Method for constructing output feedback controller of multi-degree-of-freedom series hydraulic mechanical arm system

Abstract

The application discloses a construction method of a multi-degree-of-freedom series hydraulic mechanical arm system output feedback controller. The method is as follows: firstly, a mathematical model of the multi-degree-of-freedom series hydraulic mechanical arm system is established, and a control target is determined; then, a neural network estimator is designed to estimate matched and unmatched unknown function disturbances of the system, and a disturbance observer based on the neural network estimator is designed to estimate matched and unmatched time-varying external disturbances of the system; then, a system output feedback controller and a neural network adaptive law are designed; finally, initial values of neural network weight parameters, an adaptive law matrix and controller parameters are selected, so that the output of the system can track a desired position instruction as accurately as possible. The application improves the compensation model uncertainty effect, does not depend on the rotational inertia of the system, only needs the angular position information of each joint, and is beneficial to application in complex working conditions.

Description

Technical Field

[0001] This invention relates to the field of electromechanical hydraulic servo control technology, and in particular to a method for constructing an output feedback controller for a multi-degree-of-freedom serial hydraulic robotic arm system. Background Technology

[0002] A hydraulic robotic arm is a type of robotic arm driven by hydraulic actuators. Due to its advantages in motion control, such as high power-to-weight ratio, high precision, and high response, it has broad application prospects in aerospace, marine equipment, engineering machinery, and the nuclear industry. It has been explored in applications such as precision assembly of large / heavy aircraft components, deep-sea resource exploration, mill liner replacement, and nuclear power plant maintenance, playing a vital role in liberating labor, improving production efficiency, promoting industrial transformation and upgrading, and contributing to social development. However, due to multiple factors such as the nonlinearity of the hydraulic robotic arm structure, the nonlinearity of the hydraulic system, and modeling uncertainties, the hydraulic robotic arm system exhibits very complex nonlinear factors and strong interference, making high-precision control of hydraulic robotic arms quite challenging.

[0003] Currently, position control strategies for hydraulic robotic arms mainly include adaptive robust control and active disturbance rejection adaptive control. These control methods all require measurement information such as the joint angular positions, joint angular velocities, and pressures at the hydraulic actuator's inlet and outlet ports. This means that corresponding sensors need to be installed. Joint angular velocities are generally obtained from joint angular positions through certain calculations, which not only increases system cost but also system weight, hindering the development of lightweight systems. Furthermore, installing a large number of sensors leads to reduced system reliability and increased maintenance costs. Finding a way to reduce the number of sensors while achieving the highest possible control performance is of significant engineering importance. Additionally, the aforementioned control methods require knowledge of the system's moment of inertia, but when the number of joints in the system is large, the specific expression for its moment of inertia is often difficult to obtain. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing an output feedback controller for a multi-degree-of-freedom serial hydraulic manipulator system that can improve the effect of compensating for uncertainty in the model, accurately track the desired position command, and reduce the number of system sensors.

[0005] The technical solution to achieve the objective of this invention is: a method for constructing an output feedback controller for a multi-degree-of-freedom serial hydraulic robotic arm system, comprising the following steps:

[0006] Step 1: Establish a mathematical model of the multi-degree-of-freedom serial hydraulic robotic arm system and determine the control objective;

[0007] Step 2: Design a neural network estimator based on a multi-layer feedforward neural network to estimate the matched and unmatched unknown function disturbances of the multi-degree-of-freedom serial hydraulic manipulator system;

[0008] Step 3: Design a disturbance observer based on a neural network estimator to estimate matched and unmatched time-varying external disturbances in a multi-degree-of-freedom serial hydraulic manipulator system;

[0009] Step 4: Establish the output feedback controller for the multi-degree-of-freedom serial hydraulic robotic arm system;

[0010] Step 5: Design the neural network adaptive law for the output feedback controller of the multi-degree-of-freedom serial hydraulic manipulator system;

[0011] Step 6: Select the initial values ​​of the neural network weight parameters, the adaptive law matrix, and the controller parameters so that the system output tracks the desired position command.

[0012] Furthermore, the output feedback controller of the multi-degree-of-freedom serial hydraulic manipulator system introduces multi-layer neural network row estimation and feedforward compensation for the unknown function disturbance of the manipulator system. It estimates and feeds forward compensation for unmatched and matched time-varying external disturbances through nonlinear disturbance observers and extended observers, so that the position output of the manipulator system can track the desired position command under the combined action of unknown function disturbance and time-varying external disturbance.

[0013] Furthermore, in step 1, a mathematical model of the multi-degree-of-freedom serial hydraulic manipulator system is established, and the control objective is determined, as follows:

[0014] Step 1.1: Establish the mathematical model of the multi-degree-of-freedom serial hydraulic robotic arm system: Define the system state variables as... Where q represents the joint angular displacement, A a A b P represents the effective working area of ​​the two-chamber piston rod of the hydraulic actuator. a P b Representing the pressure in both chambers, the state-space form of the nonlinear model of the system is:

[0015]

[0016]

[0017]

[0018] in:

[0019] χ2(ψ1,ψ2)=J inv (ψ1)[-V c (ψ1,ψ2)ψ2-G(ψ1)-F f(ψ2)-F e (ψ1,ψ2)]

[0020]

[0021]

[0022] Δ2(t,ψ1,ψ2,ψ3)=J inv (ψ1)[H(ψ1)ψ3+D2(t)]-ψ3

[0023] Δ3(t,ψ1,ψ2,P a ,P b ) = F dc (ψ1,ψ2,P a ,P b )+D3(t)

[0024] The expressions for the other parts of the formula are as follows:

[0025]

[0026] D2(t)=-f d (t),D3(t)=A a Q d1 (t)-A b Q d2 (t)

[0027]

[0028] In the formula, β ef V is the elastic modulus of hydraulic oil. a (q)=V a0 +A a y L (q), V b (q)=V b0 –A b y L (q) represents the volume of the two chambers of the hydraulic cylinder, V a0 V b0 Q represents the initial volume of the two chambers of the hydraulic cylinder. a Q b C represents the flow rate through the two chambers. tl P is the actuator leakage coefficient. ab =P a –P b The pressure difference between the two chambers Q is an unknown function that depends on the system state. d1 (t), Q d2 (t) represents the time-varying external disturbance, u is the system control input voltage, and K a and K bFor the total flow gain, K c This is the valve's flow-pressure coefficient;

[0029] Step 1.2: Determine the control objective: Make the system output y = ψ1 track the system's desired position command y. d =ψ 1d .

[0030] Furthermore, in step 1.1, the unknown function related to the system state All are continuous functions, and the unknown function perturbation, time-varying external disturbances, and their first derivatives are all bounded.

[0031] Furthermore, in step 1.2, the system expects to track the position command ψ. 1d (t) is first-order continuously differentiable, and the system's desired position command and its first derivative are both bounded.

[0032] Furthermore, in step 2, a neural network estimator is designed based on a multi-layer feedforward neural network to estimate the matched and unmatched unknown function disturbances of the multi-degree-of-freedom serial hydraulic manipulator system, as detailed below:

[0033] For any smooth unknown function χ j (ψ j-1 ,ψ j ),satisfy:

[0034]

[0035] In the formula, the variable is... j The subscript j in the text takes the values ​​2 and 3. Let x be the bounded, constant, ideal weight matrix of the neural network, where x j1 x j2 The number of neurons; β j The input vector and τ represents the activation function; j (β j ) represents the function reconstruction error;

[0036] From the above formula, we get:

[0037]

[0038] In the formula, The estimated value of the representative.

[0039] Furthermore, in step 3, a disturbance observer based on a neural network estimator is designed to estimate matched and unmatched time-varying external disturbances in the multi-degree-of-freedom serial hydraulic manipulator system, as detailed below:

[0040] Set a new state ψd2 =τ2(β2)+Δ2(t,ψ1,ψ2,ψ3),ψ d3 =τ3(β3)+Δ3(t,ψ1,ψ2,P a ,P b If the system state equation is:

[0041]

[0042] In the formula, It is the observer gain, σ i And σ4 parameterized as σ i =4! / i! (4-i)! ,σ4=1;ω o ρ2 is an adjustable positive constant.

[0043] Furthermore, in step 4, an output feedback controller for the multi-degree-of-freedom serial hydraulic robotic arm system is established, as follows:

[0044] Step 4.1, Definition Let the tracking error of the system be defined. and for:

[0045]

[0046] In the formula, and The filtered values ​​for the virtual control laws δ1 and δ2 are obtained through the following filters:

[0047]

[0048]

[0049] In the formula, w c(j-1) It is an adjustable positive gain. Represents the virtual control law δ j-1 The filtered value of the first derivative;

[0050] Step 4.2, Define Vector Where α i The auxiliary variables used to compensate for filtering errors are generated by the following auxiliary system:

[0051]

[0052]

[0053]

[0054] In the formula, g1, g2, and g3 are adjustable positive gains;

[0055] Step 4.3: Design the virtual control laws δ1 and δ2 and the actual control law u as follows:

[0056]

[0057]

[0058]

[0059] Furthermore, in step 5, the neural network adaptive law of the output feedback controller of the multi-degree-of-freedom serial hydraulic manipulator system is designed as follows:

[0060] Based on the controller design, an adaptive law for the neural network is designed, and the weight parameters of its multilayer feedforward neural network are updated using the following formula:

[0061]

[0062]

[0063] In the formula, Proj(·) is the continuous projection mapping function, and Γ j and Υ j Let η be the adaptive law matrix for the weight parameters. j μ o θ j , All are adjustable positive constants, f j (·) represents a function obtained from theoretical analysis.

[0064] Furthermore, in step 6, the initial values ​​of the neural network weight parameters, the adaptive law matrix, and the controller parameters are selected so that the system output tracks the desired position command, as detailed below:

[0065] Selecting initial values ​​for the neural network weights and the adaptive law matrix Γ j Υ j The value of ω is adjusted. o ρ2, g1, g2, g3, η i μ o θ i and The value of is used to compensate for the uncertainty of the system model, while making the system output y = ψ1 track the desired position command y. d =ψ 1d ; where Γ j Υ j ω o ρ2, g1, g2, g3, η i μ o θ i and The values ​​are all greater than 0.

[0066] Compared with the prior art, the present invention has the following significant advantages: (1) The output feedback controller designed in this invention can ensure that the position output of the multi-degree-of-freedom serial hydraulic manipulator system can accurately track the expected position command while ensuring that the system can improve the compensation model uncertainty effect under the combined action of unknown function disturbance and time-varying external disturbance; (2) The controller's solution does not depend on the rotational inertia of the system, but only requires the angular position information of each joint, which reduces the number of sensors, improves the system stability, and is beneficial for industrial and engineering applications. Attached Figure Description

[0067] Figure 1 This is a flowchart illustrating the construction method of the output feedback controller for a multi-degree-of-freedom serial hydraulic robotic arm system according to the present invention.

[0068] Figure 2 This is a schematic diagram of the structure of a multi-degree-of-freedom serial hydraulic robotic arm system in an embodiment of the present invention.

[0069] Figure 3 This is a graph showing the tracking performance of system joint 1 under the action of the controller designed in this embodiment of the invention, as well as the curve of tracking error changing over time.

[0070] Figure 4 This is a graph showing the tracking performance of system joint 2 under the action of the controller designed in this embodiment of the invention, as well as the curve of tracking error changing over time.

[0071] Figure 5 This is a graph showing the change in the state estimation performance of system joint 1 under the action of the controller designed in this embodiment of the invention over time.

[0072] Figure 6 This is a graph showing the change in the state estimation performance of system joint 2 under the action of the controller designed in this embodiment of the invention over time.

[0073] Figure 7 This is a graph showing the performance of the unknown function estimation of system joint 1 under the action of the controller designed in this embodiment of the invention as a function of time.

[0074] Figure 8 This is a graph showing the performance of the unknown function estimation of system joint 2 under the action of the controller designed in this embodiment of the invention as a function of time.

[0075] Figure 9 This is a graph showing the change in the external disturbance estimation performance of system joint 1 under the action of the controller designed in this embodiment of the invention over time.

[0076] Figure 10This is a curve showing the change in the external disturbance estimation performance of system joint 2 under the action of the controller designed in this embodiment of the invention over time.

[0077] Figure 11 This is a graph showing the change of the control input voltage of the controller designed in this embodiment of the invention over time. Detailed Implementation

[0078] The output feedback controller of the multi-degree-of-freedom serial hydraulic manipulator system introduces multi-layer neural network row estimation and feedforward compensation for the unknown function disturbance of the manipulator system. For unmatched and matched time-varying external disturbances, nonlinear disturbance observers and extended observers are used to estimate and feedforward compensation. Under the combined action of unknown function disturbances and time-varying external disturbances, the position output of the manipulator system can accurately track the expected position command.

[0079] Combination Figure 1 The present invention discloses a method for constructing an output feedback controller for a multi-degree-of-freedom series hydraulic robotic arm system, comprising the following steps:

[0080] Step 1: Establish a mathematical model of the multi-degree-of-freedom serial hydraulic robotic arm system and determine the control objective;

[0081] Step 2: Design a neural network estimator based on a multi-layer feedforward neural network to estimate the matched and unmatched unknown function disturbances of the multi-degree-of-freedom serial hydraulic manipulator system;

[0082] Step 3: Design a disturbance observer based on a neural network estimator to estimate matched and unmatched time-varying external disturbances in a multi-degree-of-freedom serial hydraulic manipulator system;

[0083] Step 4: Establish the output feedback controller for the multi-degree-of-freedom serial hydraulic robotic arm system;

[0084] Step 5: Design the neural network adaptive law for the output feedback controller of the multi-degree-of-freedom serial hydraulic manipulator system;

[0085] Step 6: Select the initial values ​​of the neural network weight parameters, the adaptive law matrix, and the controller parameters so that the system output tracks the desired position command.

[0086] As a specific example, step 1 establishes a mathematical model of a multi-degree-of-freedom serial hydraulic manipulator system and determines the control objective, as follows:

[0087] Step 1.1: Establish a mathematical model of a multi-degree-of-freedom serial hydraulic robotic arm system, where all joints are driven by either hydraulic cylinders or hydraulic motors. (See diagram below.) Figure 2 As shown, the actuators of each joint can also be composed of a combination of hydraulic cylinders and hydraulic motors. According to Newton's second law, the kinematic equation of the load is as follows:

[0088]

[0089] In formula (1) Indicates joint angular displacement. It is a symmetric inertia matrix. Represents the centripetal-Coriolis matrix. Represents the gravity vector. Represents a nonlinear friction function. f is an unknown function that depends on the system state. d (t) represents time-varying external disturbances. Input torque;

[0090] Input torque T c It can be described as:

[0091]

[0092] In formula (2) Represents the displacement of the hydraulic actuator. These represent the effective working areas of the two chamber piston rods of the hydraulic actuator. The pressure in both chambers is represented by the dynamic equation:

[0093]

[0094]

[0095] In formula (3) β ef V is the elastic modulus of hydraulic oil. a (q)=V a0 +A a y L (q), V b (q)=V b0 –A b y L (q) represents the volume of the two chambers of the hydraulic cylinder, V a0 V b0 Q represents the initial volume of the two chambers of the hydraulic cylinder. a Q b C represents the flow rate through the two chambers. tl P is the actuator leakage coefficient. ab =P a –P b The pressure difference between the two chambers Q is an unknown function that depends on the system state. d1 (t), Q d2 (t) represents time-varying external disturbances.

[0096] The servo valve load flow equation is:

[0097] Q a =K a u-2K c P a Q b =K b u+2K c P b (4)

[0098] In formula (4), u is the control input voltage of the system, K a and K b For the total flow gain, K c This is the valve's flow-pressure coefficient.

[0099] Define the system state variables as The state-space form of the nonlinear model of the system is:

[0100]

[0101] in:

[0102] χ2(ψ1,ψ2)=J inv (ψ1)[-V c (ψ1,ψ2)ψ2-G(ψ1)-F f (ψ2)-F e (ψ1,ψ2)] (6)

[0103]

[0104]

[0105] Δ2(t,ψ1,ψ2,ψ3)=J inv (ψ1)[H(ψ1)ψ3+D2(t)]-ψ3

[0106] Δ3(t,ψ1,ψ2,P a ,P b ) = F dc (ψ1,ψ2,P a ,P b )+D3(t)

[0107] The expressions for the other parts of formula (6) are as follows:

[0108]

[0109] Step 1.2: Define the control objective: For a multi-degree-of-freedom serial hydraulic robotic arm system, design an output feedback controller to improve the effect of compensating for uncertainties in the system model, while ensuring that the system output y = ψ1 tracks the desired position command y as accurately as possible. d =ψ 1d .

[0110] As a specific example, the unknown function related to the system state described in step 1.1 All are continuous functions, and the unknown function perturbation, time-varying external disturbances, and their first derivatives are all bounded.

[0111] As a specific example, the system described in step 1.2 expects to track the position command ψ. 1d (t) is first-order continuously differentiable, and the system expects position commands and their first derivatives are bounded.

[0112] As a specific example, in step 2, a neural network estimator is designed based on a multi-layer feedforward neural network to estimate the matched and unmatched unknown function disturbances of the multi-degree-of-freedom serial hydraulic manipulator system, as detailed below:

[0113] For any smooth unknown function χ j (ψ j-1 ,ψ j ), which satisfies:

[0114]

[0115] In formula (8), the variable is... j The subscript j in the text takes the values ​​2 and 3. Let x be the bounded, constant, ideal weight matrix of the neural network, where x j1 x j2 The number of neurons; β j The input vector and τ represents the activation function; j (β j ) represents the function reconstruction error;

[0116] From formula (8), we can obtain:

[0117]

[0118]

[0119] In the formula, The estimated value of the representative.

[0120] As a specific example, step 3 designs a disturbance observer based on a neural network estimator to estimate matched and unmatched time-varying external disturbances in a multi-degree-of-freedom serial hydraulic manipulator system, as follows:

[0121] Set a new state ψ d2 =τ2(β2)+Δ2(t,ψ1,ψ2,ψ3),ψ d3 =τ3(β3)+Δ3(t,ψ1,ψ2,P a ,P b If the system state equation can be expressed as:

[0122]

[0123] In formula (11) Introduce an auxiliary variable ζ2 and define ξ2 = ψ d2 -ρ2ψ2, taking the derivative with respect to the auxiliary variable ζ2:

[0124]

[0125] According to formula (12), the estimated value of the auxiliary variable ζ2 is... for:

[0126]

[0127] According to formulas (11) and (12), a disturbance observer with state and uncertainty estimation capabilities can be designed as follows:

[0128]

[0129] In formula (14) and It is the observer gain, σ i And σ4 can be parameterized as: σ i =4! / i! (4-i)! ,σ4=1,ω o ρ2 is an adjustable positive constant;

[0130] Define vector Let the estimation error of · be represented by the dynamic expression of the state estimation error:

[0131]

[0132] In formula (15):

[0133]

[0134] In formula (16) B j B jThe j-th element is 1, and the rest are 0. For example, the 4th element of B4 is 1, and the rest are 0.

[0135]

[0136] Therefore, there exists a positive definite matrix C. o make This holds true, where I is the identity matrix.

[0137] As a specific example, step 4 involves designing the output feedback controller for a multi-degree-of-freedom serial hydraulic robotic arm system, as detailed below:

[0138] Step 4.1, Definition Let the tracking error of the system be defined. and for:

[0139]

[0140] In formula (18) and The filtered values ​​for the virtual control laws δ1 and δ2 are respectively, and can be obtained through the following filters:

[0141]

[0142] In formula (19) w c(j-1) It is an adjustable positive gain. Represents the virtual control law δ j-1 The filtered value of the first derivative.

[0143] Define vector Formula (18) can then be written as:

[0144]

[0145] In formula (20) For virtual control law δ j-1 The second derivative, Φ c and B c for:

[0146]

[0147] Step 4.2, Define Vector Where α i These are auxiliary variables used to compensate for filtering errors, and they are generated by the following auxiliary system:

[0148]

[0149] In formula (22), g1, g2, and g3 are adjustable positive gains.

[0150] Step 4.3: Differentiate ξ1, and based on formulas (11), (18), and (22), we can obtain:

[0151]

[0152] According to formula (23), the virtual control law δ1 is obtained as follows:

[0153]

[0154] Substituting (24) into (23) yields:

[0155]

[0156] Differentiating ξ2 and applying formulas (11), (18), and (22), we obtain:

[0157]

[0158] According to formula (11), formula (26) can be rewritten as:

[0159]

[0160] According to formula (27), the virtual control law δ2 is obtained as follows:

[0161]

[0162] Substituting (28) into (27) and further transforming it, equation (28) can be written as:

[0163]

[0164] Similarly, by differentiating ξ3 and based on formulas (11), (18), and (22), we can obtain:

[0165]

[0166] According to formula (11), formula (30) can be written as:

[0167]

[0168] From formula (31), the control law u can be obtained as:

[0169]

[0170] Substituting (32) into (31) and further transforming it, equation (32) can be rewritten as:

[0171]

[0172] As a specific example, step 5 designs the neural network adaptive law for the output feedback controller of the multi-degree-of-freedom serial hydraulic manipulator system, as follows:

[0173] Based on the controller design, an adaptive law for the neural network is designed, and the weight parameters of its multilayer feedforward neural network are updated using the following formula:

[0174]

[0175] In formula (34), Proj(·) is the continuous projection mapping function, Γ j and Υ j Let η be the adaptive law matrix for the weight parameters. j μ o θ j , All are adjustable positive constants, f j (·) denotes the appropriate function obtained from theoretical analysis.

[0176] As a specific example, step 6 selects the initial values ​​of the neural network weight parameters, the adaptive law matrix, and the controller parameters to make the system output track the desired position command as accurately as possible, as follows:

[0177] Selecting initial values ​​for the neural network weights and the adaptive law matrix Γ j Υ j The value of ω is adjusted. o ρ2, g1, g2, g3, η i μ o θ i and The value of is used to ensure the effectiveness of compensating for uncertainties in the system model, while making the system output y = ψ1 track the desired position command y as accurately as possible. d =ψ 1d ; where Γ j Υ j ω o ρ2, g1, g2, g3, η i μ o θ i and The values ​​are all greater than 0.

[0178] The stability of the output feedback controller of the multi-degree-of-freedom serial hydraulic manipulator system is demonstrated through the following analysis:

[0179] Based on the stability analysis of the system in control theory, the Lyapunov function L is selected. V for:

[0180]

[0181] In formula (35), the variable is... i The subscript i in the matrix takes values ​​of 1, 2, and 3; tr(·) represents the trace of a matrix ·.

[0182] Substituting equations (25), (29), and (33) into the differential equation of equation (35) and transforming it, we can obtain:

[0183]

[0184] In formula (36), k ξ1 ,k ξj ,k εo , k εc(j-1) ,k α1 ,k α2 ,k α3 , Δ L All are positive numbers;

[0185] From formula (36), we can further obtain:

[0186]

[0187] In formula (37), k V =min{2k ξi / η i 2k εo / (μ o κ max {C o}), 2k εc(j-1) / κ max {C c},2k αi , Where min{·} represents the minimum value of ·, κ max(·) The largest eigenvalue representing ·.

[0188] Therefore, it can be concluded that all closed-loop system signals are bounded and the system tracking error can be adjusted through design parameters.

[0189] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0190] Example 1

[0191] To test and verify the integrated control algorithm, a dual-link tandem hydraulic manipulator was used. The first link was driven by a single-link hydraulic cylinder, and the second link was driven by a hydraulic motor. For simplicity, the following settings were adopted: Figure 2Hinges Z1 and Z2 are on the same horizontal line. According to the rigid body dynamics equation (1) of the hydraulic manipulator, the two-degree-of-freedom hydraulic manipulator J(q) is connected in series. G(q) is represented as:

[0192]

[0193] The expressions for each part of formula (38) are shown below:

[0194]

[0195] q in formula (39) x J represents the angular position of the x-th chain; mx and J L S represents the mass and load of the x-th chain, respectively; x S represents the length of the x-th chain; cx The x-th chain axis represents the distance from the center of gravity to the joint axis of the x-th chain; g represents the acceleration due to gravity; J Ix Let ψ1 represent the moment of inertia of the x-th chain, and let ψ1 = [ψ 11 ,ψ 12 ] T , ψ2=[ψ 21 ,ψ 22 ] T , ψ3=[ψ 31 ,ψ 32 ] T , ψ d2 =[ψ d21 ,ψ d22 ] T , ψ d3 =[ψ d31 ,ψ d32 ] T , χ2=[χ 21 ,χ 22 ] T , χ3=[χ 31 ,χ 32 ] T .

[0196] The parameters of the robotic arm system are:

[0197] J m1 = 5.6kg, J m2 =6.6kg, J I1 = 2.28 kg·m 2 J I2 =1.28 kg·m 2 J L =15.5kg, S c1 =0.2m, S c2=0.15m, S1=0.5m, S2=0.2m, L 10 =0.2m, L 11 =0.2m, L 12 =0.2m, β ef =1.26×10 9 Pa, P s =4×10 6 Pa, P r =0Pa, A a1 =1×10 -3 m 2 A b1 =5×10 -4 m 2 A a2 =1.22×10 -4 m 3 / rad, A b2 =1.22×10 -4 m 3 / rad;

[0198] C tl =diag{2.85×10 -12 2.85×10 -12}m 3 / s / Pa,K a =diag{1.25×10 -4 1.25×10 -4}m 4 / s / V,K b =diag{1.2×10 -4 1.2×10 -4}m 4 / s / V,K c =diag{1.65×10 -11 1.65×10 -11}m 3 / s / Pa;

[0199] Time-varying external disturbance f d (t) = [155sin(t), 155sin(t)] T Q d1 (t)=[1×10 6 sin(t), 8×10 6 sin(t)] T Q d2 (t)=[1×10 6 sin(t), 8×10 6 sin(t)] T ;

[0200] Added unknown functions related to system state:

[0201]

[0202]

[0203]

[0204] The initial value of the system is ψ1(0) = [q1(0), q2(0)]. T =[π / 3, 0.2] T The system expects the position command to be tracked as curve ψ 1d =[q 1d ,q 2d ] T = [0.42sin(1.25t)(1-e -0.5t )+1.05rad,0.22cos(2.2t)(1-e -0.5t )+0.5rad] T .

[0205] Controller design parameters:

[0206] After continuous adjustments, the control parameters were selected as follows:

[0207] g1=diag{300,500}, g2=diag{200,500}, g3=diag{300,300}; ω o =diag{600,600}, ρ2=diag{50,50};

[0208] ω c1 =diag{3×10 3 3×10 3}, ω c2 =diag{3.2×10 3 3.2×10 3};

[0209] Γ2=[1×10 2 I 11×11 1×10 2 I 11×11 ] T Γ3=[1×10 2 I 14×14 1×10 2 I 14×14 ] T ;

[0210] θ2=[1×10 3 I 5×5 1×10 3 I5×5 ] T θ3=[1×10 3 I 5×5 1×10 3 I 5×5 ] T ;

[0211] Υ2=[1×10 -1 I 11×11 1×10 -1 I 11×11 ] T Υ3=[1×10 -1 I 14×14 1×10 -1 I 14×14 ] T ;

[0212]

[0213] Controller function and effect: Figure 3 and Figure 4 The figures show the tracking performance of the two joints of the system and the curves of the tracking error changing over time under the action of the controller designed in this invention. As can be seen from the two figures, the steady-state tracking error reaches a high tracking accuracy under the action of the controller designed in this invention, thus verifying the effectiveness of the controller designed in this invention.

[0214] Figure 5 and Figure 6 These are curves showing the state estimation performance of the two joints of the system under the action of the controller designed in this invention as a function of time. As can be seen from the two figures, the estimated state of the system under the action of the controller designed in this invention is basically consistent with the actual state.

[0215] Figure 7 and Figure 8 The graph shows the time-varying performance of the unknown function estimation of the two joints of the system under the action of the controller designed in this invention. As can be seen from the graph, they eventually fluctuate around a certain value, thus enabling the effective estimation of the unknown function in the system.

[0216] Figure 9 and Figure 10 The graph shows the curves of the external disturbance estimation performance of the two joints of the system under the action of the controller designed in this invention as a function of time. It can be seen from the graph that they eventually fluctuate around a certain value, thus enabling effective estimation of disturbances in the system.

[0217] Figure 11 The graph shows the curve of the control input voltage of the controller designed in this invention changing over time. As can be seen from the graph, the control input signal obtained by this invention is continuous and bounded, which is beneficial for practical engineering applications.

[0218] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for constructing an output feedback controller for a multi-degree-of-freedom serial hydraulic robotic arm system, characterized in that, Includes the following steps: Step 1: Establish a mathematical model of the multi-degree-of-freedom serial hydraulic robotic arm system and determine the control objective, as follows: Step 1.1: Establish the mathematical model of the multi-degree-of-freedom serial hydraulic robotic arm system: Define the system state variables as... Where q represents the joint angular displacement, and A a A b P represents the effective working area of ​​the two-chamber piston rod of the hydraulic actuator. a P b Indicates the pressure in both chambers; Step 1.2: Determine the control objective: to make the system output... Tracking system expected position command ; Step 2: Design a neural network estimator based on a multi-layer feedforward neural network to estimate the matched and unmatched unknown function disturbances of the multi-degree-of-freedom serial hydraulic manipulator system; Step 3: Design a disturbance observer based on a neural network estimator to estimate matched and unmatched time-varying external disturbances in a multi-degree-of-freedom serial hydraulic manipulator system; Step 4: Establish the output feedback controller for the multi-degree-of-freedom serial hydraulic robotic arm system, as detailed below: Step 4.1, Definition Let the tracking error of the system be defined. and for: ； In the formula and Virtual control laws and The filtered value is obtained through the following filter: ； In the formula, It is an adjustable positive gain. Representing virtual control law The filtered value of the first derivative; Step 4.2, Define Vector ,in The auxiliary variables used to compensate for filtering errors are generated by the following auxiliary system: ； In the formula, , , It is an adjustable positive gain; Step 4.3: Design the virtual control laws δ1 and δ2 and the actual control law u as follows: ； ； K represents the elastic modulus of hydraulic oil. a and K b This represents the total flow gain; Step 5: Design the neural network adaptive law for the output feedback controller of the multi-degree-of-freedom serial hydraulic manipulator system; Step 6: Select the initial values ​​of the neural network weight parameters, the adaptive law matrix, and the controller parameters so that the system output tracks the desired position command.

2. The method for constructing the output feedback controller of the multi-degree-of-freedom serial hydraulic robotic arm system according to claim 1, characterized in that, In step 1, the state-space form of the system's nonlinear model is as follows: ； in: ； ； The expressions for the other parts of the formula are as follows: ； In the formula, V a (q) = V a0 +A a y L (q), V b (q) = V b0 –A b y L (q) represents the volume of the two chambers of the hydraulic cylinder, V a0 V b0 Q represents the initial volume of the two chambers of the hydraulic cylinder. a Q b C represents the flow rate through the two chambers. tl P is the actuator leakage coefficient. ab =P a –P b The pressure difference between the two chambers , An unknown function that is related to the system state. , For time-varying external disturbances, K c This is the valve's flow-pressure coefficient.

3. The method for constructing the output feedback controller of the multi-degree-of-freedom serial hydraulic robotic arm system according to claim 2, characterized in that, In step 1.1, the unknown functions related to the system state , All are continuous functions, and the unknown function perturbation, time-varying external disturbances, and their first derivatives are all bounded.

4. The method for constructing the output feedback controller of the multi-degree-of-freedom serial hydraulic robotic arm system according to claim 2, characterized in that, In step 1.2, the system expects to track the position command. It is first-order continuously differentiable, and the position command expected by the system and its first derivative are both bounded.

5. The method for constructing the output feedback controller of the multi-degree-of-freedom serial hydraulic robotic arm system according to claim 3 or 4, characterized in that, In step 2, a neural network estimator is designed based on a multi-layer feedforward neural network to estimate the matched and unmatched unknown function disturbances of the multi-degree-of-freedom serial hydraulic manipulator system, as detailed below: For any smooth unknown function ,satisfy: ； In the formula, variables The subscript j in the text takes the values ​​2 and 3. ∈ , ∈ Let x be the bounded, constant, ideal weight matrix of the neural network, where x j1 x j2 The number of neurons; The input vector and ; Indicates the activation function; Indicates the function reconstruction error; From the above formula, we get: ； In the formula, represent The estimated value.

6. The method for constructing the output feedback controller of the multi-degree-of-freedom serial hydraulic robotic arm system according to claim 5, characterized in that, In step 3, a disturbance observer based on a neural network estimator is designed to estimate matched and unmatched time-varying external disturbances in a multi-degree-of-freedom serial hydraulic manipulator system, as detailed below: Set a new state The system state equation is then expressed as: ； In the formula, It is the observer gain. and Parameterization , ; It is an adjustable positive number.

7. The method for constructing the output feedback controller of the multi-degree-of-freedom serial hydraulic robotic arm system according to claim 6, characterized in that, In step 5, the neural network adaptive law of the output feedback controller of the multi-degree-of-freedom serial hydraulic manipulator system is designed as follows: Based on the controller design, an adaptive law for the neural network is designed, and the weight parameters of its multilayer feedforward neural network are updated using the following formula: ； In the formula, Proj ( ) is a continuous projection mapping function. and The adaptive law matrix for the weight parameters, , , , All are adjustable positive constants, f j (•) represents a function obtained from theoretical analysis.

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