Adaptive robust control method for twin-cylinder synchronous drive system based on extended state observer

Abstract

The application discloses a kind of based on the adaptive robust control method of double-cylinder synchronous drive system of expansion observer. Method includes: the nonlinear dynamics model of double-cylinder synchronous drive system including synchronization valve and proportional reversing valve is established, and expansion observer and direct / indirect adaptive robust controller are constructed;System displacement error and shunt pressure difference are input into expansion observer and projection type adaptive law, and the estimated value of system slowly varying parameter is output by projection type adaptive law and input into expansion observer, and the load bias and shunt error of expansion observer are output to controller, and controller simultaneously outputs virtual control flow according to system error parameter processing, and after being restored to the input control voltage of proportional reversing valve, real-time control is carried out to double-cylinder synchronous drive system.The application can realize fast and accurate load bias disturbance estimation only by the pressure sensor signal and hydraulic cylinder displacement sensor signal of double-cylinder drive system, to ensure the high-precision synchronous control of double-cylinder drive.

Description

Technical Field

[0001] This invention relates to a control method for a dual-cylinder synchronous drive system, which falls under the field of hydraulic control technology, and specifically to an adaptive robust control method for a dual-cylinder synchronous drive system based on an extended observer. Background Technology

[0002] Dual hydraulic cylinder drive systems are widely used in machining, shipbuilding, aerospace, and other industries to address issues such as drive imbalance and layout limitations. High stability and synchronization accuracy are crucial for dual-cylinder drives. However, the synchronization accuracy of dual hydraulic cylinder drive systems can significantly decrease under disturbances such as load imbalance, time-varying model parameters, and subsystem differences. Therefore, achieving rapid compensation for off-center loads and unknown disturbances, and ultimately establishing a highly reliable dual-cylinder drive system with high synchronization control accuracy, is of significant application value. Summary of the Invention

[0003] To address the problems existing in the background art, the present invention provides an adaptive robust control method for a dual-cylinder synchronous drive system based on an extended observer.

[0004] The technical solution adopted in this invention is:

[0005] The adaptive robust control method for a dual-cylinder synchronous drive system based on an extended observer, as described in this invention, includes:

[0006] Step 1: Establish a nonlinear dynamic model of a dual-cylinder synchronous drive system including a synchronizing valve and a bypass proportional directional valve. Based on the nonlinear dynamic model, construct an extended observer and a direct / indirect adaptive robust controller including a feedforward model compensation term, a fast dynamic compensation term, a nonlinear feedback term, a linear feedback term, and a projected adaptive law.

[0007] Step 2: The displacement error and shunt pressure difference of the dual-cylinder synchronous drive system are input into the extended observer and the projected adaptive law, respectively. After online parameter estimation based on the model, the projected adaptive law outputs the estimated values ​​of the slowly varying system parameters of the dual-cylinder synchronous drive system and inputs them into the extended observer. After processing, the extended observer outputs the load deviation and shunt error of the dual-cylinder synchronous drive system and inputs them together with the desired trajectory into the feedforward model compensation term. The error parameters of the dual-cylinder synchronous drive system are obtained based on the displacement error and shunt pressure difference and input into the fast dynamics compensation term, the nonlinear feedback term, and the linear feedback term, respectively. Finally, the outputs of the feedforward model compensation term, the fast dynamics compensation term, the nonlinear feedback term, and the linear feedback term are added together to obtain the virtual control flow.

[0008] Step 3: Restore the virtual control flow rate to the input control voltage of the proportional directional valve and control the dual-cylinder synchronous drive system; repeat steps one to three to achieve adaptive robust real-time control of the dual-cylinder synchronous drive system. The bounded stability of the controller and the convergence of parameter estimation are proved using the Lyapunov method.

[0009] In step one, the nonlinear dynamic model of the dual-cylinder synchronous drive system is as follows:

[0010]

[0011] θ1=mA -1 θ2=BA -1 ,θ3=(K t β e ) -1 ,

[0012] B c =ΔP L / V L1 ,

[0013] Q u =M(u)u

[0014]

[0015] Where θ represents the slowly varying parameter matrix of the dual-cylinder synchronous drive system, θ i θ represents the i-th parameter in the slowly varying parameter matrix θ of the system. imax and θ imin Let θ represent the i-th parameter θ in the system's slowly varying parameter matrix θ. i upper and lower boundaries, The boundary of the slowly varying parameter matrix θ of the system; Δx, and These represent the displacement error, velocity error, and acceleration error of the piston rod in a dual-cylinder synchronous drive system, respectively; ΔP L and Let ΔP represent the pressure difference between the two hydraulic cylinders in the dual-cylinder synchronous drive system and its derivative. L =P L1 -P L2 P L1 and P L2 These represent the load pressures of the first and second hydraulic cylinders in the dual-cylinder synchronous drive system, respectively. ΔF represents the derivative of the load pressure of the second hydraulic cylinder in a dual-cylinder synchronous drive system. LA represents the load deviation experienced by the two hydraulic cylinders in a dual-cylinder synchronous drive system; A represents the effective working area of ​​the piston rod of the hydraulic cylinder in the dual-cylinder synchronous drive system; A c B c and C c These represent the first, second, and third calculated parameters of the nonlinear dynamic model, respectively; Q u ΔQ represents the input control flow rate of the proportional directional valve in a dual-cylinder synchronous drive system. f K represents the flow splitting error of the synchronizing valve in a dual-cylinder synchronous drive system. t V represents the flow regulation coefficient of the proportional directional valve in a dual-cylinder synchronous drive system. L1 β represents the compressible volume of the inlet chamber of the first hydraulic cylinder in the dual-cylinder synchronous drive system; m represents the load mass of the hydraulic cylinder in the dual-cylinder synchronous drive system; B represents the viscous damping coefficient of the piston rod of the hydraulic cylinder in the dual-cylinder synchronous drive system; e C represents the elastic modulus of the oil. j M(u0) represents the internal leakage coefficient of the hydraulic cylinder in a dual-cylinder synchronous drive system; M(u0) represents the input control voltage Q of the proportional valve in the dual-cylinder synchronous drive system. u The mapping relationship between the actual control voltage u; s() represents a 0-1 variable; D i This represents the i-th modeling error of the nonlinear dynamics model. D represents the i-th modeling error of the nonlinear dynamic model. i Uncertain boundary, δ i This represents the preset value of the i-th constant.

[0016] In step one, the extended observer is specifically as follows:

[0017]

[0018] Where s and z represent the first and second state variable matrices of the extended observer, respectively, and s1, s2, and s3 represent the first, second, and third state variables of the first state variable matrix s, respectively. and These represent the state observations of the first, second, and third state variables in the first state variable matrix s, respectively. and These represent the state observations of the first, second, and third state variables in the first state variable matrix s, respectively. and Let z1 and z2 represent the derivatives of the state observations of the first, second, and third state variables in the first state variable matrix s, respectively, and z1 and z2 represent the first and second state variables in the second state variable matrix z, respectively. and Let z represent the state observations of the first and second state variables of the second state variable matrix z, respectively. and ω1 and ω2 represent the derivatives of the state observations of the first and second state variables of the second state variable matrix z, respectively; ω1 and ω2 represent the first and second feedback gain coefficients of the extended observer, respectively; This represents the estimated value of the i-th parameter in the slowly varying parameter matrix θ of the system. The parameter estimation matrix represents the system's slowly varying parameter matrix θ. Let represent the adaptive error of the i-th parameter in the slowly varying parameter matrix θ of the system. Represents the system's slowly varying parameter matrix θ and parameter estimation matrix The estimation error matrix between them; ΔP Ld Indicates the virtual control shunt pressure difference; Q ud This represents the virtual control flow rate of the proportional directional valve. and These represent the tracking values ​​of the load deviation and flow splitting error of the synchronizing valve in the dual-cylinder synchronous drive system, respectively.

[0019] In step one, the direct / indirect adaptive robust controller is specifically as follows:

[0020] Q ud =Q uda1 +Q uda2 +Q uds1 +Q uds2

[0021] ΔP Ld =ΔP Lda1 +ΔP Lda2 +ΔP Lds1 +ΔP Lds2

[0022] Among them, Q ud and ΔP Ld ΔP represents the virtual control flow rate and virtual control shunt pressure difference of the proportional directional valve, respectively. Lda1 and Q uda1 These represent the compensation terms of the first and second feedforward models, respectively; ΔP Lda2 and Q uda2 These represent the first and second fast dynamic compensation terms, respectively; ΔP Lds1 and Q uds1 These represent the first and second linear feedback terms, respectively; ΔP Lds2 and Q uds2 These represent the first and second nonlinear feedback terms, respectively.

[0023] a) The feedforward model compensation term and linear feedback term are as follows:

[0024] ΔP Lds1 =-k 2s1e2

[0025] Q uds1 =-k 3s1 e3

[0026] e1=Δx-Δx d , e3=ΔP L -ΔP Ld

[0027]

[0028] Wherein, φ1 and φ2 represent the first and second linear regression matrices of the feedforward model compensation term, respectively; The parameter estimation matrix represents the slowly varying parameter matrix θ of the system; This represents the state observation value of the third state variable in the first state variable matrix s. k represents the state observations of the second state variable of the second state variable matrix z; 2s1 and k 3s1 e1 and e2 represent the first and second linear feedback gains, respectively; e1 and e2 represent the first and second linear feedback gains, respectively. Let e² and e² represent the two-cylinder synchronous tracking error of the two-cylinder synchronous drive system and its derivative, respectively. Let e3 and e3 represent the synovial-like quantity and its derivative, respectively. Represent the differential pressure tracking error of the dual-cylinder synchronous drive system and its derivative, respectively; γ Q Indicates the backstepping compensation term; Δx d , and Let represent the desired trajectory, desired velocity difference, and desired acceleration difference of the piston rods in a dual-cylinder synchronous drive system, respectively. k1 represents the positive definite coefficient of the synovial membrane quantity; Indicates the virtual control shunt pressure difference ΔP Ld The computable part; This indicates the acceleration error of the piston rod of the two cylinders in a dual-cylinder synchronous drive system. The estimated values; w1 and w2 represent the first and second order-of-magnitude balancing parameters, respectively, used to balance the orders of magnitude of e2 and e3.

[0029] The load deviation and shunt error of the dual-cylinder synchronous drive system are input into the state observation values ​​of the third state variable of the first state variable matrix s in the feedforward model compensation term. State observations of the second state variable of the second state variable matrix z In the context of the dual-cylinder synchronous drive system, the dual-cylinder synchronous tracking error e1, the sliding diaphragm quantity, and the shunt pressure difference tracking error e3 are used as error parameters of the dual-cylinder synchronous drive system.

[0030] b) The fast dynamics compensation term and the nonlinear feedback term are as follows:

[0031]

[0032] ΔP Lds2 =-k 2s2 e2,

[0033] Q uds2 =-k 3s2 e3,

[0034] e2ΔP Lds2 ≤0,e3Q uds2 ≤0

[0035]

[0036] Where d1 and d2 represent the virtual control shunt pressure difference ΔP, respectively. Ld The virtual control flow Q of the proportional directional valve ud The low-frequency component of lumped uncertainty in the data. and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The estimate of the low-frequency component of the lumped uncertainty in the data. and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The derivative of the estimate of the low-frequency part of the lumped uncertainty in the equation. and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The high-frequency component of lumped uncertainty in [the context] and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The error between the low-frequency component of the lumped uncertainty and the estimated value; γ1 and γ2 represent the first and second update gains of the fast dynamics compensation term, respectively; Represents the system's slowly varying parameter matrix θ and parameter estimation matrix The adaptive estimation error matrix between; D1 and D2 represent the first and second modeling errors of the nonlinear dynamics model, respectively; Indicates the virtual control shunt pressure difference ΔP Ld The incalculable part; k 2s2 and k3s2 η1 and η2 represent the first and second nonlinear feedback gains, respectively; η1 and η2 represent arbitrarily small preset first and second constant values, respectively; d 1M and d 2M These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The preset boundary of the low-frequency component of the lumped uncertainty in θ; max and θ min δ1 and δ2 represent the upper and lower bounds of the slowly varying parameter matrix θ of the system, respectively; δ1 and δ2 represent the known boundary functions of the first and second modeling errors of the nonlinear dynamic model, respectively; express The preset boundary; This represents the error between the third state variable and its estimated value in the first state variable matrix s. This represents the error between the second state variable and its estimated value in the second state variable matrix z.

[0037] In step one, the projection-type adaptive law is as follows:

[0038]

[0039] ζ i =(1+v) i Φ i T Γ i Φ i ) -1 i = 1, 2

[0040]

[0041] in, The parameter estimation matrix representing the slowly varying parameter matrix θ of the system. The derivative; Φ represents a projective mapping function with input x; i Γ represents the i-th linear regression matrix estimated online by squares estimation; i Φ represents the i-th linear regression matrix in the online squared estimation of the nonlinear dynamic model. i The online estimation of the corresponding positive definite gain matrix, the online square estimation of the first linear regression matrix Φ1, the corresponding parameters of which include the first and second parameters in the system's slowly varying parameter matrix θ, and the online square estimation of the second linear regression matrix Φ2, the corresponding parameters of which include the third, fourth, and fifth parameters in the system's slowly varying parameter matrix θ; τ i Represents an i-th order adaptive function; ζ i Represents the adaptive function τ i The adaptive coefficient; v iThis represents the update scaling factor of the i-th order adaptive law; and These represent the interior and boundary of the feasible region of the parameter set, respectively. This represents the parameter estimation matrix when the system's slowly varying parameter matrix θ is... Located at the border The unit normal vector pointing outside the boundary; I represents the identity matrix.

[0042] In step three, the virtual control flow rate is restored to the input control voltage of the proportional directional valve as follows:

[0043] u d =Q ud / M(u d )

[0044] Among them, u d Q represents the actual input control voltage of the proportional directional valve. ud Indicates virtual control flow, M(u) d The virtual control flow rate Q of the proportional valve in a dual-cylinder synchronous drive system is represented by ) ud and actual input control voltage u d The mapping relationship.

[0045] The electronic device of the present invention includes: a memory and a processor coupled to each other, wherein the memory stores program data, and the processor invokes the program data to execute the method described above.

[0046] The present invention provides a computer-readable storage medium having program data stored thereon, which, when executed by a processor, implements the method described above.

[0047] The method of this invention enables rapid estimation of system parameters and load deviations, improves feedforward compensation efficiency, reduces the controller's dependence on high feedback gain, and ultimately significantly improves the synchronous control accuracy of the dual hydraulic cylinder drive system.

[0048] The beneficial effects of this invention are:

[0049] The method of the present invention can achieve fast and accurate load deviation disturbance estimation using only the pressure sensor signal and hydraulic cylinder displacement sensor signal of the dual-cylinder drive system, thus ensuring high-precision synchronous control of the dual-cylinder drive. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the dual-cylinder synchronous drive hydraulic system of the present invention, including a synchronizing valve and a bypass proportional directional valve.

[0051] Figure 2 This is a block diagram of the adaptive robust synchronous control system for a dual-cylinder drive system based on an extended observer, according to the present invention.

[0052] Figure 3 This is a comparison curve of the load deviation estimation of the adaptive robust synchronous controller and other controllers in the dual-cylinder drive system based on the extended observer of the present invention under the operating condition. Figure 3 (a) represents a comparison curve of the adaptive robust synchronous controller and other controllers estimating the load deviation in the dual-cylinder drive system based on the extended observer of the present invention under the operating condition. Figure 3 (b) represents a comparison curve of the estimated load deviation of the adaptive robust synchronous controller and other controllers in the dual-cylinder drive system based on the extended observer of the present invention during piston rod retraction.

[0053] Figure 4 This is a comparison curve of the load deviation estimation between the adaptive robust synchronous controller and other controllers of the dual-cylinder drive system based on the extended observer of the present invention under operating condition two. Figure 4 (a) is a comparison curve of the estimated load deviation of the adaptive robust synchronous controller and other controllers in the dual-cylinder drive system based on the extended observer of the present invention under operating condition two. Figure 4 (b) is a comparison curve of the estimated load deviation of the adaptive robust synchronous controller and other controllers of the dual-cylinder drive system based on the extended observer of the present invention during piston rod retraction under operating condition 2.

[0054] Figure 5 This is a synchronization effect diagram of the adaptive robust synchronization controller of the dual-cylinder drive system based on the extended observer of the present invention with other controllers under operating condition 1. Figure 5 (a) is a diagram showing the synchronization effect of the adaptive robust synchronization controller and other controllers of the dual-cylinder drive system based on the extended observer of the present invention under operating condition one when the piston rod is extended. Figure 5 (b) is a diagram showing the synchronization effect of the adaptive robust synchronous controller and other controllers of the dual-cylinder drive system based on the extended observer of the present invention during piston rod retraction under operating condition.

[0055] Figure 6 This is a synchronization effect diagram of the adaptive robust synchronization controller of the dual-cylinder drive system based on the extended observer of the present invention and other controllers under operating condition two. Figure 6 (a) is a synchronization effect diagram of the adaptive robust synchronization controller and other controllers of the dual-cylinder drive system based on the extended observer of the present invention under operating condition two when the piston rod is extended. Figure 6 (b) is a diagram showing the synchronization effect of the adaptive robust synchronous controller and other controllers of the dual-cylinder drive system based on the extended observer of the present invention during piston rod retraction under operating condition two.

[0056] In the diagram: 1. Hydraulic power source, 2. Oil tank, 3. Solenoid directional valve, 4.1. First pressure sensor, 4.2. Second pressure sensor, 4.3. Third pressure sensor, 5. Synchronization valve, 6. Proportional directional valve, 7.1. First hydraulic cylinder, 7.2. Second hydraulic cylinder, 8.1. First displacement sensor, 8.2. Second displacement sensor. Detailed Implementation

[0057] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] like Figure 1 As shown, the dual-cylinder synchronous drive system of the present invention, including a synchronizing valve and a proportional directional valve, comprises a hydraulic power source 1, an oil tank 2, an electromagnetic directional valve 3, a first pressure sensor 4.1, a second pressure sensor 4.2, a third pressure sensor 4.3, a synchronizing valve 5, a proportional directional valve 6, a first hydraulic cylinder 7.1, a second hydraulic cylinder 7.2, a first displacement sensor 8.1, and a second displacement sensor 8.2. During synchronous extension, hydraulic fluid flows from the hydraulic power source 1 through the electromagnetic directional valve 3 and the synchronizing valve 5 until it reaches the left chamber of the first hydraulic cylinder 7.1 and the second hydraulic cylinder 7.2. This controls the displacement of the valve core of the proportional directional valve 6, causing the oil supply circuit of the relatively faster-moving first hydraulic cylinder 7.1 or second hydraulic cylinder 7.2 to be released, thereby achieving synchronous operation of the first hydraulic cylinder 7.1 and the second hydraulic cylinder 7.2. During synchronous retraction, hydraulic fluid flows from hydraulic power source 1 through solenoid directional valve 3 into the right chamber of first hydraulic cylinder 7.1 and second hydraulic cylinder 7.2. The fluid in the left chamber of first hydraulic cylinder 7.1 and second hydraulic cylinder 7.2 returns to oil tank 2 via synchronizing valve 5 and solenoid directional valve 3, controlling the valve core displacement of proportional directional valve 6. This allows the return oil path of the relatively slower-moving first hydraulic cylinder 7.1 or second hydraulic cylinder 7.2 to be released, achieving synchronous operation of first hydraulic cylinder 7.1 and second hydraulic cylinder 7.2. Wherein, P... L1 and P L2 The real-time signals from the second pressure sensor 4.2 and the third pressure sensor 4.3 are respectively, representing the shunt pressure difference ΔP. L =P L1 -P L2 x1 and x2 are the real-time signals of the first displacement sensor 8.1 and the second displacement sensor 8.2, respectively, and the displacement difference Δx = x1 - x2; A represents the effective working area of ​​the pistons of the first hydraulic cylinder 7.1 and the second hydraulic cylinder 7.2; F L1 and F L2 These represent the external loads of the first hydraulic cylinder 7.1 and the second hydraulic cylinder 7.2, respectively, with a load deviation ΔF. L =F L1 -F L2 Q u This indicates the flow rate controlled and discharged by the proportional directional valve.

[0059] like Figure 2 As shown, the adaptive robust control method for a dual-cylinder synchronous drive system based on an extended observer according to the present invention is as follows:

[0060] Step 1: Establish a nonlinear dynamic model of a dual-cylinder synchronous drive system including a synchronizing valve and a bypass proportional directional valve. Based on the nonlinear dynamic model, construct an extended observer and a direct / indirect adaptive robust controller including a feedforward model compensation term, a fast dynamic compensation term, a nonlinear feedback term, a linear feedback term, and a projected adaptive law.

[0061] The nonlinear dynamic model of the dual-cylinder synchronous drive system is as follows:

[0062]

[0063] θ1=mA -1 θ2=BA -1 ,θ3=(K t β e ) -1 ,

[0064] B c =ΔP L / V L1 ,

[0065] Q u =M9u)u

[0066]

[0067] Where θ represents the slowly varying parameter matrix of the dual-cylinder synchronous drive system, θ i θ represents the i-th parameter in the slowly varying parameter matrix θ of the system. imax and θ imin Let θ represent the i-th parameter θ in the system's slowly varying parameter matrix θ. i upper and lower boundaries, The boundary of the slowly varying parameter matrix θ of the system; Δx, and These represent the displacement error, velocity error, and acceleration error of the piston rod in a dual-cylinder synchronous drive system, respectively; ΔP L and Let ΔP represent the pressure difference between the two hydraulic cylinders in the dual-cylinder synchronous drive system and its derivative. L =P L1 -P L2 P L1 and P L2 These represent the load pressures of the first and second hydraulic cylinders in the dual-cylinder synchronous drive system, respectively. ΔF represents the derivative of the load pressure of the second hydraulic cylinder in a dual-cylinder synchronous drive system. L A represents the load deviation experienced by the two hydraulic cylinders in a dual-cylinder synchronous drive system; A represents the effective working area of ​​the piston rod of the hydraulic cylinder in the dual-cylinder synchronous drive system; A c B c and C c These represent the first, second, and third calculated parameters of the nonlinear dynamic model, respectively; Q u ΔQ represents the input control flow rate of the proportional directional valve in a dual-cylinder synchronous drive system. f K represents the flow splitting error of the synchronizing valve in a dual-cylinder synchronous drive system. t V represents the flow regulation coefficient of the proportional directional valve in a dual-cylinder synchronous drive system. L1 β represents the compressible volume of the inlet chamber of the first hydraulic cylinder in the dual-cylinder synchronous drive system; m represents the load mass of the hydraulic cylinder in the dual-cylinder synchronous drive system; B represents the viscous damping coefficient of the piston rod of the hydraulic cylinder in the dual-cylinder synchronous drive system; e C represents the elastic modulus of the oil. j M(u) represents the internal leakage coefficient of the hydraulic cylinder in a dual-cylinder synchronous drive system; M(u) represents the input control voltage Q of the proportional valve in the dual-cylinder synchronous drive system. u The mapping relationship between the actual control voltage u; s() represents a 0-1 variable; D i This represents the i-th modeling error of the nonlinear dynamics model. D represents the i-th modeling error of the nonlinear dynamic model. i Uncertain boundary, δ i This represents the preset value of the i-th constant.

[0068] The extended observer is as follows:

[0069]

[0070] Where s and z represent the first and second state variable matrices of the extended observer, respectively, and s1, s2, and s3 represent the first, second, and third state variables of the first state variable matrix s, respectively. and These represent the state observations of the first, second, and third state variables in the first state variable matrix s, respectively. and These represent the state observations of the first, second, and third state variables in the first state variable matrix s, respectively. and Let z1 and z2 represent the derivatives of the state observations of the first, second, and third state variables in the first state variable matrix s, respectively, and z1 and z2 represent the first and second state variables in the second state variable matrix z, respectively. and Let z represent the state observations of the first and second state variables of the second state variable matrix z, respectively. and ω1 and ω2 represent the derivatives of the state observations of the first and second state variables of the second state variable matrix z, respectively; ω1 and ω2 represent the first and second feedback gain coefficients of the extended observer, respectively; This represents the estimated value of the i-th parameter in the slowly varying parameter matrix θ of the system. The parameter estimation matrix represents the system's slowly varying parameter matrix θ. Let represent the adaptive error of the i-th parameter in the slowly varying parameter matrix θ of the system. Represents the system's slowly varying parameter matrix θ and parameter estimation matrix The estimation error matrix between them; ΔP Ld Indicates the virtual control shunt pressure difference; Q ud This represents the virtual control flow rate of the proportional directional valve. and These represent the tracking values ​​of the load deviation and flow splitting error of the synchronizing valve in the dual-cylinder synchronous drive system, respectively.

[0071] The direct / indirect adaptive robust controller is as follows:

[0072] Q ud =Q uda1 +Q uda2 +Q uds1 +Q uds2

[0073] ΔP Ld =ΔP Lda1 +ΔP Lda2 +ΔP Lds1 +ΔP Lds2

[0074] Among them, Q ud and ΔP Ld ΔP represents the virtual control flow rate and virtual control shunt pressure difference of the proportional directional valve, respectively. Lda1 and Q uda1 These represent the compensation terms of the first and second feedforward models, respectively; ΔP Lda2 and Q uda2 These represent the first and second fast dynamic compensation terms, respectively; ΔP Lds1 and Q uds1 These represent the first and second linear feedback terms, respectively; ΔP Lds2 and Q uds2 These represent the first and second nonlinear feedback terms, respectively.

[0075] a) The feedforward model compensation term and linear feedback term are as follows:

[0076] ΔP Lds1 =-k 2s1 e2

[0077] Q uds1 =-k 3s1 e3

[0078] e1=Δx-Δx d , e3=ΔP L -ΔP Ld

[0079]

[0080] Wherein, φ1 and φ2 represent the first and second linear regression matrices of the feedforward model compensation term, respectively; The parameter estimation matrix represents the slowly varying parameter matrix θ of the system; This represents the state observation value of the third state variable in the first state variable matrix s. k represents the state observations of the second state variable of the second state variable matrix z; 2s1 and k 3s1 e1 and e2 represent the first and second linear feedback gains, respectively; e1 and e2 represent the first and second linear feedback gains, respectively. Let e² and e² represent the two-cylinder synchronous tracking error of the two-cylinder synchronous drive system and its derivative, respectively. Let e3 and e3 represent the synovial-like quantity and its derivative, respectively. Represent the differential pressure tracking error of the dual-cylinder synchronous drive system and its derivative, respectively; γ Q Indicates the backstepping compensation term; Δx d , and Let represent the desired trajectory, desired velocity difference, and desired acceleration difference of the piston rods in a dual-cylinder synchronous drive system, respectively. k1 represents the positive definite coefficient of the synovial membrane quantity; Indicates the virtual control shunt pressure difference ΔP Ld The computable part; This indicates the acceleration error of the piston rod of the two cylinders in a dual-cylinder synchronous drive system. The estimated values; w1 and w2 represent the first and second order-of-magnitude balancing parameters, respectively, used to balance the orders of magnitude of e2 and e3.

[0081] The load deviation and shunt error of the dual-cylinder synchronous drive system are input into the state observation values ​​of the third state variable of the first state variable matrix s in the feedforward model compensation term. State observations of the second state variable of the second state variable matrix z In the context of the dual-cylinder synchronous drive system, the dual-cylinder synchronous tracking error e1, the sliding diaphragm quantity, and the shunt pressure difference tracking error e3 are used as error parameters of the dual-cylinder synchronous drive system.

[0082] b) The fast dynamics compensation term and the nonlinear feedback term are as follows:

[0083]

[0084] ΔP Lds2 =-k 2s2 e2,

[0085] Q uds2 =-k 3s2 e3,

[0086] e2ΔP Lds2 ≤0,e3Q uds2 ≤0

[0087]

[0088] Where d1 and d2 represent the virtual control shunt pressure difference ΔP, respectively. Ld The virtual control flow Q of the proportional directional valve ud The low-frequency component of lumped uncertainty in the data. and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The estimate of the low-frequency component of the lumped uncertainty in the data. and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The derivative of the estimate of the low-frequency part of the lumped uncertainty in the equation. and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The high-frequency component of lumped uncertainty in [the context] and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The error between the low-frequency component of the lumped uncertainty and the estimated value; γ1 and γ2 represent the first and second update gains of the fast dynamics compensation term, respectively; Represents the system's slowly varying parameter matrix θ and parameter estimation matrix The adaptive estimation error matrix between; D1 and D2 represent the first and second modeling errors of the nonlinear dynamics model, respectively; Indicates the virtual control shunt pressure difference ΔP Ld The incalculable part; k 2s2 and k 3s2 η1 and η2 represent the first and second nonlinear feedback gains, respectively; η1 and η2 represent arbitrarily small preset first and second constant values, respectively; d 1M and d 2M These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The preset boundary of the low-frequency component of the lumped uncertainty in θ; max and θ min δ1 and δ2 represent the upper and lower bounds of the slowly varying parameter matrix θ of the system, respectively; δ1 and δ2 represent the known boundary functions of the first and second modeling errors of the nonlinear dynamic model, respectively; express The preset boundary; This represents the error between the third state variable and its estimated value in the first state variable matrix s. This represents the error between the second state variable and its estimated value in the second state variable matrix z.

[0089] The specific projection-type adaptive law is as follows:

[0090]

[0091] ζ i =(1+v) i Φ i T Γ i Φ i ) -1 i = 1, 2

[0092]

[0093] in, The parameter estimation matrix representing the slowly varying parameter matrix θ of the system. The derivative; Φ represents a projective mapping function with input x; i Γ represents the i-th linear regression matrix estimated online by squares estimation; i Φ represents the i-th linear regression matrix in the online squared estimation of the nonlinear dynamic model. iThe online estimation of the corresponding positive definite gain matrix, the online square estimation of the first linear regression matrix Φ1, the corresponding parameters of which include the first and second parameters in the system's slowly varying parameter matrix θ, and the online square estimation of the second linear regression matrix Φ2, the corresponding parameters of which include the third, fourth, and fifth parameters in the system's slowly varying parameter matrix θ; τ i Represents an i-th order adaptive function; ζ i Represents the adaptive function τ i The adaptive coefficient; v i This represents the update scaling factor of the i-th order adaptive law; and These represent the interior and boundary of the feasible region of the parameter set, respectively. This represents the parameter estimation matrix when the system's slowly varying parameter matrix θ is... Located at the border The unit normal vector pointing outside the boundary; I represents the identity matrix.

[0094] Step 2: The displacement error and shunt pressure difference of the dual-cylinder synchronous drive system are input into the extended observer and the projected adaptive law, respectively. After online parameter estimation based on the model, the projected adaptive law outputs the estimated values ​​of the slowly varying system parameters of the dual-cylinder synchronous drive system, which are then input into the extended observer. After processing, the extended observer outputs the load deviation and shunt error of the dual-cylinder synchronous drive system, which, together with the desired trajectory, are input into the feedforward model compensation term. The error parameters of the dual-cylinder synchronous drive system are obtained based on the displacement error and shunt pressure difference, and are input into the fast dynamics compensation term, the nonlinear feedback term, and the linear feedback term, respectively. Finally, the outputs of the feedforward model compensation term, the fast dynamics compensation term, the nonlinear feedback term, and the linear feedback term are summed to obtain the virtual control flow rate.

[0095] Step 3: Restore the virtual control flow rate to the input control voltage of the proportional directional valve and control the dual-cylinder synchronous drive system; repeat steps one to three to achieve adaptive robust real-time control of the dual-cylinder synchronous drive system. The bounded stability of the controller and the convergence of parameter estimation are proved using the Lyapunov method.

[0096] The virtual control flow rate is restored to the input control voltage of the proportional directional valve as follows:

[0097] u d =Q ud / M(u d )

[0098] Among them, u d Q represents the actual input control voltage of the proportional directional valve. ud Indicates virtual control flow, M(u) d The virtual control flow rate Q of the proportional valve in a dual-cylinder synchronous drive system is represented by ) udand actual input control voltage u d The mapping relationship.

[0099] The present invention uses the Lyapunov method to prove the bounded stability of the controller and the convergence of parameter estimation. The process is as follows:

[0100] 1) All signals in the system are bounded.

[0101] 2) After a certain moment, the load deviation and shunting error If the estimate is accurate, then It can converge to the true value, that is Furthermore, based on 1), it is also possible to realize Δx for Δx d The asymptotic tracking, i.e., e1→0 as t→∞.

[0102] Proof 1):

[0103] Define a positive definite function V s as follows:

[0104]

[0105] Differentiating it, we get:

[0106]

[0107] λ=min{2k 2s1 / θ 1max 2k 3s1 / θ 3max}

[0108] η = w1η1 + w2η2

[0109] Where λ represents the convergence coefficient and η represents the initial convergence constant, integrating both sides:

[0110]

[0111] This proves 1).

[0112] Proof 2):

[0113] Define the Lyapunov function V θ as follows:

[0114]

[0115] Differentiating it, we get:

[0116]

[0117] because It belongs to a square-integrable region and φ1 and φ2 are bounded, therefore and It also belongs to the square-integrable field. Therefore, e2 and e3 also belong to the square-integrable field. Applying Barbalat's lemma, e1→0 when t→∞, thus proving 2).

[0118] Finally, a co-simulation was performed using Amesim and MATLAB / Simulink. Two external load conditions were selected for the simulation, and the simulation was compared with three other controllers: 1) Proportional Integral Differential (PID), 2) Direct Adaptive Robust Control (DARC), and 3) Direct / Indirect Adaptive Robust Control (DIARC).

[0119] Operating Condition 1: Step Load. During the dual-cylinder drive extension and retraction process, each hydraulic cylinder 7.1 and 7.2 is subjected to a base load of 50,000 N, with an additional step load deviation signal of 20,000 N and a period of 4 seconds. The synchronization errors of the four controllers are compared and the load estimation is detected.

[0120] Operating Condition 2: Sinusoidal Off-center Load. During the dual-cylinder drive extension and retraction process, each hydraulic cylinder (7.1, 7.2) is subjected to a base load of 50,000 N, with an additional sinusoidal load deviation signal of 20,000 N and a period of 2 seconds. The synchronization errors of the four controllers are compared, and the off-center load estimation is detected.

[0121] like Figure 3 of (a), Figure 3 (b) Figure 4 (a) and Figure 4 As shown in (b), the present invention proposes an adaptive robust controller ESO-DIARC (Direct / Indirect Adaptive Robust Control Based on Extended State Observer) with the ability to quickly and accurately track load deviations. Therefore, the controller is capable of accurately estimating load deviations and compensating for their impact on the dual-cylinder drive system.

[0122] like Figure 5 of (a), Figure 5 (b) Figure 6 (a) and Figure 6As shown in (b), the proposed ESO-DIARC controller exhibits high synchronization control accuracy, demonstrating significant advantages over the other three controllers. In operating condition one, the maximum synchronization error is only 0.27 mm, with a settling time of only 0.2 s. In contrast, the PID controller has a maximum synchronization error of 1.62 mm and a settling time of 0.7 s; the DARC controller has a maximum synchronization error of 0.61 mm and a settling time of 0.3 s; and the DIARC controller controls the error to 0.34 mm with a settling time of 0.24 s. In operating condition two, the maximum synchronization error is only 0.003 mm, and the settling time is difficult to assess. However, in comparison, the PID controller has a maximum synchronization error of 0.46 mm; the DARC controller has a maximum synchronization error of 0.04 mm; and the DIARC controller has a maximum synchronization error of 0.011 mm. In summary, the ESO-DIARC controller can guarantee high-precision synchronous control of dual-cylinder drives and achieve rapid and accurate estimation of load deviation disturbances, demonstrating superior control performance.

[0123] The above content is merely a technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. An adaptive robust control method for a dual-cylinder synchronous drive system based on an extended observer, characterized in that, include: Step 1: Establish a nonlinear dynamic model of a dual-cylinder synchronous drive system including a synchronizing valve and a proportional directional valve. Based on the nonlinear dynamic model, construct an extended observer and a direct / indirect adaptive robust controller including a feedforward model compensation term, a fast dynamic compensation term, a nonlinear feedback term, a linear feedback term, and a projected adaptive law. Step 2: The displacement error and shunt pressure difference of the dual-cylinder synchronous drive system are input into the extended observer and the projected adaptive law, respectively. After online parameter estimation, the projected adaptive law outputs the estimated values ​​of the slowly varying system parameters of the dual-cylinder synchronous drive system and inputs them into the extended observer. After processing, the extended observer outputs the load deviation and shunt error of the dual-cylinder synchronous drive system and inputs them together with the desired trajectory into the feedforward model compensation term. The error parameters of the dual-cylinder synchronous drive system are obtained based on the displacement error and shunt pressure difference and input into the fast dynamics compensation term, the nonlinear feedback term, and the linear feedback term, respectively. Finally, the outputs of the feedforward model compensation term, the fast dynamics compensation term, the nonlinear feedback term, and the linear feedback term are added together to obtain the virtual control flow rate. Step 3: Restore the virtual control flow to the input control voltage of the proportional directional valve and control the dual-cylinder synchronous drive system; repeat steps one to three to achieve adaptive robust real-time control of the dual-cylinder synchronous drive system.

2. The adaptive robust control method for a dual-cylinder synchronous drive system based on an extended observer according to claim 1, characterized in that: In step one, the nonlinear dynamic model of the dual-cylinder synchronous drive system is as follows: θ1=mA -1 ,θ2=BA -1 ,θ3=(K t b e ) -1 , Where θ represents the slowly varying parameter matrix of the dual-cylinder synchronous drive system, θ i θ represents the i-th parameter in the slowly varying parameter matrix θ of the system. imax and θ imin Let θ represent the i-th parameter θ in the system's slowly varying parameter matrix θ. i upper and lower boundaries, The boundary of the slowly varying parameter matrix θ of the system; Δx, and These represent the displacement error, velocity error, and acceleration error of the piston rod in a dual-cylinder synchronous drive system, respectively; ΔP L and Let ΔP represent the pressure difference between the two hydraulic cylinders in the dual-cylinder synchronous drive system and its derivative. L =P L1 -P L2 P L1 and P L2 These represent the load pressures of the first and second hydraulic cylinders in the dual-cylinder synchronous drive system, respectively. ΔF represents the derivative of the load pressure of the second hydraulic cylinder in a dual-cylinder synchronous drive system. L A represents the load deviation experienced by the two hydraulic cylinders in a dual-cylinder synchronous drive system; A represents the effective working area of ​​the piston rod of the hydraulic cylinder in the dual-cylinder synchronous drive system; A c B c and C c These represent the first, second, and third calculated parameters of the nonlinear dynamic model, respectively; Q u ΔQ represents the input control flow rate of the proportional directional valve in a dual-cylinder synchronous drive system. f K represents the flow splitting error of the synchronizing valve in a dual-cylinder synchronous drive system. t V represents the flow regulation coefficient of the proportional directional valve in a dual-cylinder synchronous drive system. L1 β represents the compressible volume of the inlet chamber of the first hydraulic cylinder in the dual-cylinder synchronous drive system; m represents the load mass of the hydraulic cylinder in the dual-cylinder synchronous drive system; B represents the viscous damping coefficient of the piston rod of the hydraulic cylinder in the dual-cylinder synchronous drive system; e C represents the elastic modulus of the oil. j M(u) represents the internal leakage coefficient of the hydraulic cylinder in a dual-cylinder synchronous drive system; M(u) represents the input control voltage Q of the proportional valve in the dual-cylinder synchronous drive system. u The mapping relationship between the actual control voltage u; s() represents a 0-1 variable; D i This represents the i-th modeling error of the nonlinear dynamics model. D represents the i-th modeling error of the nonlinear dynamic model. i Uncertain boundary, δ i This represents the preset value of the i-th constant.

3. The adaptive robust control method for a dual-cylinder synchronous drive system based on an extended observer according to claim 2, characterized in that: In step one, the extended observer is specifically as follows: Where s and z represent the first and second state variable matrices of the extended observer, respectively, and s1, s2, and s3 represent the first, second, and third state variables of the first state variable matrix s, respectively. and These represent the state observations of the first, second, and third state variables in the first state variable matrix s, respectively. and These represent the state observations of the first, second, and third state variables in the first state variable matrix s, respectively. and Let z1 and z2 represent the derivatives of the state observations of the first, second, and third state variables in the first state variable matrix s, respectively, and z1 and z2 represent the first and second state variables in the second state variable matrix z, respectively. and Let z represent the state observations of the first and second state variables of the second state variable matrix z, respectively. and ω1 and ω2 represent the derivatives of the state observations of the first and second state variables of the second state variable matrix z, respectively; ω1 and ω2 represent the first and second feedback gain coefficients of the extended observer, respectively; This represents the estimated value of the i-th parameter in the slowly varying parameter matrix θ of the system. The parameter estimation matrix represents the system's slowly varying parameter matrix θ. Let represent the adaptive error of the i-th parameter in the slowly varying parameter matrix θ of the system. Represents the system's slowly varying parameter matrix θ and parameter estimation matrix The estimation error matrix between them; ΔP Ld Indicates the virtual control shunt pressure difference; Q ud This represents the virtual control flow rate of the proportional directional valve. and These represent the tracking values ​​of the load deviation and flow splitting error of the synchronizing valve in the dual-cylinder synchronous drive system, respectively.

4. The adaptive robust control method for a dual-cylinder synchronous drive system based on an extended observer according to claim 2, characterized in that: In step one, the direct / indirect adaptive robust controller is specifically as follows: Q ud =Q uda1 +Q uda2 +Q uds1 +Q uds2 ΔP Ld =ΔP Lda1 +ΔP Lda2 +ΔP Lds1 +ΔP Lds2 Among them, Q ud and ΔP Ld ΔP represents the virtual control flow rate and virtual control shunt pressure difference of the proportional directional valve, respectively. Lda1 and Q uda1 These represent the compensation terms of the first and second feedforward models, respectively; ΔP Lda2 and Q uda2 These represent the first and second fast dynamic compensation terms, respectively; ΔP Lds1 and Q uds1 These represent the first and second linear feedback terms, respectively; ΔP Lds2 and Q uds2 These represent the first and second nonlinear feedback terms, respectively. a) The feedforward model compensation term and linear feedback term are as follows: Wherein, φ1 and φ2 represent the first and second linear regression matrices of the feedforward model compensation term, respectively; The parameter estimation matrix represents the slowly varying parameter matrix θ of the system; This represents the state observation value of the third state variable in the first state variable matrix s. k represents the state observations of the second state variable of the second state variable matrix z; 2s1 and k 3s1 e1 and e2 represent the first and second linear feedback gains, respectively; e1 and e2 represent the first and second linear feedback gains, respectively. Let e² and e² represent the two-cylinder synchronous tracking error of the two-cylinder synchronous drive system and its derivative, respectively. Let e3 and e3 represent the synovial-like quantity and its derivative, respectively. Represent the differential pressure tracking error of the dual-cylinder synchronous drive system and its derivative, respectively; γ Q Indicates the backstepping compensation term; Δx d , and represents the desired trajectory, desired velocity difference, and desired acceleration difference of the piston rod of the two cylinders in the dual-cylinder synchronous drive system, respectively; k1 represents the positive definite coefficient of the quasi-slippery film amount; Indicates the virtual control shunt pressure difference ΔP Ld The computable part; This indicates the acceleration error of the piston rod of the two cylinders in a dual-cylinder synchronous drive system. The estimated values; w1 and w2 represent the first and second order of magnitude balance parameters, respectively; The load deviation and shunt error of the dual-cylinder synchronous drive system are input into the state observation values ​​of the third state variable of the first state variable matrix s in the feedforward model compensation term. State observations of the second state variable of the second state variable matrix z In the middle, the dual-cylinder synchronous drive system's dual-cylinder synchronous tracking error e1, the sliding diaphragm quantity, and the dual-cylinder synchronous drive system's shunt pressure difference tracking error e3 are used as the error parameters of the dual-cylinder synchronous drive system; b) The fast dynamics compensation term and the nonlinear feedback term are as follows: Where d1 and d2 represent the virtual control shunt pressure difference ΔP, respectively. Ld The virtual control flow Q of the proportional directional valve ud The low-frequency component of lumped uncertainty in the data. and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The estimate of the low-frequency component of the lumped uncertainty in the data. and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The derivative of the estimate of the low-frequency part of the lumped uncertainty in the equation. and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The high-frequency component of lumped uncertainty in [the context] and These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The error between the low-frequency component of the lumped uncertainty and the estimated value; γ1 and γ2 represent the first and second update gains of the fast dynamics compensation term, respectively; Represents the system's slowly varying parameter matrix θ and parameter estimation matrix The adaptive estimation error matrix between them; D1 and D2 represent the first and second modeling errors of the nonlinear dynamics model, respectively; Indicates the virtual control shunt pressure difference ΔP Ld The incalculable part; k 2s2 and k 3s2 η1 and η2 represent the first and second nonlinear feedback gains, respectively; η1 and η2 represent the first and second preset constant values, respectively; d 1M and d 2M These represent the virtual control shunt pressure difference ΔP. Ld The virtual control flow Q of the proportional directional valve ud The preset boundary of the low-frequency component of the lumped uncertainty in θ; max and θ min δ1 and δ2 represent the upper and lower bounds of the slowly varying parameter matrix θ of the system, respectively; δ1 and δ2 represent the known boundary functions of the first and second modeling errors of the nonlinear dynamic model, respectively. express Preset boundaries; This represents the error between the third state variable and its estimated value in the first state variable matrix s. This represents the error between the second state variable and its estimated value in the second state variable matrix z.

5. The adaptive robust control method for a dual-cylinder synchronous drive system based on an extended observer according to claim 2, characterized in that: In step one, the projection-type adaptive law is as follows: g i =(1+v i F i T C i F i ) -1 ,i=1.2 in, The parameter estimation matrix representing the slowly varying parameter matrix θ of the system. The derivative; Φ represents a projective mapping function with input x; i Γ represents the i-th linear regression matrix estimated online by squares estimation; i Φ represents the i-th linear regression matrix in the online squared estimation of the nonlinear dynamic model. i The online estimation of the corresponding positive definite gain matrix, the online square estimation of the first linear regression matrix Φ1, the corresponding parameters of which include the first and second parameters in the system's slowly varying parameter matrix θ, and the online square estimation of the second linear regression matrix Φ2, the corresponding parameters of which include the third, fourth, and fifth parameters in the system's slowly varying parameter matrix θ; τ i Represents an i-th order adaptive function; ζ i Represents the adaptive function τ i The adaptive coefficient; ν i Represents the update scaling factor of the i-th order adaptive law; and These represent the interior and boundary of the feasible region of the parameter set, respectively. This represents the parameter estimation matrix when the system's slowly varying parameter matrix θ is... Located at the border The unit normal vector pointing outside the boundary; I represents the identity matrix.

6. The adaptive robust control method for a dual-cylinder synchronous drive system based on an extended observer according to claim 1, characterized in that: In step three, the virtual control flow rate is restored to the input control voltage of the proportional directional valve as follows: u d =Q ud / M(u d ) Among them, u d Q represents the actual input control voltage of the proportional directional valve. ud Indicates virtual control flow, M(u) d The virtual control flow rate Q of the proportional valve in a dual-cylinder synchronous drive system is represented by ) ud and actual input control voltage u d The mapping relationship.

7. An electronic device, characterized in that, include: A memory and a processor are coupled to each other, wherein the memory stores program data, and the processor invokes the program data to perform the method as described in any one of claims 1-6.

8. A computer-readable storage medium storing program data thereon, characterized in that, When the program data is executed by the processor, it implements the method as described in any one of claims 1-6.

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