A hydraulic mechanical arm system fixed time compensation control method with input dead zone and unknown disturbance

Abstract

The application provides a hydraulic mechanical arm system fixed time compensation control method with input dead zone and unknown disturbance, and is aimed at a hydraulic mechanical arm system with input dead zone and unknown disturbance, and based on a backstepping design framework, a novel adaptive compensation controller with fixed time convergence is provided by using relevant mathematical lemmas and adaptive control technology. First, an observer is designed for parameter uncertainty and unknown disturbance of the system model by using the sliding mode control and fixed time theory, and the observer is compensated; second, a controller is designed based on the backstepping design framework; third, an input dead zone adaptive compensation mechanism is constructed based on Lyapunov stability theory. Simulation experiments show that the observer can well estimate and compensate the system output uncertainty caused by parameter uncertainty and unknown disturbance, and the system can maintain good tracking accuracy and realize rapid stability even if the system is affected by the input dead zone.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic robotic arms, and specifically relates to a fixed-time compensation control method for a hydraulic robotic arm system with input dead zone and unknown disturbance. Background Technology

[0002] Electro-hydraulic servo systems are important control devices in the field of automation, widely used in industrial control applications requiring high precision and high output power. While liquids, as the medium for power transmission and control, have some disadvantages and are more expensive than electricity, they offer advantages such as fast response speed, high power-to-weight ratio, and high load stiffness. Therefore, electro-hydraulic servo systems possess unique advantages in control applications demanding high precision and high output power. Electro-hydraulic servo control technology has been widely applied in many fields. In industry, robotic arms are very common devices, offering advantages such as flexible operation and high production efficiency, leading to their widespread use in modern industry. However, they are characterized by strong coupling, multiple variables, and high nonlinearity, and the dynamic model of the system is difficult to obtain accurately, posing significant challenges to high-performance control of robotic arm systems. In particular, the combination of hydraulic systems and robotic arms generates numerous problems, and achieving rapid stabilization of robotic arm systems has always been a hot research topic in academia.

[0003] Due to the inherent characteristics of hydraulic systems, they are often affected by various nonlinear properties, such as the uncertainty of hydraulic oil and the input dead zone of hydraulic valves. The input dead zone of hydraulic valves is a very common nonlinear characteristic, causing a nonlinear difference between the system control input (controller output) and the actual control quantity applied to the system. Ignoring the influence of the input dead zone in controller design can affect the system's transient performance and steady-state error, and even lead to system instability. Researchers have studied uncertain nonlinear systems with input dead zones, developed corresponding disturbance observers to compensate for them, and verified the feasibility of these methods through simulation experiments. Many input dead zone compensation methods can address the input dead zone problem in systems, but these methods are all non-fixed-time control methods, and theoretically, achieving final stability of the system requires an infinitely long time. In practical industrial applications, as robotic arm operations become increasingly complex, the performance requirements for systems become increasingly stringent, including strict requirements on convergence time and steady-state accuracy. Therefore, researching fixed-time compensation control for hydraulic robotic arm systems with input dead zones and unknown disturbances has significant practical implications. Summary of the Invention

[0004] In view of the above-mentioned deficiencies of the prior art, the present invention provides a fixed-time compensation control method for a hydraulic robotic arm system with input dead zone and unknown disturbance, in order to solve the problems mentioned in the background art.

[0005] This invention provides a fixed-time compensation control method for a hydraulic robotic arm system with input dead zone and unknown disturbances, comprising the following steps:

[0006] S1: Model the two-degree-of-freedom hydraulic manipulator system with input dead zone and unknown disturbance to obtain the mathematical model of the manipulator system;

[0007] S2: Design a sliding mode observer for the robotic arm to compensate for its parameter uncertainties and unknown disturbances;

[0008] S3: Design a virtual control law α based on the error of the robotic arm system. i β i Intermediate control rate γ i Design an adaptive law for its input dead zone characteristics. Finally, design the final control law u. i .

[0009] S4: Simulation analysis. If all closed-loop signals of the system are bounded, and the upper bound of the system convergence time is independent of the initial state of the system, then for the hydraulic robotic arm system, the observer and the virtual control law α... i β i Intermediate control rate γ i Adaptive law and the final control law u i It can achieve system stability at a fixed time.

[0010] This invention provides a fixed-time compensation control method for a hydraulic robotic arm system with input dead zone and unknown disturbances, which has the following advantages: it can track the desired trajectory well, and the system converges faster than traditional backstepping and asymptotic convergence algorithms. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of a hydraulic robotic arm system;

[0012] Figure 2 This is a schematic diagram of the tracking curve for joint 1;

[0013] Figure 3 This is a schematic diagram of the tracking curve for joint 2;

[0014] Figure 4 This is a schematic diagram of unknown disturbance tracking for joint 1;

[0015] Figure 5 This is a schematic diagram of unknown disturbance tracking at joint 2;

[0016] Figure 6 This is a schematic diagram of uncertainty tracking in the Joint 1 system;

[0017] Figure 7 This is a schematic diagram of uncertainty tracking in the Joint 2 system;

[0018] Figure 8 It is the adaptive parameter of joint 1. Schematic diagram of the curve;

[0019] Figure 9 It is the adaptive parameter of joint 1. Schematic diagram of the curve;

[0020] Figure 10 Joint 2 adaptive parameters Schematic diagram of the curve;

[0021] Figure 11 Joint 2 adaptive parameters Schematic diagram of the curve. Detailed Implementation

[0022] The embodiments of the present invention will be described in detail below. The embodiments described below are implemented based on the technical solution of the present invention, and detailed implementation methods and specific operation processes are given. However, the protection scope of the present invention is not limited to the embodiments described below.

[0023] A fixed-time compensation control method for a hydraulic robotic arm system with input dead zone and unknown disturbances includes the following steps:

[0024] S1: Model the two-degree-of-freedom hydraulic manipulator system with input dead zone and unknown disturbance to obtain the mathematical model of the manipulator system;

[0025] S2: Design a sliding mode observer for the robotic arm to compensate for its parameter uncertainties and unknown disturbances;

[0026] S3: Design a virtual control law α based on the error of the robotic arm system. i β i Intermediate control rate γ i Design an adaptive law for its input dead zone characteristics. and the final control law u i .

[0027] S4: Simulation analysis.

[0028] In S1, the mathematical model of the two-degree-of-freedom hydraulic manipulator system is as follows:

[0029]

[0030] Where x1 = [θ1, θ2] T It is the joint angle (system output). It's angular velocity. It is angular acceleration, x3 = [p L1A p ,p L2 A p ] T It represents the hydraulic pressure generated by the hydraulic cylinder; H(θ) is the inertia matrix. Let G(θ) be the centrifugal force and Coriolis force matrix, G(θ) be the gravity vector, and J be the lever arm of the force exerted by the hydraulic cylinder on the robotic arm. This refers to the speed of the hydraulic cylinder.

[0031] Γ=Γ(x3)=diag{Γ1(x3),Γ2(x3)}, All parameters are nominal parameters of the hydraulic system.

[0032] Δ2=H -1 Δ T (H,C,G), For unknown Coulomb friction torque and external load disturbances, etc., there are lumped uncertainties. It is the uncertainty of the input caused by the uncertainty of the system, and it is a bounded quantity that is less than u.

[0033] The two uncertainties Δ2 and Δ3 satisfy the following inequality: |Δ 2i |≤Λ 2i , i∈{1,2};|Δ 3i |≤Λ 3i , i∈{1,2}. Λ 2i and Λ 3i It is an unknown positive real number.

[0034] For input dead-zone nonlinearity, This is the control voltage for the servo valve.

[0035]

[0036] Among them, h i,1 >0 and h i,2 >0 represents the unknown slope of the straight line in the negative and positive semi-axis, respectively, g i,1 <0 and g i,2 >0 is an unknown turning point, D i (u i ) represents the output of the input dead-zone model.

[0037] make

[0038] That is, D i (u i ) = h i u i -g isgn(u i ), h i ≥0, g i ≥0.

[0039] In S2, to compensate for uncertainties, two auxiliary variables are defined as follows:

[0040]

[0041] v2 = [v 21 ,v 22 ] T v3 = [v 31 ,v 32 ] T s2=[s 21 ,s 22 ] T , s3=[s 31 ,s 32 ] T ,

[0042] The designs for v2 and v3 are as follows:

[0043]

[0044] in, 1 < q, 0 < p < 1, k a2i k b2i k a3i k b3i Λ 2i and Λ 3i All are positive real numbers to be designed.

[0045] This leads to the estimation form of the uncertainty:

[0046]

[0047] Design the following Lyapunov function to verify the above observer:

[0048]

[0049] Verification has shown that the observer designed above can estimate the uncertainty within a fixed time, and the error is stable in the neighborhood of 0.

[0050] The error of the robotic arm system in S3 is:

[0051]

[0052] Where, θ d α1 and α2 are the expected output of the system and are virtual control variables in the backstepping controller.

[0053] Selecting Lyapunov functions:

[0054] Design virtual control variables based on the Lyapunov function described above:

[0055] b 1i d 1i Let be the positive real number to be designed.

[0056] The following lemma is used after differentiating the chosen Lyapunov function:

[0057] For any x i For all integers > 0 (i = 1, 2, ..., n), the following inequality holds:

[0058]

[0059] For any a∈R, b∈R, r>1

[0060]

[0061] Further selection of Lyapunov functions:

[0062] Design virtual control variables based on the Lyapunov function described above:

[0063] make β 2i =-b 2i sgn(z 2i )|z 2i | 2q-1 -d 2i sgn(z 2i )|z 2i | 2p-1 -B i , i∈{1,2}, b 2i d 2i Let be the positive real number to be designed.

[0064] The dead zone in S3 is designed as follows:

[0065] The final control rate is designed to be Q i =[γ i ,sgn(γ i )] T , Represent The estimated value,

[0066] consider Due to the influence of this, the Lyapunov function is selected:

[0067]

[0068] Design intermediate control rate γ i As follows: b 3i d 3i Let be the positive real number to be designed.

[0069] Design Adaptive Law

[0070]

[0071] Where b 4j d 4j b 5j d 5j , j∈{1,2} are positive real numbers to be designed.

[0072] Furthermore, in step S4, considering the two-bar hydraulic manipulator system, the system dynamics model is given as follows: H 11 =I1+I2+m1(P1P m1 ) 2 +m2(P1P2) 2 +m2(P2P m2 ) 2 +2m2P1P2·P2P m2 cosθ2, H 12 =H 21 =I² + m²(P²P) m2 ) 2 +m2P1P2·P2P m2 cosθ2, H 22 =I² + m²(P²P) m2 ) 2 , G1=-m1gP1P m1 sinθ1-m2g(P1P2sinθ1+P2P m2 sin(θ1+θ2)),

[0073] Where m1 and m2 are the masses of the arm and forearm, respectively, and I1 and I2 are the moments of inertia of the arm and forearm about their centers of mass, respectively.

[0074] Furthermore, the system has an input dead zone, the relevant parameter being h. i,1 =h i,2 =1, g i,1 =-0.5 and g i,2=0.5, i=1,2. The initial state of the system is q=[-30°,100°] T , The system's expected output is:

[0075]

[0076] The controller parameters are designed as follows: k a2 =[100 100]、k b2 =[200 200], Λ2=[6 20];k a3 =[4×10 -3 4×10 -4 ]、k b3 =[400 200]、Λ3=[4×10 5 3×10 5 b1 =

[10] 4 10 4 ], d1=[1200 300]; b2=[10 -6 10 -6 ]、d2=[100 160];b3=[10 -10 10 -11 ], d3=[1000 2500]; k1=10 11 k2 = 10 12 b4 = [10 6 10 6 ]、d4=[10 7 10 7 b5 =

[10] 7 10 7 ]、d5=[10 8 10 8 The simulation step size is 0.1ms.

[0077] from Figures 2 to 11 It can be seen that all signals in a closed-loop system are bounded. From Figure 2 and Figure 3 As can be seen, the two joint angles of the robotic arm can track the desired output angle very well. In the figure, TBC represents the traditional backstepping control, and FTC represents the method of the present invention. It can be seen intuitively that the convergence time of the method of the present invention is much shorter than that of the traditional backstepping method. Figure 4 and Figure 5 These are the observed and simulated values ​​of Δ2. It can be seen that the observer can quickly estimate the simulated value with the error within the allowable range, and can effectively compensate for external disturbances to the system. Figure 6 and Figure 7These are the observed and simulated values ​​of Δ3. The observer can accurately estimate the amount of system uncertainty caused by parameter uncertainty and thus accurately compensate for it. Figures 8 to 11 The description is of the adaptive estimates of the dead zone parameters of two hydraulic valves and the values ​​given by the simulation. Both are bounded. Although the adaptive estimates tend to deviate from the actual values, the error is still very small, less than 0.3%.

[0078] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A fixed-time compensation control method for a hydraulic robotic arm system with input dead zone and unknown disturbance, comprising the following steps: S1: Model the two-degree-of-freedom hydraulic manipulator system with input dead zone and unknown disturbance to obtain the mathematical model of the manipulator system; the mathematical model of the hydraulic manipulator system in step S1 is as follows: ； in, It's the joint angle. It's angular velocity. It is angular acceleration. It is the hydraulic pressure generated by the hydraulic cylinder; The inertia matrix, The matrix represents the centrifugal force and the Coriolis force. It is the gravity vector. The lever arm is the force exerted by the hydraulic cylinder on the robotic arm. For the speed of the hydraulic cylinder, , , , , , These are all nominal parameters for hydraulic systems. , For unknown Coulomb friction torque and external load disturbances, etc., there are lumped uncertainties. , , It is the uncertainty of the input caused by the uncertainty of the system, which is a bounded quantity and less than 1 / 2. The amount; In S1, due to the structural characteristics of the machine, the mathematical model considering the input dead zone is as follows: ； in, and These are the unknown slopes of the lines in the negative and positive semi-axes, respectively. and It is an unknown turning point. It is the control torque. The input dead zone model output; make , ; Right now , , ; S2: Design a sliding mode observer for the robotic arm to compensate for its parameter uncertainties and unknown disturbances; in step S2, the sliding mode observer is designed as follows: Define two auxiliary variables: ; The designs for v2 and v3 are as follows: ； in, , , , , , , , , and All are positive real numbers to be designed; This leads to the estimation form of the uncertainty: ； S3: Design a virtual control law based on the error of the robotic arm system. , Intermediate control rate Design an adaptive law for its input dead zone characteristics. and the final control law ; S4: Simulation analysis.

2. The fixed-time compensation control method for a hydraulic robotic arm system with input dead zone and unknown disturbance as described in claim 1, characterized in that, In step S3, the error of the robotic arm system is defined as follows: ； in, This is the system's expected output. , These are two auxiliary variables of the sliding mode observer. , These are virtual control variables to be designed.

3. The fixed-time compensation control method for a hydraulic robotic arm system with input dead zone and unknown disturbance as described in claim 2, characterized in that, In step S3, the virtual control law , Intermediate control rate Design an adaptive law for its input dead zone characteristics. and the final control law The design is as follows: , , , Let the positive real number be the one to be designed; , , , , , Let the positive real number be the one to be designed; The final control rate is designed to be , , , , Represent , The estimated value, , ; ， ， , , Let the positive real number be the one to be designed; ； in , , , , Let be the positive real number to be designed.

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