A position control method for a dual-flexible robot arm electromechanical coupling system

Abstract

The present application relates to a kind of double flexible mechanical arm electromechanical coupling system position control method, belong to the field of mechanical arm electromechanical coupling system control.The method includes: establishing double flexible mechanical arm electromechanical coupling system, based on the total kinetic energy of the system, total potential energy and damping dissipation energy are modeled, obtain double flexible mechanical arm dynamics model, and based on the uncertainty of double flexible mechanical arm parameter and external disturbance optimization;Design double closed-loop position control system, obtain double flexible mechanical arm electromechanical coupling position control system, and design LESO state observer and linear feedback controller, obtain position controller parameters and as input, to double flexible mechanical arm electromechanical coupling position control system is iteratively solved, according to the result of solving result setting position controller parameters, to realize the position control of double flexible mechanical arm electromechanical coupling system.The purpose is to solve the problem of double flexible mechanical arm electromechanical coupling system position control.

Description

Technical Field

[0001] This invention relates to a position control method for a dual flexible robotic arm electromechanical coupling system, belonging to the field of robotic arm electromechanical coupling system control. Background Technology

[0002] A space robotic arm consists of joints, a lever, and an end effector. The joint, as the core component, is crucial for generating and transmitting power, sensing position, and establishing mechanical connections. It is key to ensuring the robotic arm's motion capability, accuracy, smoothness, and safety. It mainly includes: a power source (usually a motor), a transmission device (usually a harmonic gear reducer), motion shafts, sensors (commonly position sensors and torque sensors), wiring harness management devices, and drive and data acquisition and processing circuits. It is a typical complex unit integrating mechanics, electronics, and control. Harmonic gear reducers are commonly used for the joint transmission because they offer advantages such as high transmission ratio, high load capacity, light weight, compact structure, and high efficiency, making them widely used in the transmission of space robotic arm joints. However, the presence of flexible elements within the harmonic reducer introduces significant flexibility into the joint, which greatly affects the accuracy of the space robotic arm and can lead to significant flexible vibrations. Meanwhile, due to the operating environment of the space robotic arm, which is characterized by vacuum, weightlessness, and large temperature differences, the space robotic arm is subject to external disturbances. In addition, during the operation of the space robotic arm, the stiffness and moment of inertia of the joints will change with the load and the movement of the joints, thus the dynamic parameters of the joints are uncertain.

[0003] Currently, permanent magnet synchronous motors are generally used as drive motors for robotic arms due to their advantages such as low loss, light weight, compact structure, high reliability, and high efficiency. Existing research generally treats the drive motor as an ideal torque source, rarely considering its dynamic characteristics. In practical applications, the ability of the drive motor to provide stable torque affects the position control accuracy of the robotic arm, especially under high speeds or large load variations. Ignoring the motor's dynamic characteristics can lead to a decline in the control performance of the robotic arm system. Therefore, considering the dynamic characteristics of the drive motor and designing high-performance control strategies for it is crucial for improving the control accuracy of the robotic arm system.

[0004] Active disturbance rejection technology (ADRC) has been developed for over two decades since its inception, and many scholars have explored various applications of ADRC in the field of motor control. An ADRC controller consists of three parts: a tracking differentiator, an extended state observer, and a nonlinear error feedback control law. Addressing the numerous nonlinear, strongly coupled, and uncertain disturbance problems encountered in practical engineering, ADRC offers a novel approach: it constructs a controlled object model using a simple cascaded integral canonical form, reducing dependence on model parameters; then, it uses a state observer to estimate concentrated disturbances and compensates for them with control inputs to counteract the impact of concentrated disturbances on the system, thus giving the system strong robustness against large-scale disturbances.

[0005] All three components of an active disturbance rejection control (ADRC) strategy are nonlinear, and all parameters are also nonlinear. The difficulty in parameter design limits its widespread application in engineering. Furthermore, the gain of the state observer is limited, and the performance of nonlinear ADRC may begin to degrade when the amplitude or gradient of the total disturbance increases to a certain extent. To address this problem, Gao Z. of Cleveland State University introduced bandwidth from classical control and first proposed a bandwidth-based parameter tuning strategy, simplifying parameter tuning and leading to the development of Linear ADRC (LADRC), which propelled the rapid development of ADRC theory. Scholars have systematically analyzed the control principle of ADRC, concisely explaining how parameters change system performance. Huang Yi et al. also explored the essence of ADRC, detailing the principles of the three components of the strategy.

[0006] In summary, although there are many existing ADRC control strategies for permanent magnet synchronous motors (PMSMs), the control structure needs to be designed specifically according to the specific model of the controlled object and actual needs. In addition, control strategies that maintain excellent nonlinear performance under linearization modules and improve the disturbance rejection of single motor control systems still need further research. Summary of the Invention

[0007] The purpose of this invention is to provide a position control method for a dual flexible manipulator electromechanical coupling system, aiming to fill the gap in the existing modeling and analysis of dual flexible manipulator electromechanical coupling systems and solve the problem of position control of dual flexible manipulator electromechanical coupling systems.

[0008] To achieve the above objectives, the technical solution of the present invention is: a position control method for a dual flexible robotic arm electromechanical coupling system, comprising the following steps: S1: Establish a dual flexible manipulator electromechanical coupling system, and model the dynamic model of the dual flexible manipulator based on the total kinetic energy, total potential energy and damping dissipation energy of the dual flexible manipulator electromechanical coupling system. S2: Optimize the dynamic model of the dual flexible manipulator based on the uncertainty of the parameters and external disturbances; S3: Design a dual closed-loop position control system for the optimized dynamic model of the dual flexible manipulator, resulting in an electromechanical coupling position control system for the dual flexible manipulator; wherein, the dual closed-loop position control system includes an inner loop position control system and an outer loop position control system, the inner loop position control system is used for motor position control, and the outer loop position control system is used for joint position control; S4: Design a LESO state observer and a linear feedback controller for the electromechanical coupling position control system of the dual flexible manipulator, obtain the position controller parameters, use the position controller parameters as input, iteratively solve the electromechanical coupling position control system of the dual flexible manipulator, and tune the position controller parameters according to the solution results to realize the position control of the electromechanical coupling system of the dual flexible manipulator.

[0009] Optionally, the dual flexible robotic arm electromechanical coupling system includes a servo motor, a flexible joint, a flexible robotic arm, and an end-effector load. The flexible joint is a harmonic reducer with flexible components and an elastic coupling. The end of the flexible robotic arm is equipped with a position sensor or is subject to a gripping operation, thereby forming an end-effector load.

[0010] Optionally, the total kinetic energy consists of three parts: the rotational kinetic energy of the motor and the robotic arm, the kinetic energy of the robotic arm itself, and the kinetic energy of the end-effector load, expressed as:

[0011] in, For total kinetic energy, This provides the kinetic energy for the rotation of the motor and the robotic arm. For the main body kinetic energy of the robotic arm, The kinetic energy of the end load. Let be the moment of inertia of the motor. The moment of inertia of the flexible robotic arm. For the motor rotation angle, For the robotic arm to turn, For the material density of the robotic arm, Let the cross-sectional area of ​​the robotic arm be , The length of the robotic arm. for coordinate axis point At the moment On the flexible robotic arm The lateral elastic deformation of a point, where... For when = Lateral elastic deformation at that time For end-load quality, .

[0012] Optionally, the total potential energy consists of the torsional potential energy of the joints, the elastic potential energy of the flexible robotic arm deformation, and the gravitational potential energy of the concentrated mass of the robotic arm and its end effector, expressed as:

[0013] in, For total potential energy, This represents the torsional potential energy of the joint. This represents the elastic potential energy generated by the deformation of the flexible robotic arm. This refers to the gravitational potential energy of the robotic arm and its concentrated end effector mass. For joint stiffness, For harmonic reducers, the reduction ratio is... It is the acceleration due to gravity. The Young's modulus of the material. Let be the moment of inertia of the cross section about the neutral axis.

[0014] Optionally, the expression for the damping dissipation energy is:

[0015] in, To dampen energy dissipation, and These are the viscous damping coefficients of the motor and the reducer, respectively.

[0016] Optionally, the obtained dynamic model of the dual flexible robotic arm is specifically as follows: By incorporating joint current information, an electromagnetic torque equation based on the joint current is established. Then, a coordinate transformation is performed to convert the inductance matrix into a diagonal matrix with constant coefficients, thereby transforming the time-varying coefficient differential equations into a system of constant coefficient differential equations. This yields two electromagnetic torque equations in a rotating coordinate system, expressed as follows:

[0017] in, For electromagnetic torque, The number of magnetic pole pairs For magnetic linkage, for shaft current, for d shaft current, for d Shaft inductance, for q Shaft inductance; Replacing the input torque of the dual flexible manipulator with the electromagnetic torque, and then substituting the total kinetic energy and the total potential energy into the Lagrange equation considering non-conservative forces, the dynamic model of the dual flexible manipulator considering motor characteristics is obtained as follows:

[0018] The other non-conservative forces include damping forces and electromagnetic torques.

[0019] Optionally, the optimization of the dynamic model of the dual flexible manipulator based on the uncertainty of the parameters and external disturbances specifically involves: definition The uncertainty of the rotational inertia of the flexible joint; External disturbances to flexible joints; The uncertainty of the motor's moment of inertia; Considering the external disturbance to the motor, the optimized dynamic model of the dual flexible robotic arm is as follows:

[0020] Among them, the definition The total disturbance of the flexible joint portion; The control quantity for flexible joint position control; To control the amount Gain; To The estimate; The total disturbance of the motor section; This is the control quantity for motor position control; To control the amount Gain; To The estimate.

[0021] Optionally, the design of the dual closed-loop position control system for the optimized dual flexible manipulator dynamics model specifically involves: Based on the position of the robotic arm joints For the output of the robotic arm position loop, the motor rotation angle This is the control input for the robotic arm's position loop, and also the reference input for the motor's position loop; motor rotation angle. For the output of the motor position loop, the motor's shaft current It serves as the control input for the motor position loop and also as the reference input for the current loop; the motor's , shaft current , For the output of the motor current loop, the motor's d , q shaft voltage , The control quantity for the motor current loop is used to design a dual closed-loop position control system for the optimized dual flexible manipulator dynamic model, resulting in a dual flexible manipulator electromechanical coupling position control system. The dual closed-loop position control system includes an inner loop position control system and an outer loop position control system. The inner loop position control system is used for motor position control, and the outer loop position control system is used for joint position control.

[0022] Optionally, the position controller parameters are specifically: Bandwidth parameters of LESO state observer and and the bandwidth parameters of the linear feedback controller and ;in, and These are the parameters for the motor. and These are the parameters for the joint.

[0023] The beneficial effects of this invention are as follows: This invention establishes a dual flexible robotic arm electromechanical coupling system based on a comprehensive consideration of the vibration characteristics of the robotic arm, the characteristics of the joint motor, and the influence of gravity. Based on the input and output of the system, a control method based on linear active disturbance rejection is proposed, which reduces the system positioning time and suppresses the elastic vibration of the robotic arm end. Attached Figure Description

[0024] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0025] Figure 1 This is a flowchart of the steps of the present invention; Figure 2 This is a schematic diagram of the dynamic model of the dual flexible robotic arm of the present invention; Figure 3 This invention provides a virtual simulation platform for the electromechanical coupling system of a dual flexible robotic arm. Figure 4 The output speed waveforms of the AC permanent magnet synchronous motor under different voltage frequencies are shown in the figure. Figure 5 The present invention describes the changes in elastic vibration at the end of a flexible robotic arm when given different three-phase stator voltage frequencies of an AC permanent magnet synchronous motor. Figure 6 Figure showing the effect of gravity on electromagnetic torque and end-effector vibration in this invention. Figure 7 This is a block diagram of the dual-position feedback control structure of the present invention; Figure 8 This is the MATLAB / Simulink simulation model of the motor position loop of this invention; Figure 9 This is a MATLAB / Simulink simulation model of the joint position ring of the present invention; Figure 10 The curves showing the comparison between the electromechanical coupling position control system of the dual flexible robotic arm of this invention and the joint angle position without control are shown. Figure 11 The figures show a comparison curve of the electromechanical coupling position control system of the dual flexible robotic arm of the present invention and the elastic vibration of the end effector of the robotic arm when there is no control. Detailed Implementation

[0026] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0027] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0028] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms describing positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. Those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances. The present invention will now be described in detail with reference to the accompanying drawings and examples.

[0029] Example 1: As Figure 1 As shown, a position control method for a dual flexible robotic arm electromechanical coupling system includes the following steps: S1: Establish a dual flexible manipulator electromechanical coupling system, and model the dynamic model of the dual flexible manipulator based on the total kinetic energy, total potential energy and damping dissipation energy of the dual flexible manipulator electromechanical coupling system. Optionally, a simplified model diagram of the dual flexible robotic arm electromechanical coupling system is shown below. Figure 2 As shown, it includes a servo motor, a flexible joint, a flexible robotic arm, and an end-effector load. The flexible joint is a harmonic reducer with flexible components and an elastic coupling. The end of the flexible robotic arm is equipped with a position sensor or performs a gripping operation, thereby forming an end-effector load. In this embodiment, the flexible joint is simplified to a torsion spring with a certain torsional stiffness.

[0030] Specifically, such as Figure 2 As shown, For a fixed coordinate system, Let be the rotating coordinate system fixed to the robotic arm system. Due to the strong coupling and nonlinear dynamic characteristics of the dual flexible robotic arm electromechanical coupling system, its direct solution is extremely difficult. Therefore, this embodiment uses the assumed modal method to discretize the partial differential equations of the flexible robotic arm.

[0031] Furthermore, considering the working environment and functional implementation of the flexible robotic arm, this embodiment simplifies the flexible robotic arm into a cantilever beam, i.e., an Euler beam, for modeling and analysis. Before modeling, the following assumptions are made (Euler-Bernoulli beam assumption): (1) Ignore the axial deformation, torsional deformation and shear deformation that occur when the connecting rod is under force, and only calculate the transverse elastic deformation; (2) The length of the flexible arm is much larger than its cross-sectional area; (3) The mass added at the end is negligible in size and can be regarded as a point mass; (4) The radius of the drive motor shaft is negligible.

[0032] Based on the hypothetical modal method theory, the modal shape function and natural frequencies of the flexible robotic arm need to be calculated first. The derivation process is as follows: definition For any point on the axis of the cantilever beam, the mathematical expression for the lateral displacement of the cantilever beam can be obtained according to the principle of bending vibration:

[0033] in, for coordinate axis point At the moment On the flexible robotic arm Lateral elastic deformation of a point For the material density of the robotic arm, Let the cross-sectional area of ​​the robotic arm be , The Young's modulus of the material. Let be the moment of inertia of the cross section about the neutral axis; Furthermore, by solving the vibration equation, the mode shape function can be obtained. For the cantilever beam considering the end mass in this embodiment, the boundary conditions are as follows:

[0034] in, The bending moment at the free end of the cantilever beam. for coordinate axis point At the moment On the flexible robotic arm Lateral elastic deformation of a point Considering the end-load mass and the above boundary conditions, we can further derive the natural frequencies and mode shapes of the cantilever beam taking into account the end-load mass:

[0035]

[0036] in, is an undetermined constant. The mass of the cantilever beam is the mass of the robotic arm itself. For the cantilever beam First natural frequency, It is the first of the transcendental equations. A true root.

[0037] Furthermore, based on the orthogonality of the mode shape functions, we can obtain:

[0038] in, The length of the robotic arm; Furthermore, the final expression for the lateral elastic deformation of the flexible robotic arm is as follows:

[0039] in, These are modal coordinates.

[0040] Furthermore, based on the obtained Specifically, the electromechanical coupling system of the dual flexible robotic arm is modeled, wherein the total kinetic energy consists of three parts: the rotational kinetic energy of the motor and the robotic arm, the kinetic energy of the robotic arm itself, and the kinetic energy of the end effector load. The expression is as follows:

[0041] in, For total kinetic energy, This provides the kinetic energy for the rotation of the motor and the robotic arm. For the main body kinetic energy of the robotic arm, The kinetic energy of the end load. Let be the moment of inertia of the motor. The moment of inertia of the flexible robotic arm. For the motor rotation angle, For the robotic arm to turn, .

[0042] It is important to understand that, unlike traditional robotic arm modeling, this embodiment focuses on the influence of gravity and motor characteristics on the vibration characteristics of the flexible robotic arm. Since the robotic arm moves in a vertical plane, with the vertical plane perpendicular to the ground as the zero potential energy level, the total potential energy described in this embodiment consists of the torsional potential energy of the joints, the elastic potential energy of the flexible robotic arm deformation, and the gravitational potential energy of the concentrated mass at the end effector of the robotic arm. The expression is as follows:

[0043] in, For total potential energy, This represents the torsional potential energy of the joint. This represents the elastic potential energy generated by the deformation of the flexible robotic arm. This refers to the gravitational potential energy of the robotic arm and its concentrated end effector mass. For joint stiffness, For harmonic reducers, the reduction ratio is... This is the acceleration due to gravity.

[0044] It should be understood that flexible robotic arms inevitably experience damping effects. Therefore, this embodiment considers the damping energy dissipation characteristics of the motor drive system, and the expression for the damping dissipation energy is obtained as follows:

[0045] in, To dampen energy dissipation, and These are the viscous damping coefficients of the motor and the reducer, respectively.

[0046] Optionally, the obtained dynamic model of the dual flexible robotic arm is specifically as follows: By incorporating joint current information, an electromagnetic torque equation based on the joint current is established. Then, a coordinate transformation is performed to convert the inductance matrix into a diagonal matrix with constant coefficients, thereby transforming the time-varying coefficient differential equations into a system of constant coefficient differential equations. This yields two electromagnetic torque equations in a rotating coordinate system, expressed as follows:

[0047] in, For electromagnetic torque, The number of magnetic pole pairs For magnetic linkage, for shaft current, ford shaft current, for d Shaft inductance, for q Shaft inductance; Furthermore, the equations of the robotic arm and the motor are connected by direct electromagnetic torque coupling, that is, the electromagnetic torque replaces the input torque of the dual flexible robotic arm. Then, the total kinetic energy and the total potential energy are substituted into the Lagrange equation considering non-conservative forces to obtain the dynamic model of the dual flexible robotic arm considering the motor characteristics as follows:

[0048] The other non-conservative forces include damping forces and electromagnetic torques.

[0049] Understandably, in order to accurately describe the state of a permanent magnet synchronous motor, its mathematical model must include voltage equations, flux linkage equations, torque equations, and motion equations. Therefore, this embodiment utilizes coordinate transformation to convert the inductance matrix into a diagonal matrix with constant coefficients. The inductance matrix after coordinate transformation is a diagonal matrix with constant coefficients, and the original complex set of time-varying coefficient differential equations is transformed into a set of constant coefficient differential equations that are easy to solve.

[0050] Optionally, in this embodiment, epoxy resin composite material is selected as the material for the flexible robotic arm for numerical calculation. The simulation parameters of the electromechanical coupling system of the dual flexible robotic arm are shown in Table 1.

[0051] Table 1. Some simulation parameters of the electromechanical coupling system of the dual flexible robotic arm

[0052] Furthermore, this embodiment also verifies the correctness of the established dual flexible robotic arm electromechanical coupling system by building a simulation experimental platform: S100: The simulation platform for the electromechanical coupling system of the dual flexible robotic arm adopts a modeling method that combines modules and programming. In this embodiment, the simulation platform for the electromechanical coupling system of the dual flexible robotic arm is built in MATLAB / Simulink.

[0053] S200: such as Figure 3 As shown, the simulation system includes a voltage generator module, a forward coordinate transformation module, a motor module, an inverse coordinate transformation module, and a dual flexible robotic arm module.

[0054] S300: The specific calculation process of this simulation platform is as follows: First, the output speed and output torque of the motor are calculated based on the given three-phase stator voltage. Then, the results are transmitted to the dual flexible robotic arm system to quantitatively calculate the dynamic characteristics and output characteristics of the dual flexible robotic arm under direct electromagnetic torque coupling.

[0055] S400: Based on the synchronous motor speed calculation formula ,in This refers to the stator voltage frequency of an AC permanent magnet synchronous motor. Given different stator voltage frequencies for the three phases of an AC permanent magnet synchronous motor, the corresponding motor speed can be determined. For example... Figure 4 As shown, when the given three-phase stator voltage frequencies are 5 Hz, 10 Hz, and 15 Hz, the motor speeds output by the dual flexible robotic arm electromechanical coupling system established in this invention are 75 r / min, 150 r / min, and 225 r / min, respectively, which are consistent with the calculation results of the theoretical formula, thus verifying the correctness of the model established in this invention.

[0056] S500: In the past, the analysis of robotic arm vibration problems only considered the influence of parameters such as robotic arm length and end-effector load on the vibration characteristics of the robotic arm end, without considering the influence of motor characteristics and gravity on the system vibration characteristics. This embodiment will build a virtual simulation experimental platform for a flexible manipulator system based on the derived theoretical formulas and conduct numerical example analysis.

[0057] S600: Building upon S400, this further considers different three-phase stator voltage frequencies to analyze the impact of non-smooth motor startup on the elastic vibration of the robotic arm's end effector at different target speeds. For example... Figure 5 As shown in the figure, this embodiment analyzes the changes in the elastic vibration of the flexible robotic arm end during the non-smooth transition process of the motor startup stage when the three-phase stator voltage frequencies of the AC permanent magnet synchronous motor are 5Hz, 10Hz and 15Hz, respectively, at different target speeds. According to the results, considering the non-smooth start of the motor, the amplitude of the elastic vibration of the robotic arm end will increase by 5-6mm. Therefore, for applications with high positioning accuracy requirements, the influence of the non-smooth start of the motor cannot be ignored.

[0058] S700: such as Figure 6 It can be seen that when the influence of gravity is considered, the output electromagnetic torque and end elastic vibration will exhibit periodic fluctuations to overcome the influence of gravity, and the fluctuation amplitude is consistent with the magnitude of gravity.

[0059] S2: Optimize the dynamic model of the dual flexible manipulator based on the uncertainty of the parameters and external disturbances; Optionally, the optimization of the dynamic model of the dual flexible manipulator based on the uncertainty of the parameters and external disturbances specifically involves: definition The uncertainty of the rotational inertia of the flexible joint; External disturbances to flexible joints; The uncertainty of the motor's moment of inertia; Considering the external disturbance to the motor, the optimized dynamic model of the dual flexible robotic arm is as follows:

[0060] Among them, the definition The total disturbance of the flexible joint portion; The control quantity for flexible joint position control; To control the amount Gain; To The estimate; The total disturbance of the motor section; This is the control quantity for motor position control; To control the amount Gain; To The estimate.

[0061] S3: Design a dual closed-loop position control system for the optimized dynamic model of the dual flexible manipulator, resulting in an electromechanical coupling position control system for the dual flexible manipulator; wherein, the dual closed-loop position control system includes an inner loop position control system and an outer loop position control system, the inner loop position control system is used for motor position control, and the outer loop position control system is used for joint position control; Optionally, such as Figure 7 The feedback control structure block diagram is shown, based on the position of the robotic arm joints. For the output of the robotic arm position loop, the motor rotation angle This is the control input for the robotic arm's position loop, and also the reference input for the motor's position loop; motor rotation angle. For the output of the motor position loop, the motor's shaft current It serves as the control input for the motor position loop and also as the reference input for the current loop; the motor's , shaft current , For the output of the motor current loop, the motor's d , q shaft voltage , The control quantity for the motor current loop is used to design a dual closed-loop position control system for the optimized dual flexible manipulator dynamic model, resulting in a dual flexible manipulator electromechanical coupling position control system. The dual closed-loop position control system includes an inner loop position control system and an outer loop position control system. The inner loop position control system is used for motor position control, and the outer loop position control system is used for joint position control.

[0062] S4: Design a LESO state observer and a linear feedback controller for the electromechanical coupling position control system of the dual flexible manipulator, obtain the position controller parameters, use the position controller parameters as input, iteratively solve the electromechanical coupling position control system of the dual flexible manipulator, and tune the position controller parameters according to the solution results to realize the position control of the electromechanical coupling system of the dual flexible manipulator.

[0063] Optionally, the position controller parameters are specifically the bandwidth parameters of the LESO state observer. and and the bandwidth parameters of the linear feedback controller and ;in, and These are some parameters for the motor. and These are parameters for the joint.

[0064] Furthermore, in this embodiment, a position controller module is built in the Matlab / Simulink simulation platform, as follows: Figures 8-9 As shown, it mainly includes a linear feedback control module (PD controller, disturbance compensation), LESO, coordinate transformation module, PMSM module, detection module, etc. The position controller module is connected to the motor and robotic arm modules through various inputs and outputs, forming an electromechanical coupled dual closed-loop position control system for the robotic arm.

[0065] Furthermore, the position controller parameters are input, and the electromechanical coupling position control system of the dual flexible robotic arm is iteratively solved in the simulation platform. The iterative process involves first estimating the disturbance and calculating the control quantity based on the current state of the electromechanical coupling system using the controller, then updating the state of the electromechanical coupling system based on the control quantity using the Simulink built-in solver, and repeating this process until the simulation ends. In this embodiment, the specific simulation parameters for the LADRC-based position control system are as follows: , , , Enable the system to track A step signal in rad.

[0066] Furthermore, such as Figure 10 As shown, under the LADRC controller, the robotic arm can achieve the expected angle, thus proving the effectiveness of the controller. Compared to the angular position curve without control, this invention enables the motor angular position to be positioned more quickly, smoothly, and accurately.

[0067] Furthermore, such as Figure 11As shown, under the LADRC controller, the elastic position of the robotic arm's end effector is greatly reduced, effectively suppressing the elastic vibration of the robotic arm's end effector. This demonstrates that the position control method for the dual flexible robotic arm electromechanical coupling system proposed in this invention not only enables precise system positioning but also suppresses the elastic vibration of the robotic arm's end effector.

[0068] It is understandable that this embodiment uses S1-S4 to comprehensively consider the vibration characteristics of the robotic arm, the dynamics of the joint motor, and the influence of gravity to accurately model the robotic arm. It considers the input and output of the system and designs a dual closed-loop position controller based on the linear active disturbance rejection control method. The controller parameters are tuned to obtain a more accurate electromechanical coupling model of the dual flexible robotic arm and a control model with faster positioning and less residual vibration at the end compared to the traditional robotic arm model.

[0069] In summary, this invention addresses the issue of dual flexible robotic arms by comprehensively considering their vibration characteristics and joint motor dynamics to achieve joint modeling of both. Furthermore, it considers the influence of gravity on the flexible robotic arm, filling the current gap in modeling and simulation analysis of electromechanical coupling systems for dual flexible robotic arms. Based on a linear active disturbance rejection control method, a dual-closed-loop position controller is designed considering the system's input and output, achieving precise position control of the electromechanical coupling system of the flexible robotic arm. Optimization of the controller parameters improves the system's positioning speed and effectively suppresses residual vibration at the robotic arm's end effector, thus solving the problem of position control in electromechanical coupling systems for dual flexible robotic arms.

[0070] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A position control method for a dual flexible robotic arm electromechanical coupling system, characterized in that, The method includes the following steps: S1: Establish a dual flexible manipulator electromechanical coupling system, and model the dynamic model of the dual flexible manipulator based on the total kinetic energy, total potential energy and damping dissipation energy of the dual flexible manipulator electromechanical coupling system. S2: Optimize the dynamic model of the dual flexible manipulator based on the uncertainty of the parameters and external disturbances; S3: Design a dual closed-loop position control system for the optimized dynamic model of the dual flexible manipulator, resulting in an electromechanical coupling position control system for the dual flexible manipulator; wherein, the dual closed-loop position control system includes an inner loop position control system and an outer loop position control system, the inner loop position control system is used for motor position control, and the outer loop position control system is used for joint position control; S4: Design a LESO state observer and a linear feedback controller for the electromechanical coupling position control system of the dual flexible manipulator, obtain the position controller parameters, use the position controller parameters as input, iteratively solve the electromechanical coupling position control system of the dual flexible manipulator, and tune the position controller parameters according to the solution results to realize the position control of the electromechanical coupling system of the dual flexible manipulator. The optimization of the dynamic model of the dual flexible manipulator based on the uncertainty of the parameters and external disturbances is specifically as follows: definition The uncertainty of the rotational inertia of the flexible joint; External disturbances to flexible joints; The uncertainty of the motor's moment of inertia; Considering the external disturbance to the motor, the optimized dynamic model of the dual flexible robotic arm is as follows: ； Among them, the definition The total disturbance of the flexible joint portion; The control quantity for flexible joint position control; To control the amount Gain; To The estimate; The total disturbance of the motor section; This is the control quantity for motor position control; To control the amount Gain; To The estimate; Let be the moment of inertia of the motor. The moment of inertia of the flexible robotic arm. For the motor rotation angle, For the robotic arm to turn, For end-load quality, The length of the robotic arm. For joint stiffness, For the reduction ratio of the harmonic reducer, It is the acceleration due to gravity. and These are the viscous damping coefficients of the motor and the reducer, respectively. The number of magnetic pole pairs For magnetic linkage, for Axis current.

2. The position control method for a dual flexible robotic arm electromechanical coupling system according to claim 1, characterized in that, The dual flexible robotic arm electromechanical coupling system includes a servo motor, a flexible joint, a flexible robotic arm, and an end-effector load. The flexible joint is a harmonic reducer with flexible components and an elastic coupling. The end of the flexible robotic arm is equipped with a position sensor or is subject to a gripping operation, thereby forming an end-effector load.

3. The position control method for a dual flexible robotic arm electromechanical coupling system according to claim 2, characterized in that, The total kinetic energy consists of three parts: the rotational kinetic energy of the motor and robotic arm, the kinetic energy of the robotic arm itself, and the kinetic energy of the end-effector load. The expression is as follows: ； in, For total kinetic energy, This provides the kinetic energy for the rotation of the motor and the robotic arm. For the main body kinetic energy of the robotic arm, The kinetic energy of the end load. For the material density of the robotic arm, Let the cross-sectional area of ​​the robotic arm be , for coordinate axis point At the moment On the flexible robotic arm The lateral elastic deformation of a point, where... For when = Lateral elastic deformation at that time .

4. The position control method for a dual flexible robotic arm electromechanical coupling system according to claim 3, characterized in that, The total potential energy consists of the torsional potential energy of the joints, the elastic potential energy of the flexible robotic arm deformation, and the gravitational potential energy of the robotic arm and the concentrated mass at the end effector, expressed as: ； in, For total potential energy, This represents the torsional potential energy of the joint. This represents the elastic potential energy generated by the deformation of the flexible robotic arm. This refers to the gravitational potential energy of the robotic arm and its concentrated end effector mass. The Young's modulus of the material. Let be the moment of inertia of the cross section about the neutral axis.

5. The position control method for a dual flexible robotic arm electromechanical coupling system according to claim 4, characterized in that, The expression for the damping dissipation energy is: ； in, This is to dampen and dissipate energy.

6. The position control method for a dual flexible robotic arm electromechanical coupling system according to claim 5, characterized in that, The obtained dynamic model of the dual flexible robotic arm is specifically as follows: By incorporating joint current information, an electromagnetic torque equation based on the joint current is established. Then, a coordinate transformation is performed to convert the inductance matrix into a diagonal matrix with constant coefficients, thereby transforming the time-varying coefficient differential equations into a system of constant coefficient differential equations. This yields two electromagnetic torque equations in a rotating coordinate system, expressed as follows: ； in, For electromagnetic torque, for d shaft current, for d Shaft inductance, for q Shaft inductance; Replacing the input torque of the dual flexible manipulator with the electromagnetic torque, and then substituting the total kinetic energy and the total potential energy into the Lagrange equation considering non-conservative forces, the dynamic model of the dual flexible manipulator considering motor characteristics is obtained as follows: ； Other non-conservative forces include damping forces and electromagnetic torques.

7. The position control method for a dual flexible robotic arm electromechanical coupling system according to claim 6, characterized in that, The design of the dual closed-loop position control system based on the optimized dynamic model of the dual flexible robotic arm is as follows: Based on the position of the robotic arm joints For the output of the robotic arm position loop, the motor rotation angle This is the control input for the robotic arm's position loop, and also the reference input for the motor's position loop; motor rotation angle. For the output of the motor position loop, the motor's shaft current It serves as the control input for the motor position loop and also as the reference input for the current loop; the motor's , shaft current , For the output of the motor current loop, the motor's d , q shaft voltage , The control quantity for the motor current loop is used to design a dual closed-loop position control system for the optimized dual flexible manipulator dynamic model, resulting in a dual flexible manipulator electromechanical coupling position control system. The dual closed-loop position control system includes an inner loop position control system and an outer loop position control system. The inner loop position control system is used for motor position control, and the outer loop position control system is used for joint position control.

8. The position control method for a dual flexible robotic arm electromechanical coupling system according to claim 7, characterized in that, The specific parameters of the position controller are as follows: Bandwidth parameters of LESO state observer and and the bandwidth parameters of the linear feedback controller and ;in, and These are the parameters for the motor. and These are the parameters for the joint.

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