Robust control method and system for a hoist robotic arm

Abstract

This invention belongs to the field of robotic arm control and provides a robust control method and system for a lifting robotic arm. It includes determining five nonlinear motion equations of the robotic arm dynamics using the Euler-Lagrange equations and representing them in matrix form. The robotic arm dynamics matrix form is divided into driven and non-driven forms, and after reduction processing, a reduced-mode dynamic model of the robotic arm is obtained. A robust controller is constructed by building a second-order sliding mode controller and a fast terminal sliding mode controller. The robotic arm dynamics matrix form is transformed into a state-space form to obtain a state observer. The state observer is subtracted from the state-space form to obtain the estimation error dynamic equation. The dynamic state of the robotic arm is inferred using the state observer. The control mode of the robust controller is determined based on the estimation error dynamic equation corresponding to the dynamic state, and the corresponding control signal is generated based on the robust controller. This invention significantly improves the safety and efficiency of robotic arms in practical applications.

Description

Technical Field

[0001] This invention belongs to the field of robotic arm control technology, specifically relating to a robust control method and system for a lifting robotic arm. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the rapid development of industrial automation, robotic arms, as important material handling equipment, are increasingly widely used in construction sites and other industrial environments. Tilting and lifting robotic arms, widely used in construction and industrial fields, are favored for their high mobility and versatility. However, existing technologies have several shortcomings in dynamic modeling and control. First, many studies focus only on dynamic modeling and numerical simulation, lacking in-depth exploration of control strategies, leading to insufficient control accuracy in actual operation. Second, traditional PID controllers often fail to maintain stable control performance when facing nonlinear systems and parameter variations, resulting in load sway and inaccurate operation. Furthermore, existing models typically neglect important physical characteristics of the robotic arm, such as boom mass, moment of inertia, and the rotational mass of the lifting mechanism, causing significant deviations between the dynamic model and reality. Finally, although the application of state observers is gradually increasing, their effectiveness in compensating for insufficient sensors still needs further verification. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a robust control method and system for a lifting and flipping robotic arm. This invention aims to solve the problems of inaccurate dynamic modeling, low control precision, and system instability in the prior art, and significantly improves the safety and efficiency of the robotic arm in practical applications.

[0005] According to some embodiments, the first aspect of the present invention provides a robust control method for a lifting robot arm, employing the following technical solution:

[0006] A robust control method for a lifting robot arm includes:

[0007] Five nonlinear motion equations of the robotic arm dynamics are determined by the Euler-Lagrange equations and expressed in matrix form to obtain the robotic arm dynamics matrix form. The robotic arm dynamics matrix form is divided into two forms: driven and non-driven. After order reduction processing, the reduced-order dynamics model of the robotic arm is obtained.

[0008] A second-order sliding mode controller and a fast termination sliding mode controller are constructed respectively, and the two together form a robust controller;

[0009] The dynamic matrix form of the robotic arm is transformed into the state space form, and then the state observer is obtained. The state observer is subtracted from the state space form to obtain the dynamic equation of the estimation error.

[0010] The dynamic state of the lifting robot arm is inferred using a state observer. The control mode of the robust controller is determined based on the dynamic equation of the estimation error corresponding to the dynamic state. The corresponding control signal is generated based on the robust controller to control the lifting robot arm.

[0011] According to some embodiments, a second aspect of the present invention provides a robust control system for a lifting robot arm, employing the following technical solution:

[0012] A robust control system for a lifting robot arm includes:

[0013] The dynamics model construction module is configured to determine five nonlinear motion equations of the robotic arm dynamics through the Euler-Lagrange equations and represent them in matrix form to obtain the robotic arm dynamics matrix form. The robotic arm dynamics matrix form is divided into driven form and non-driven form, and after order reduction processing, the reduced-order dynamics model of the robotic arm is obtained.

[0014] The robust controller building module is configured to build a second-order sliding mode controller and a fast termination sliding mode controller, which together form a robust controller;

[0015] The state observer construction module is configured to transform the dynamic matrix form of the robotic arm into the state space form, thereby obtaining the state observer. Subtracting the state observer from the state space form yields the dynamic equations for the estimation error.

[0016] The control module is configured to infer the dynamic state of the lifting robot arm using a state observer, determine the control mode of the robust controller based on the dynamic equation of the estimation error corresponding to the dynamic state, and generate corresponding control signals based on the robust controller to control the lifting robot arm.

[0017] According to some embodiments, a third aspect of the present invention provides a computer-readable storage medium.

[0018] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in a robust control method for a lifting robot arm as described in the first aspect above.

[0019] According to some embodiments, a fourth aspect of the present invention provides a computer device.

[0020] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the steps of a robust control method for a lifting robot arm as described in the first aspect above.

[0021] According to some embodiments, a fifth aspect of the present invention provides a computer program product or computer program.

[0022] This invention provides a computer program product or computer program comprising computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform steps in a robust control method for a lifting robot arm as described in the first aspect above.

[0023] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0024] This invention establishes a comprehensive dynamic model, which derives five nonlinear motion equations from the Euler-Lagrange equations. Initial conditions are defined for these five nonlinear motion equations, which are then expressed in matrix form. This matrix form is categorized into driven and non-driven forms, and a reduced-order dynamic model of the robotic arm is obtained after order reduction. A robust controller is designed, incorporating second-order sliding mode control and fast terminal sliding mode control. Differential analysis is performed on this controller to obtain its basic form. A state observer is designed; by subtracting the state observer from the dynamic state-space form, the dynamic equations for estimating the error are obtained. Through comprehensive consideration of the dynamic characteristics and control strategies of the lifting robotic arm, the safety and efficiency of the robotic arm in practical applications are significantly improved. Attached Figure Description

[0025] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0026] Figure 1 The control flowchart provided for embodiments of the present invention;

[0027] Figure 2 A flowchart of a robust controller provided for an embodiment of the present invention;

[0028] Figure 3 Wind disturbance diagram provided for embodiments of the present invention;

[0029] Figure 4 This is a diagram illustrating the control effect of the winch drum provided in an embodiment of the present invention.

[0030] Figure 5 This is a diagram illustrating the boom elevation angle control effect provided in an embodiment of the present invention.

[0031] Figure 6 A diagram illustrating the boom length control effect provided in an embodiment of the present invention;

[0032] Figure 7 The input torque diagram of the hoisting drum provided in the embodiment of the present invention;

[0033] Figure 8 This is a diagram showing the force control input for the lifting hydraulic cylinder provided in an embodiment of the present invention.

[0034] Figure 9 This is a force control input diagram for a telescopic hydraulic cylinder provided in an embodiment of the present invention. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0036] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0037] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0038] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0039] Example 1

[0040] like Figure 1 As shown, this embodiment provides a robust control method for a lifting robot arm. In this embodiment, the method includes the following steps:

[0041] Five nonlinear motion equations for the robotic arm dynamics are determined by the Euler-Lagrange equations and expressed in matrix form to obtain the robotic arm dynamics matrix form. The robotic arm dynamics matrix form is divided into driven form and non-driven form. After order reduction processing, the reduced-order dynamics model of the robotic arm is obtained.

[0042] A second-order sliding mode controller and a fast termination sliding mode controller are constructed respectively, and the two together form a robust controller;

[0043] The dynamic matrix form of the robotic arm is transformed into the state space form, and then the state observer is obtained. The state observer is subtracted from the state space form to obtain the dynamic equation of the estimation error.

[0044] The dynamic state of the lifting robot arm is inferred using a state observer. The control mode of the robust controller is determined based on the dynamic equation of the estimation error corresponding to the dynamic state. The corresponding control signal is generated based on the robust controller to control the lifting robot arm.

[0045] like Figure 1 and Figure 2 As shown, this embodiment provides a DMRC (Dynamic Modeling and Robust Control) method for dynamic modeling and robust control of a lifting robot arm, including:

[0046] Step S1: Establish a comprehensive robotic arm dynamics model. Five nonlinear motion equations for the robotic arm dynamics are determined using the Euler-Lagrange equations and expressed in matrix form, resulting in the robotic arm dynamics matrix form. This matrix form is then divided into driven and non-driven forms, and after order reduction processing, a reduced-order robotic arm dynamics model is obtained.

[0047] First, the system parameters, i.e., the parameters of the lifting manipulator control system, are defined. The manipulator dynamics model includes the boom's mass, moment of inertia, rotational mass of the lifting mechanism, and the boom's viscoelastic properties. The payload is considered a particle, and only its total mass is studied; the payload's size, volume, and shape are not reflected, but its wind-resistant area is included in the manipulator modeling and control. The movement of the payload swing, boom lifting, boom extension, and the two hydraulic cylinders are analyzed in a spatial coordinate system, meaning that the rotation of the manipulator base is not considered. When lifting and transporting the payload, the manipulator stands on the ground and is positioned by outriggers, meaning that the base movement and the elasticity of the rubber base are not considered. The load rope is assumed to be a massless rope. Since the payload is considered a point mass, the longitudinal deformation of the rope is considered, while its torsional deformation and the load's rotation about the rope axis are ignored. Modern control technology allows for automatic extension and locking of manipulator sections. In most cases, only two sections move relative to each other, while pins lock the other sections.

[0048] The robotic arm includes a geared motor and a winch drum connected to it. To the right of the winch drum is a lifting motor. At the bottom of the robotic arm is a fixed base. The robotic arm has three hydraulic cylinders: a lifting cylinder, a top cylinder, and a telescopic cylinder. The robotic arm is divided into an upper section, a middle section, and a lower section. The lifting cylinder is connected to the fixed base and the middle section of the robotic arm. The telescopic cylinder is located in the middle section of the robotic arm. The wire rope passes through the geared motor, the winch drum, the lifting motor, and the bottom pivot, and then through the lower section, middle section, upper section, and top cylinder of the robotic arm. Under the action of the top pulley and the top sliding pulley, the effective load is lifted and lowered.

[0049] Step S1.1: Determine five nonlinear equations of motion using the Euler-Lagrange equations, specifically:

[0050] Establish the Euler-Lagrange equations;

[0051] Substitute the total kinetic energy, total potential energy, power dissipation caused by friction, and generalized force corresponding to the generalized coordinates of the robotic arm into the Euler-Lagrange equations.

[0052] Five nonlinear motion equations for the robotic arm dynamics were obtained.

[0053] This embodiment establishes kinematic equations based on the Lagrange equations, and establishes the dynamic characteristics of the robotic arm controlled by five differential equations. The lifting robotic arm control system consists of three control signals. Tracking five raw outputs , This represents the number of original outputs. The three control inputs include the payload and the boost motor torque. Mechanical lever - lifting cylinder force and telescopic hydraulic cylinder force Five raw outputs It has five degrees of freedom corresponding to five generalized coordinates: The rotation angle of the lifting motor for the effective load. For the mechanical rod around the bottom pivot The amplitude angle, The center of the two tubes and center The distance between them represents the relative motion between the flight segment and the base segment. The longitudinal oscillation of the effective load caused by the elasticity of the rope. For payload The swing angle;

[0054] The Euler-Lagrange equations are expressed as:

[0055] (1);

[0056] in, For full kinetic energy, For total potential energy, For power dissipation energy caused by friction, five original outputs Corresponding to the five generalized coordinates, These are the generalized forces corresponding to the five generalized coordinates.

[0057] Full Kinetic Energy Including payload Kinetic energy of robotic arm movement and the kinetic energy of the robotic arm's rotation The details are as follows:

[0058] (2);

[0059] (3);

[0060] in, The distance between the top pulley and the top bottom pulley; length. and , Bottom Pivot arrive The length of the center, for From center to top The length and mass are respectively and ; and To revolve around the center and center Moment of inertia; To increase the equivalent inertia on the motor shaft;

[0061] Total potential energy Including load , lower section , upper section , lifting rope Lifting cylinder robotic arm The details are as follows:

[0062] (4);

[0063] (5);

[0064] in, The radius of the winch drum; and The stiffness and friction of a massless flexible steel wire rope; and For the stiffness and damping of the telescopic cylinder; and For lifting cylinder Stiffness and viscous damper; It is the acceleration due to gravity; The number of control ropes; To be from the fixed base to the bottom pivot Height; For fixed base to the bottom pivot The distance; Bottom Pivot Distance to the telescopic hydraulic cylinder This is the initial angle for the robotic arm's amplitude transformation; For the robotic arm to rotate around the bottom pivot The initial angle; This is the initial position of the flight segment within the basic moving frame; To increase the initial elongation of the rope; For payload The initial swing angle; For fixing the base To the bottom hub Angle in the horizontal direction For the center of the robotic arm and fixed base The angle between the steel wire rope at the lifting cylinder and the connection point of the robotic arm; This refers to the static deformation of the lifting cylinder; This refers to the static deformation of the telescopic hydraulic cylinder.

[0065] Power dissipation energy Including power dissipation caused by friction at the load lifting rope. Dissipation caused by viscosity at the lifting cylinder of the robotic arm And dissipation caused by viscosity at the extension cylinder of the robotic arm :

[0066] (6);

[0067] (7).

[0068] Substituting its total kinetic energy, total potential energy, power dissipation energy, and generalized force into the Euler-Lagrange equations, we obtain five complete nonlinear equations of motion, as follows:

[0069] (8);

[0070] (9);

[0071] (10);

[0072] (11);

[0073] (12);

[0074] in, To increase the equivalent torque of the motor on the drum shaft; , and For wind load Three components acting on the centroid of the payload, the base segment, and the top segment, respectively; To increase the height;

[0075] Step S1.2: Represent the five nonlinear motion equations of the robotic arm dynamics in matrix form to obtain the robotic arm dynamics matrix form. Divide the robotic arm dynamics matrix form into driven and non-driven forms, and after order reduction processing, obtain the reduced-order dynamic model of the robotic arm, specifically:

[0076] To make the calculation of the dynamic system response of the lifting robot arm physically meaningful and mathematically feasible, the initial conditions and initial velocities of the five generalized coordinates are determined by considering the influence of the robot arm's parking posture and initial load on the initial deformation.

[0077] To obtain the system response based on the five nonlinear equations in the robotic arm dynamics model, initial conditions for five generalized coordinates are defined. and initial velocity :

[0078] (13);

[0079] (14);

[0080] In the initial state, the effective load wire rope is perpendicular to the ground, then Static deformation of the effective load wire rope The boom is at the bottom pivot. The static displacement of the lifting cylinder is as follows:

[0081] (15);

[0082] in, The initial force of the lifting cylinder is given, and the initial position of the middle section of the bottom moving frame is given. The static deformation of the telescopic hydraulic cylinder is as follows:

[0083] (16).

[0084] Representing the motion of the five fully nonlinear equations in matrix form, and constructing a fully nonlinear model of the lifting robot arm under the general operation condition of simultaneous activation of three control signals, yields the robot arm's dynamic matrix form, as shown below:

[0085] (17);

[0086] in, It is a positive definite mass matrix. It is the damping matrix. It is a gravitational vector;

[0087] It is an equivalent complex vector that encompasses all the nonlinear complexities of the robotic arm's dynamics. It is the activation input vector. It is the wind disturbance vector. and It is the constraint Jacobian matrix corresponding to the control signal and wind load.

[0088] Positive definite mass matrix:

[0089] (18);

[0090] in, The details are as follows:

[0091] (19);

[0092] Damping matrix The details are as follows:

[0093] (20);

[0094] Gravitational vector The details are as follows:

[0095] (twenty one);

[0096] Equivalent complex vector The details are as follows:

[0097] (twenty two);

[0098] The dynamic matrix form of the robotic arm is divided into driven and non-driven forms, and a reduced-order dynamic model of the robotic arm is obtained after order reduction processing. Five outputs. In the middle, control signals Direct tracking drive output The control does not drive the output. Depends on and The kinematic constraints between them. However, due to the flexibility of the rope and the elasticity of the boom lifting cylinder, some constraints are released, thereby reducing... and The interaction between them. For ease of control design, the dynamic matrix of the robotic arm is divided into two parts: driven and non-driven.

[0099] The driver status is as follows:

[0100] (twenty three);

[0101] The non-driving state is as follows:

[0102] (twenty four);

[0103] in, , , yes submatrix, and yes submatrix, , yes Two vectors, and yes The two submatrices, , , , and yes The two components.

[0104] Extract from non-driving model Substituting into the driving model, we obtain the reduced-order dynamic model of the lifting robot arm:

[0105] (25);

[0106] in, , , , , .

[0107] Step S2: Design a robust controller, including second-order sliding mode control and fast terminal sliding mode control, perform derivative analysis on it, and finally obtain the basic form of the robust controller.

[0108] A robust controller is designed considering input and disturbances, employing second-order sliding mode control. Multi-level convergence is used to prevent concessions at the system output and high switching gain.

[0109] Step S2.1: Construct a second-order sliding mode controller, specifically as follows:

[0110] Define the first-stage sliding surface, adjust the positive gain matrix, and use a power-law convergence method to make the driving output and non-driving output converge toward the corresponding target value on the first-stage sliding surface, asymptotically tracking the driving output and stabilizing the non-driving output.

[0111] Define a second-stage sliding surface, combine the tracking error of the robotic arm control system, and adjust the gain matrix in real time according to the response of the robotic arm control system. Use linear convergence to make the driven output and non-driven output converge toward the corresponding target value on the second-stage sliding surface, asymptotically tracking the driven output and stabilizing the non-driven output.

[0112] A second-order sliding mode controller is constructed based on the convergence of the first-stage sliding surface and the second-stage sliding surface.

[0113] Phase 1: After the system starts up or is subjected to significant disturbance, convergence rules are used to make the manifold converge asymptotically.

[0114] Define the first stage sliding surface That is, the first-stage sliding surface (first manifold). The asymptotic convergence will be achieved using formula (26), as follows:

[0115] (26);

[0116] in, Xiang Shi The exponential stability, and The item maintains the consistency of the sliding area. and It is a diagonal matrix with positive gain, that is, the gain matrix.

[0117] The second stage involves selecting a suitable gain matrix based on the system's tracking error and adjusting the gain in real time according to the system response. The stability is proven using the Lyapunov function. In this stage, the system output first converges exponentially to a power, then the slope is... The linear convergence asymptotically tracks the driven output and stabilizes the non-driven output, reducing output chattering.

[0118] Define the second-stage sliding surface That is, the second-stage sliding surface (second manifold). Specifically:

[0119] (27);

[0120] in, Represents the gain matrix. and It is tracking error.

[0121] Obviously (or It has two-stage stability: the first stage is The exponential convergence of the powers occurs in the second stage, where the slope is... The linear convergence is achieved. To drive the output, Non-driven output, and This represents the corresponding target value. By selecting an appropriate gain matrix... , , The gain is adjusted in real time according to the system response, and its stability is proved by using the Lyapunov function to reduce output chattering. The output in the driving state is asymptotically tracked and the output in the non-driving state is stabilized.

[0122] Design a second-order sliding mode controller. This allows the drive output to be enabled. asymptotic tracking target value and make Stabilize at the target value nearby:

[0123] (28);

[0124] Gain Constraints must be met:

[0125] (29);

[0126] (30);

[0127] in, , , and These are the drive outputs. Non-drive output middle , , , The corresponding target value.

[0128] Construct the Lyapunov function as follows:

[0129] (31);

[0130] Its derivative is:

[0131] (32);

[0132] Substituting formula (27) and its derivative into formula (32), we get:

[0133] (33);

[0134] We can derive the following from formula (25):

[0135] (34);

[0136] For each positive gain matrix and ,because It is positive semidefinite, therefore Therefore Bounded, the system is stable and It will gradually subside.

[0137] Lyapunov Find the second derivative and derive it using formula (25):

[0138] (35);

[0139] because convergence, , For a given positive gain, and It is bounded, therefore we conclude It is bounded. According to Barbalat's lemma, when a function... (here The derivative of ) is bounded and When it exists, Therefore, it can be inferred that It will approach zero over time.

[0140] when As it approaches zero, we get:

[0141] (36);

[0142] We construct a new Lyapunov function to analyze the system stability. The new Lyapunov function is:

[0143] (37);

[0144] Ask about time Substituting the derivative of into formula (36), we get:

[0145] (38);

[0146] Due to gain The constraints of formulas (29) and (30) need to be satisfied, therefore we can conclude that... ,Right now ,therefore and It is bounded. Applying Barbalat's lemma again, we can prove that when... At that time, tracking error and It will converge to zero, which is the original output of the system. Approaching the target value .

[0147] Constructing a fast terminal sliding mode controller, specifically:

[0148] Based on the convergence methods of the first-stage and second-stage sliding surfaces, a new sliding surface is obtained by enhancing the reduced-order dynamics of the sliding surface while maintaining the sliding mode.

[0149] Adjust the gain matrix to make the driven and non-driven outputs converge toward the corresponding target values ​​on the new sliding surface within a steady time.

[0150] Based on the convergence method of the new sliding surface, a fast terminal sliding mode controller is constructed.

[0151] The robust controller employs fast terminal sliding mode control (LTVSC) technology, based on the finite-time stability principle, and designs a new sliding surface to control the system state. The control input consists of multiple parts, including feedback on the system's dynamic characteristics and compensation for external disturbances. By adjusting the relevant parameters and gain matrix of the new sliding surface, its finite-time convergence is proven using Lyapunov functions, enabling the system output to converge rapidly to the target value within a finite time. Furthermore, during convergence, the gain parameters are optimized and adjusted based on the relationship between the convergence time, the initial state of the new sliding surface, and the minimum value of the gain parameters, thereby improving the system's convergence performance.

[0152] For nonlinear systems If a Lyapunov function exists The following conditions must be met:

[0153] (39);

[0154] Then the system state It is exponentially stable, and the stable period is... Defined as:

[0155] (40);

[0156] By using formulas (26) and (27), a new sliding surface is obtained by enhancing the manifold order reduction dynamics while maintaining the sliding mode. :

[0157] (41);

[0158] in, It is a diagonal matrix with positive gain. It is to satisfy odd powers. In fact... It is a power-law stable at the terminal. It is a power that promotes the convergence speed.

[0159] Fast terminal sliding mode controller design through new sliding surface This is used to control the system state. Control input It consists of multiple parts, including feedback on the dynamic characteristics of the system (such as...). and ), and compensation for external disturbances (such as and The introduction of sliding mode control ensures the robustness of the system in the face of uncertainties and external disturbances. The structure of the fast termination sliding mode controller is as follows:

[0160] (42);

[0161] in, It's a new sliding surface. It is the gain matrix.

[0162] The convergence time and the new sliding surface initial state Gain parameters and minimum value and This is relevant. By adjusting these parameters, the convergence performance of the system can be optimized.

[0163] In gain Under the same constraints as a second-order sliding mode controller, a fast sliding mode controller can make the system output... During the stable period Converging to the target value Stabilization time for:

[0164] (43);

[0165] in, and These are the minimum values ​​of the gain. This is the initial state of the new sliding surface. for The transpose of .

[0166] The negative value of the Lyapunov derivative indicates a reduction in system energy, ensuring system stability. The negative contributions of each term (such as...) and Ensure the new sliding surface The convergence, and The terms are related to tracking error, ensuring that the system output can track the target.

[0167] Construct the Lyapunov function as follows:

[0168] (44);

[0169] The Lyapunov derivative is calculated as follows:

[0170] (45);

[0171] The first term of the Lyapunov derivative is:

[0172] (46);

[0173] in, , It is the smallest element of the gain matrix and is greater than zero. To meet odd powers, therefore the new sliding surface It converges exponentially over a finite time.

[0174] When the sliding surface approaches zero, the second term of the Lyapunov derivative is:

[0175] (47);

[0176] Therefore, tracking error and control input It exhibits convergence. Negative values ​​ensure that these errors decrease over time, thus allowing the system output to gradually approach the target value.

[0177] Barbalat's lemma provides a powerful tool for proving the stability of a system in infinite time. When At that time, tracking error and It will converge to zero, which is the original output of the system. Approaching the target value This ensures that the system not only converges within a finite time but also remains stable during long-term operation.

[0178] Step S3: Using the design of a state observer, the dynamic matrix form of the robotic arm is transformed into a state space form, and then the state observer is obtained. Subtracting the state observer from the state space form respectively, the dynamic equation of the estimation error is obtained.

[0179] The state-space form of the robotic arm dynamics can be obtained from formula (17) as follows:

[0180] (48);

[0181] (49);

[0182] in , .

[0183] The structure of the state observer is as follows:

[0184] (50);

[0185] (51);

[0186] in, and The state variable to be estimated, and its input is Its output is an approximation. and . and It is a positive gain. , It has boundaries of Element-wise saturation.

[0187] The approximation error can be defined as follows: By subtracting the state observer from the state-space form of the robotic arm dynamics described above, we can obtain the dynamic equation for the estimation error:

[0188] (52);

[0189] (53);

[0190] in, It is the positive definite mass matrix in the state-space form of the robot arm dynamics. yes The reverse, It is the matrix of equivalent vectors in the state-space form of the robotic arm dynamics. It is the damping matrix in the state-space form of the robotic arm dynamics. It is the matrix of the gravitational vector in the state-space form of the robotic arm dynamics. It is the matrix of the wind disturbance vector in the state-space form of the robotic arm dynamics.

[0191] Formulas (52) and (53) can be simplified to:

[0192] (54);

[0193] in:

[0194] (55);

[0195] (56);

[0196] (57);

[0197] in, and It is a positive gain matrix. It is a 5×5 identity matrix. It is a Herwitz matrix if and only if the real parts of all its eigenvalues ​​are less than zero. This means that the dynamic behavior of the system will be stable, and the solution of any initial state will tend to zero over time.

[0198] and It is a positive gain matrix. Since it is a Herwitz matrix, the linear part of the error dynamic equation will lead to errors. It decays exponentially over time; while It is bounded, satisfying The disturbance term does not cause the system to lose stability. This means that the state observer can effectively estimate the system state and remain stable in the face of disturbances.

[0199] To verify the beneficial effects of this embodiment, a comparative experiment was conducted for scientific demonstration.

[0200] To verify the beneficial effects, the simulation used a WSR-6-1500 robotic arm. In an open environment, the actual parameters show that the lifting robotic arm is affected by wind, which may reduce its stability and even cause structural deformation, or significant swinging of the boom and load. Therefore, the impact of wind on the lifting robotic arm must be considered. A simplified model of wind force is shown below:

[0201] (58);

[0202] Among them, wind power , and It acts on the bottom of the boom, the top of the boom, and the center of the load, respectively. It is the shape factor. This refers to the frontal area of ​​each component affected by wind. Taking into account changes in wind intensity and direction, a wind direction indicator has been added. and wind speed The change. According to FEM (Finite Element Method) and ISO 4320 standards, wind speed The corresponding dynamic wind pressure is .

[0203] Step S4: The dynamic state of the lifting robot arm is inferred using a state observer. Based on the dynamic equation of the estimation error corresponding to the dynamic state, the control mode of the robust controller is determined. Based on the robust controller, corresponding control signals are generated to control the lifting robot arm. Specifically:

[0204] Five measurement position signals of the lifting robot arm are acquired, and state estimation is performed using a state observer to obtain five state variables, namely five estimated velocity signals.

[0205] Determine whether the dynamic equations of the estimation errors corresponding to the five estimated velocity signals satisfy the exponential convergence condition, thereby determining the control mode of the robust controller;

[0206] Based on five estimated velocity signals and measured position signals, a robust controller with a deterministic control method is used to generate corresponding control signals to control the tilting and lifting robotic arm.

[0207] A state observer design is employed. In this control system, the system measures five position signals via sensors, which are then used as input to the observer. The observer processes this measurement data and, using its own structure and parameters, estimates five other unmeasured state variables based on a state-space model of the system dynamics. These are the estimated velocity signals corresponding to the five position signals. By calculating the error between the estimated and actual values, the error dynamic equation is analyzed to determine if it satisfies the exponential convergence condition. If not, an adaptive control strategy is used to adjust the observer's gain matrix, causing the linear part of the error dynamic equation to drive the error to decay exponentially over time. Furthermore, fault diagnosis and fault tolerance mechanisms are incorporated to ensure the observer maintains stable estimation performance even when faced with disturbances or sensor failures. Finally, the observer outputs approximate state variable estimates, which are fed back into the control system, providing data support for control decisions and helping the robust controller to more accurately adjust the control input, thus achieving precise control of the robotic arm.

[0208] Second-order sliding mode control and fast terminal sliding mode control both require position and velocity signals. The role of the state observer is to derive the velocity signal from the position signal, which saves on sensors and the derived signal is more robust to disturbances. The gain matrix is ​​used to adjust the error function to achieve convergence and ensure greater accuracy.

[0209] The impact of wind is typically considered static wind in standards, but in actual operation, changes in wind force, such as wind speed and direction, directly affect the stability and control accuracy of the robotic arm. To improve the accuracy of the wind force model, this paper introduces changes in wind direction and speed and integrates them into the wind force model, thereby more realistically reflecting actual wind conditions. The wind force effect is assumed to act on the robotic arm during a period of 12 to 16 seconds, and the wind disturbance effect is as follows: Figure 3 As shown, the simulation environment more closely resembles the actual operating conditions of a hydraulic unloading machine. The controller scheme proposed in this paper demonstrates excellent applicability and reliability in the simulation, proving that it can be effectively applied to the actual operation of the hydraulic unloading platform, maintaining high performance even in the presence of wind interference.

[0210] like Figure 4 , Figure 5 and Figure 6 As shown, under the control of the Dynamic Model Robust Controller (DMRC), the lifting, extension, and winch drum operations of the tilting plate can all accurately reach the predetermined target position. From Figure 4 It can be seen that the number of rotations of the robotic arm's winch drum converges from the initial state to the desired steady-state value: DMRC approximately 3.8s, PID 5.2s, and FTC 6.1s. Furthermore, the graph clearly shows that DMRC has a significantly slower adjustment speed during the convergence start-up phase. After being subjected to external disturbances, all three controllers are affected to varying degrees. The maximum vibration amplitudes for PID and FTC are 0.25rev and 0.23rev, respectively, while for DMRC it is 0.02rev. From... Figure 5 It can be seen that the boom elevation angle converges from the initial state to the desired steady-state value in approximately 3.4s for DMRC, 5.4s for PID, and 6.3s for FTC. Furthermore, the graph clearly shows that DMRC has a significantly slower adjustment speed during the convergence start-up phase. After being subjected to external disturbances, all three controllers are affected to varying degrees. The maximum amplitude of vibration for PID and FTC is 0.014rad and 0.013rad, respectively, while that for DMRC is 0.0015rad. Figure 7 It can be seen that the boom extension converges from the initial state to the desired steady-state value in approximately 3.2s for DMRC, 4.9s for PID, and 5.0s for FTC. Furthermore, the graph clearly shows that DMRC has a significantly slower adjustment speed during the convergence start-up phase. After being subjected to external disturbances, all three controllers are affected to varying degrees. The maximum vibration amplitude for PID and FTC is 0.15m, while that for DMRC is 0.0025m.

[0211] like Figure 7 , Figure 8 and Figure 9As shown, it is evident that after an external disturbance is introduced during the steady-state phase of the unloading machine, in order to maintain system stability, the control inputs of the three controllers—the torque of the hoisting drum, the force of the lifting hydraulic cylinder, and the force of the telescopic hydraulic cylinder—all exhibited a certain degree of vibration. From Figure 7 It can be seen that the maximum amplitude of the hoist drum's torque vibration under PID and FTC conditions is 1455 N·m and 2218 N·m, respectively, while that under DMRC is only 197 N·m. From... Figure 8 It can be seen that the maximum vibration amplitude of the lifting hydraulic cylinder force under PID and FTC is 225N and 213N respectively, while that under DMRC is only 32N. From Figure 9 It can be seen that the maximum vibration amplitude of the telescopic hydraulic cylinder under PID and FTC is 196N and 210N respectively, while that under DMRC is only 47N.

[0212] In summary, experiments demonstrate that under the control of the proposed Dynamic Model Robust Controller (DMRC), the hydraulic tipper can accurately reach the predetermined target position during lifting, extension, and winch drum operation. The effects of external disturbances and unknown flexibility-induced tipper oscillations are almost completely suppressed. Furthermore, under the same initial state of the hydraulic tipper, compared to the proportional-integral-derivative (PID) control method and the finite-time control (FTC) method, the DMRC significantly reduces the convergence time for tipper lifting, extension, and winch drum operation. Simultaneously, during the control adjustment phase of the unloading machine, the DMRC not only has the shortest convergence time but also the smallest adjustment acceleration in the initial control stage. This contributes to smoother control of the tipper's tilting angle and length, and effectively reduces strong vibrations caused by rapid changes. Moreover, after introducing external disturbances during the steady-state phase of the unloading machine, the control inputs of the three controllers—the torque of the winch drum, the lifting hydraulic cylinder force, and the extension hydraulic cylinder force—all exhibited a certain degree of vibration in order to maintain system stability. However, compared to PID and FTC, DMRC performs better in terms of vibration amplitude and vibration convergence speed, which helps to mitigate the impact of external disturbances and protect the system from damage.

[0213] Example 2

[0214] This embodiment provides a robust control system for a lifting robot arm, including:

[0215] The dynamics model construction module is configured to determine five nonlinear motion equations of the robotic arm dynamics through the Euler-Lagrange equations and represent them in matrix form to obtain the robotic arm dynamics matrix form. The robotic arm dynamics matrix form is divided into driven form and non-driven form, and after order reduction processing, the reduced order dynamics model of the robotic arm is obtained.

[0216] The robust controller building module is configured to build a second-order sliding mode controller and a fast termination sliding mode controller, which together form a robust controller;

[0217] The state observer construction module is configured to transform the dynamic matrix form of the robotic arm into the state space form, thereby obtaining the state observer. Subtracting the state observer from the state space form yields the dynamic equations for the estimation error.

[0218] The control module is configured to infer the dynamic state of the lifting robot arm using a state observer, determine the control mode of the robust controller based on the dynamic equation of the estimation error corresponding to the dynamic state, and generate corresponding control signals based on the robust controller to control the lifting robot arm.

[0219] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0220] The proposed system can be implemented in other ways. For example, the system embodiments described above are merely illustrative, and the division of modules described above is only a logical functional division. In actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed.

[0221] Example 3

[0222] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a robust control method for a lifting robot arm as described in Embodiment 1 above.

[0223] Example 4

[0224] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in a robust control method for a lifting robot arm as described in Embodiment 1 above.

[0225] Example 5

[0226] This embodiment provides a computer program product or computer program that includes computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the steps in the robust control method for a lifting robot arm described in Embodiment 1 above.

[0227] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A robust control method for a hoisting robotic arm, characterized in that, include: Five nonlinear motion equations for the robotic arm dynamics are determined by the Euler-Lagrange equations and expressed in matrix form to obtain the robotic arm dynamics matrix form. The robotic arm dynamics matrix form is divided into driven form and non-driven form. After order reduction processing, the reduced-order dynamics model of the robotic arm is obtained. A second-order sliding mode controller and a fast termination sliding mode controller are constructed respectively, and the two together form a robust controller; The dynamic matrix form of the robotic arm is transformed into the state space form, and then the state observer is obtained. The state observer is subtracted from the state space form to obtain the dynamic equation of the estimation error. The dynamic state of the lifting robot arm is inferred using a state observer. The control mode of the robust controller is determined based on the dynamic equation of the estimation error corresponding to the dynamic state. The corresponding control signal is generated based on the robust controller to control the lifting robot arm.

2. The robust control method for a lifting robot arm as described in claim 1, characterized in that, The five nonlinear motion equations of the robotic arm dynamics, determined by the Euler-Lagrange equations and expressed in matrix form, yield the matrix form of the robotic arm dynamics, specifically: Establish the Euler-Lagrange equations; Substitute the total kinetic energy, total potential energy, power dissipation caused by friction, and generalized force corresponding to the generalized coordinates of the robotic arm into the Euler-Lagrange equations. Five nonlinear motion equations for the robotic arm dynamics were obtained; Define the initial conditions for five generalized coordinates and their corresponding initial velocities; The five nonlinear motion equations are represented in matrix form to obtain the dynamic matrix form of the robotic arm.

3. A robust control method for a lifting robot arm as described in claim 1, characterized in that, Construct a second-order sliding mode controller, specifically as follows: Define the first-stage sliding surface, adjust the positive gain matrix, and use a power-law convergence method to make the driving output and non-driving output converge toward the corresponding target value on the first-stage sliding surface, asymptotically tracking the driving output and stabilizing the non-driving output. Define a second-stage sliding surface, combine the tracking error of the robotic arm control system, and adjust the gain matrix in real time according to the response of the robotic arm control system. Use linear convergence to make the driven output and non-driven output converge toward the corresponding target value on the second-stage sliding surface, asymptotically tracking the driven output and stabilizing the non-driven output. A second-order sliding mode controller is constructed based on the convergence of the first-stage sliding surface and the second-stage sliding surface.

4. A robust control method for a lifting robot arm as described in claim 1, characterized in that, Constructing a fast terminal sliding mode controller, specifically: Based on the convergence methods of the first-stage and second-stage sliding surfaces, a new sliding surface is obtained by enhancing the reduced-order dynamics of the sliding surface while maintaining the sliding mode. Adjust the gain matrix to make the driven and non-driven outputs converge toward the corresponding target values ​​on the new sliding surface within a steady time. Based on the convergence method of the new sliding surface, a fast terminal sliding mode controller is constructed.

5. A robust control method for a lifting robot arm as described in claim 1, characterized in that, The dynamic equation for the estimation error is as follows: ； ； in, It is the positive definite mass matrix in the state-space form of the robot arm dynamics. yes The reverse, It is the matrix of equivalent vectors in the state-space form of the robotic arm dynamics. It is the damping matrix in the state-space form of the robotic arm dynamics; , , Five raw outputs , This represents the number of original outputs; The rotation angle of the lifting motor for the effective load. For the mechanical rod around the bottom pivot The amplitude angle, The center of the two tubes and center The distance between them represents the relative motion between the flight segment and the base segment. The longitudinal oscillation of the effective load caused by the elasticity of the rope. For payload The swing angle, It is a positive gain. It is element-wise saturation.

6. A robust control method for a lifting robot arm as described in claim 1, characterized in that, The process involves using a state observer to determine the dynamic state of the lifting robot arm, determining the control mode of the robust controller based on the dynamic equation of the estimation error corresponding to the dynamic state, and generating corresponding control signals based on the robust controller to control the lifting robot arm. Specifically: Five measurement position signals of the lifting robot arm are acquired, and state estimation is performed using a state observer to obtain five state variables, namely five estimated velocity signals. Determine whether the dynamic equations of the estimation errors corresponding to the five estimated velocity signals satisfy the exponential convergence condition, thereby determining the control mode of the robust controller; Based on five estimated velocity signals and measured position signals, a robust controller with a deterministic control method is used to generate corresponding control signals to control the tilting and lifting robotic arm.

7. A robust control system for a lifting robot arm, characterized in that, include: The dynamics model construction module is configured to determine five nonlinear motion equations of the robotic arm dynamics through the Euler-Lagrange equations and represent them in matrix form to obtain the robotic arm dynamics matrix form. The robotic arm dynamics matrix form is divided into driven form and non-driven form, and after order reduction processing, the reduced-order dynamics model of the robotic arm is obtained. The robust controller building module is configured to build a second-order sliding mode controller and a fast termination sliding mode controller, which together form a robust controller; The state observer construction module is configured to transform the dynamic matrix form of the robotic arm into the state space form, thereby obtaining the state observer. Subtracting the state observer from the state space form yields the dynamic equations for the estimation error. The control module is configured to infer the dynamic state of the lifting robot arm using a state observer, determine the control mode of the robust controller based on the dynamic equation of the estimation error corresponding to the dynamic state, and generate corresponding control signals based on the robust controller to control the lifting robot arm.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in a robust control method for a lifting robot arm as described in any one of claims 1-6.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in a robust control method for a lifting robot arm as described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the steps of a robust control method for a lifting robot arm as described in any one of claims 1-6.

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