback control and to 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 in 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 motion tracking; controllers C2 and C3 represent the mainstream method of modeling and controlling the bulk elastic modulus as a concentrated parameter. After careful adjustment and debugging, controller C2 basically achieves good control performance in motion tracking without obvious oscillation, but the control accuracy is slightly inferior to the controller C1 proposed in the present invention. Controller C3 further improves the control gain relative to controller C2. Although the peak error is reduced, more obvious oscillation occurs, which indicates that controller C3 is already at the boundary of the limit performance, and it can be confirmed that controller C2 has achieved the optimal performance that can be achieved by the mainstream control method, so 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 From the tracking process, the controller C3 oscillates obviously. Therefore, combined with the motion tracking error comparison chart and the quantitative results in Table 1, by taking the bulk elastic modulus nonlinearity into account in modeling and control, the controller C1 proposed in the present invention achieves better control performance than the mainstream method.

[0135] Table 1

[0136]

[0137] Further, Figure 5 (a) Figure 5 (b) Figure 5 (c) Figure 6 (a) Figure 6 (b) and Figure 6As shown in (c), the tracking errors of the rod cavity with respect to the pressure reference trajectory in the two groups of experiments of the three methods are shown. It can be seen that from the perspective of control accuracy and smoothness, controller C1 is better than the existing mainstream controllers C2 and C3; controller C3 also has obvious oscillations, proving that its performance has reached the limit. This type of pressure tracking control performance is not only very important in the load port independent system concerned by the present invention, but also an important foundation of the electro-hydraulic servo force control system. Therefore, the control method proposed in the present invention has a certain reference role in the 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, it is the online adaptive result of the parameters of controller C1 and controller C2 for the bulk elastic modulus, as 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 (b) shows the adaptive situation of the concentrated parameter of the bulk elastic modulus of controller C2. It can be seen that the bulk elastic modulus of both the rod cavity and the rodless cavity changes significantly. The reason is analyzed in combination with the research results of the present invention. The bulk elastic modulus itself is affected by pressure changes. During the movement of the actuator, the pressure of the cavity changes significantly. Therefore, the bulk elastic modulus is described by concentrated parameters, and its true value is always changing, causing the estimated value to change accordingly, and it is difficult to converge to a relatively fixed range. Therefore, the method C1 proposed by the present invention can better realize the online adaptation of the bulk elastic modulus model.

[0139] In summary, compared with the mainstream control method, the control method proposed in the present invention further improves the motion tracking and pressure tracking control effects, and improves the online adaptive effect of the bulk elastic modulus. Mechanistically, there is an obvious connection between the bulk elastic modulus of hydraulic transmission and the working pressure, but the existing model-based control method does not take it into account. To this end, the present invention analyzes the change mechanism of the bulk elastic modulus, considers the accuracy of the model description and the feasibility of the control design, and proposes a parameterized fractional bulk elastic modulus model. Taking the rotary actuator driven by the hydraulic cylinder as an example, the backstepping method is used for model-based motion control design under the adaptive robust control framework. By designing the exchange lemma mechanism, effective model compensation of the bulk elastic modulus and online adaptation of the main parameters are achieved, and the closed-loop system performance is theoretically ensured. A series of comparative tests were carried out. In motion tracking and pressure tracking, compared with the mainstream control method that regards the bulk elastic modulus as a centralized parameter, the method proposed in the present invention shows a performance improvement effect, and can achieve an online adaptive effect on the bulk elastic modulus model of the hydraulic transmission.

[0140] The above contents are only the technical ideas 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 ideas 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 low-pressure nonlinear elastic modulus of a hydraulic swivel 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 bulk elastic modulus in the form of parameterized fractions; In the second step, according to the linear parameterized dynamic model of the rotary joint of the hydraulic manipulator, the adaptive robust controller of the rotary joint is designed using the backstepping method. 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, and then the hydraulic valve of the rotary joint is controlled. 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.

2. The low-pressure nonlinear elastic modulus adaptive compensation method of a hydraulic swivel joint according to claim 1, characterized in that: 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 Respectively represent the viscous friction coefficient and the Coulomb friction coefficient; S( ) represents a continuous smooth function; d1 represents the concentrated 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 Respectively represent the derivatives of the pressure of the rodless chamber and the rod chamber, 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 cavity without rod and the cavity with rod, respectively; Represents the derivative of the displacement of the hydraulic cylinder; Q 1d and Q 2d Respectively represent the ideal control flow of the rodless cavity and the rod cavity; 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 the pressure dynamics, Δd1, Δd 21 and Δd 22 Respectively represent the fast-changing error of the concentrated modeling error, the first and second modeling errors of pressure dynamics; 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 They represent the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth, thirteenth, fourteenth, fifteenth and sixteenth model parameters respectively.

3. The low-pressure nonlinear elastic modulus adaptive compensation method of a hydraulic swivel joint according to claim 2, characterized in that: In the second step, the adaptive robust controller of the rotary joint is as follows: Q 1d =Q 1da +Q 1ds Q 1da =Q 1da1 +Q 1da2 +Q 1da3 ,Q 1ds =Q 1ds1 +Q 1ds2 Q 1da3 =-V1A1μz2 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 2da3 =-V2A2μz2 Q 2ds1 =V2k 4s1 With p2 ,Q 2ds2 =V2k 4s2 With p2 z1=qq d , z3=τ-τ d t d =t da +t ds t da =t da1 +t da2 ,t ds =t ds1 +t ds2 t 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 rate 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 chamber 1d The derivative of The computable part p 1dc The derivative of Indicates the reference pressure p of the rodless chamber 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; 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 rate Q of the rodless cavity respectively 1d The linear feedback gain and nonlinear robust feedback gain of z p1 Represents 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 They represent the slow variables of the rod cavity and their estimated values ​​and estimation errors respectively; 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 Represent the total slow variable and its estimated value and estimation error respectively; represents the overall uncertain fast variable; ε1, ε 21 and ε 22 Respectively represent the first, second and third preset parameters; and Respectively represent the uncertain fast variables of the rodless cavity and the rod cavity; z1 and Respectively represent the angle tracking error of the rotary joint and its derivative; q, p d and They represent the actual joint angle and ideal joint angle of the revolute 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 1d and p 2d Respectively represent the reference pressure of the rodless cavity and the rod cavity; 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.

4. The low-pressure nonlinear elastic modulus adaptive compensation method of a hydraulic swivel joint according to claim 2, 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), L 21 =-[φ 11 ,f 12 ,f 13 ,f 14 ,0] T L 22 =-[φ 21 ,f 22 ,f 23 ,f 24 ,0] T 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 Respectively represent the first, second and third filter input quantities; 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 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 Respectively represent the first, second and third filter time constants; Φ1, Φ 22 and Φ 22 denote the fourth, fifth and sixth filtering 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 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; The parameters of the adaptive robust controller are updated online adaptively, and the estimated values ​​of the first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters in the adaptive robust controller are updated using the obtained first, second, third, fourth, fifth, sixth, fifteenth and sixteenth model parameters.

5. The low-pressure nonlinear elastic modulus adaptive compensation method of a hydraulic swivel joint according to claim 2, characterized in that: In the second step, the ideal control flow rate 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 chamber 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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