Double-closed-loop active-disturbance-rejection control system and method for flexible joint mechanical arm

Abstract

The invention discloses a double-closed-loop active disturbance rejection control system and method for a flexible joint mechanical arm. In order to solve the problems of endpoint jitter, poor anti-interference capability and the like of a flexible joint mechanical arm under traditional PID control, a double-closed-loop active-disturbance-rejection controller composed of a tracking differentiator, a nonlinear state error feedback law and an expansion state observer is designed by establishing a mathematical model of a permanent magnet synchronous motor and a flexible joint; wherein the expansion state observer can estimate and compensate the total disturbance inside and outside the system in real time, and linearizes a complex nonlinear system, so that the endpoint jitter of the mechanical arm is effectively inhibited, and the trajectory tracking precision, the dynamic response speed and the robustness to parameter change and external disturbance of the system are remarkably improved; the control performance of the flexible joint mechanical arm is verified through Simulink simulation, and an effective solution is provided for high-precision control of the flexible joint mechanical arm.

Description

Technical Field

[0001] This invention relates to the field of robotic arm control technology, and in particular to a dual closed-loop active disturbance rejection control system and method for a flexible joint robotic arm. Background Technology

[0002] Flexible joint robotic arms, as key actuators in the field of robotics, are widely used in high-precision fields such as aerospace, precision assembly, and medical surgery due to their advantages such as light weight, low energy consumption, and high load-to-weight ratio. However, the flexibility of the joints (usually due to the elastic deformation of components such as harmonic reducers and long drive shafts) also makes the system a typical underactuated, strongly coupled nonlinear system, which poses a severe challenge to high-precision control. Currently, in both industry and academia, proportional-integral-derivative (PID) control and its variants remain the most widely used control methods for flexible joint robotic arms due to their simple structure and ease of engineering implementation. However, PID control exhibits several significant limitations when dealing with the inherently complex dynamic characteristics of flexible joint systems: Insufficient end-effector jitter and vibration suppression: PID controllers are essentially linear controllers, and their control performance heavily relies on the precise linear model of the controlled object. For nonlinear dynamics such as mechanical resonance and elastic vibration present in flexible joint systems, linear PID controllers struggle to effectively suppress them. This often leads to persistent and difficult-to-eliminate jitter in the robotic arm's end effector, severely impacting positioning accuracy and operational stability. Poor robustness to model uncertainties and internal / external disturbances: In practical applications, the system parameters of flexible joint robotic arms (such as load inertia, joint stiffness, damping coefficient, etc.) may change, and they are also subject to external disturbances from the motor side and the load side (such as frictional torque, load changes, etc.). PID controllers lack real-time estimation and compensation mechanisms for such "total disturbances" (including unmodeled dynamics and external disturbances), resulting in a significant decrease in control performance or even instability when parameters change or disturbances are present. The trade-off between dynamic performance and overshoot: To improve the system's response speed, it is usually necessary to increase the control gain of the PID controller. However, this can exacerbate the system's overshoot and may induce vibrations in the flexible mode, leading to a longer settling time. This trade-off between response speed and overshoot / vibration suppression makes PID controller parameter tuning difficult, and it is hard to achieve ideal control results under various operating conditions. To overcome the aforementioned shortcomings of PID control, researchers have explored advanced control methods such as adaptive control and sliding mode variable structure control. While these methods have improved the ability to handle nonlinearity and uncertainty to some extent, they often require accurate system models, suffer from chattering problems, and have complex controller structures and high computational demands, making their application and implementation in practical engineering challenging. Active Disturbance Rejection Control (ADRC), a novel control technique that does not rely on an exact model, utilizes its unique Extended State Observer (ESO) to estimate and compensate for the "total disturbance" of all uncertainties in a system in real time. This transforms complex nonlinear uncertain systems into standard integrator-cascaded systems, enabling robust control with simple control laws. This characteristic gives it great potential in handling systems with internal and external disturbances and strong nonlinearities, such as flexible articulated robotic arms. Therefore, this patent is based on active disturbance rejection control theory and aims to propose a dual closed-loop active disturbance rejection controller specifically for flexible joint robotic arms to effectively suppress endpoint jitter and improve the robustness and dynamic control performance of the system when facing model uncertainties and external disturbances. Summary of the Invention

[0003] The main objective of this invention is to provide a dual closed-loop self-disturbance rejection control system and method for a flexible joint robotic arm, aiming to solve existing technical problems.

[0004] To achieve the above objectives, the present invention provides a dual closed-loop active disturbance rejection control system for a flexible joint robotic arm, comprising: The permanent magnet synchronous motor model module is used to describe the dynamic behavior of the motor; Flexible joint robotic arm model module, used to describe the flexible joint dynamics of the robotic arm; A dual-loop active disturbance rejection controller, comprising inner-loop current control and outer-loop position control; Tracking differentiator, nonlinear state error feedback law, extended state observer module; The parameter tuning module is used to optimize controller parameters; The simulation verification module is used to verify the performance of the control system in the Matlab / Simulink environment.

[0005] Furthermore, the permanent magnet synchronous motor model is established based on the dq axis coordinate system, and its stator voltage equation is:

[0006]

[0007] Where ud, uq are stator voltages; id, iq are stator currents; ψd, ψq are flux linkages; Rs is stator resistance; and ωr is rotor angular velocity.

[0008] Furthermore, the flexible joint robotic arm model satisfies the following dynamic equations:

[0009] in, This represents the axial displacement output by the joint. This represents the shaft displacement of the permanent magnet synchronous motor. For load inertia, Here, N is the special coefficient for the rotational spring, and N is the hysteresis ratio. Obstacles from the system it carries. The drag ratio of a permanent magnet synchronous motor. The torque that makes the motor rotate. The system disturbance carried by the circuit. This represents the uncertainty term for the permanent magnet synchronous motor.

[0010] Furthermore, the active disturbance rejection controller includes: A tracking differentiator is used to schedule the transition process and extract the differential signal; Nonlinear state error feedback law is used to combine error signals and generate control quantities; An extended state observer is used to estimate the total system disturbance and perform feedforward compensation.

[0011] Furthermore, the extended state observer treats both internal system dynamics and external disturbances as a total disturbance and achieves disturbance rejection control through real-time estimation and compensation.

[0012] Furthermore, the parameter tuning module determines the optimal parameters of each module in the active disturbance rejection controller through simulation optimization methods, including the velocity factor of the tracking differentiator, the weighting coefficient of the nonlinear combination, and the bandwidth of the extended state observer.

[0013] A method for active disturbance rejection control of a flexible joint robotic arm includes the following steps: Establish a mathematical model of a permanent magnet synchronous motor and a flexible joint robotic arm; Design a dual-closed-loop active disturbance rejection controller structure; Configure a tracking differentiator, a nonlinear combination, and an extended state observer; Perform controller parameter tuning and simulation verification; Build a system model and perform performance tests in the Simulink environment.

[0014] Furthermore, the simulation verification includes building a system simulation model in the Matlab / Simulink environment and comparing the performance differences between PID control and active disturbance rejection control in terms of endpoint jitter, response speed and disturbance rejection capability.

[0015] A hardware and software platform for implementing the above system includes: The computer equipment is configured with an Intel Core i5-9300HF processor, 16GB of memory, and a GTX 1660 Ti graphics card; The software environment includes SOLIDWORKS 2023, Matlab 2017b, PyCharm Community Edition 2022.2.3, Visio 2013, Origin 2018 64Bit, and LTspice; Among them, SOLIDWORKS is used for mechanical structure modeling, Matlab / Simulink is used for control system simulation, PyCharm is used for data processing, Visio is used for flowchart drawing, Origin is used for data visualization, and LTspice is used for circuit simulation.

[0016] The beneficial effects of this invention are reflected in: Effectively suppressing end-point jitter and mechanical vibration, significantly improving trajectory tracking accuracy: This invention utilizes an extended state observer (ESO) to treat complex nonlinear factors such as mechanical resonance caused by flexible joints and unmodeled dynamics as a unified "total disturbance," and performs real-time estimation and compensation. This feedforward compensation mechanism fundamentally eliminates the intrinsic factors causing jitter, resulting in smoother and more stable motion of the robotic arm's end effector. Compared to PID control, this invention can significantly reduce or even eliminate persistent end-point jitter, thereby achieving higher-precision trajectory tracking. Strong robustness and anti-interference capability: The described active disturbance rejection controller does not rely on a precise mathematical model of the system. ESO can observe and compensate for internal and external disturbances in real time, including but not limited to: load changes, parameter perturbations (such as changes in load inertia $J_L$, spring constant $K_s$), and external torque disturbances ($\omega_L, \omega_m$). Therefore, when system parameters fluctuate or unknown external disturbances exist, this invention can automatically maintain the stability and control performance of the system, exhibiting extremely strong robustness and solving the problem of PID controllers experiencing a sharp performance decline when facing uncertainty. The superior dynamic response performance resolves the conflict between speed and overshoot: the tracking differentiator (TD) in this invention provides a smooth and reasonable transition process for the system, avoiding overshoot caused by sudden changes in the given signal. Combined with the nonlinear combination of nonlinear state error feedback (NLSEF), the control force can be adaptively adjusted according to the magnitude of the error. This allows the system to track quickly in the initial stage of response and brake smoothly as it approaches the target, thus ensuring a fast response while significantly reducing overshoot, shortening settling time, and optimizing dynamic performance. The controller design is simplified, and the system is highly user-friendly in engineering: This invention utilizes active disturbance rejection (ADRR) technology to approximately "linearize" a complex, nonlinear flexible articulated robotic arm system into a simple series integral system under ESO compensation. This simplifies the subsequent controller design, eliminating the need for tedious linearization or complex controller structure design for complex nonlinear models. Furthermore, this invention provides explicit parameter tuning modules and methods. Although the parameters have physical meaning, the tuning process is systematic and follows established procedures, reducing the difficulty of debugging and application in engineering practice. This invention provides a complete, simulation-verified solution: It not only proposes a control algorithm but also constructs a complete technical closed loop, from mathematical model establishment (PMSM model, flexible joint dynamics model) → controller design (dual-loop ADRC structure) → simulation environment setup (based on Matlab / Simulink) → performance verification. By conducting system simulation studies using the simulation model built in Simulink, the effectiveness of the control scheme can be verified predictively, ensuring the reliability of the theoretical solution before practical application and laying a solid foundation for subsequent physical experiments and engineering deployment. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the dual closed-loop active disturbance rejection control system of the articulated robotic arm of the present invention. Figure 2 This is a schematic diagram of the dual closed-loop active disturbance rejection control method for the articulated robotic arm of the present invention. Figure 3 This is a schematic diagram of the ABC axis PMSM of the present invention; Figure 4 This is a schematic diagram of the PMSM for the dq axis of the present invention; Figure 5 This is a simplified schematic diagram of the dq axis of the present invention; Figure 6 This is a schematic diagram of the unit step response of the flexible joint manipulator of the present invention when r=100 and h=0.02; Figure 7 This is a schematic diagram of the unit step response of the flexible joint manipulator of the present invention when r=200 and h=0.02; Figure 8 This is a schematic diagram of the unit step response of the flexible joint manipulator of the present invention when r=200 and h=0.05; Figure 9 This is a schematic diagram of the output curve of the flexible joint robotic arm of the present invention; Figure 10 This is a schematic diagram of the error response curve of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Please see Figure 1-3 This invention provides a dual closed-loop self-disturbance rejection control system for a flexible joint robotic arm, comprising: The permanent magnet synchronous motor model module is used to describe the dynamic behavior of the motor; Flexible joint robotic arm model module, used to describe the flexible joint dynamics of the robotic arm; A dual-loop active disturbance rejection controller, comprising inner-loop current control and outer-loop position control; Tracking differentiator, nonlinear state error feedback law, extended state observer module; The parameter tuning module is used to optimize controller parameters; The simulation verification module is used to verify the performance of the control system in the Matlab / Simulink environment.

[0020] The system employs a dual closed-loop structure of "outer loop position control + inner loop current (torque) control". The inner loop (current loop) has a fast response and is responsible for controlling the motor torque, overcoming the electromagnetic inertia within the motor. The outer loop (position loop) has a slightly slower response and is responsible for ultimately controlling the angle of the robotic arm joints, overcoming the inertia and flexible vibration of the mechanical load. This structure decouples electrical dynamics from mechanical dynamics, making control more efficient. The active disturbance rejection controller is the core of the outer position loop. It does not rely on an accurate model of the controlled object, but actively “resists” and “compensates” for all factors (i.e., “total disturbances”) that affect control performance through its internal modules (TD, ESO, NLSEF). The entire system was modeled in Simulink, and simulations were used to verify that its performance was superior to traditional methods, thus reducing the cost and risk of direct physical experiments. In one embodiment, the permanent magnet synchronous motor model is established based on the dq-axis coordinate system, and its stator voltage equation is: ; ; Where ud, uq are stator voltages; id, iq are stator currents; ψd, ψq are flux linkages; Rs is stator resistance; and ωr is rotor angular velocity.

[0021] In this embodiment, the AC quantities (voltage and current) in the three-phase stationary coordinate system (ABC) are converted into DC quantities in the two-phase rotating coordinate system (dq) through Clarke and Park transformations. This makes controlling the AC motor as simple as controlling the DC motor. Decoupling control: The equations u_q = R_s i_q + pψ_q + ω_r ψ_d and u_d = R_s i_d + pψ_d - ω_r ψ_q reveal the coupling relationship between the d-axis and q-axis (ω_r ψ_d and -ω_r ψ_q terms). In modern vector control, these coupling terms are eliminated through methods such as feedforward compensation, thereby achieving independent and precise control of the d-axis current (used to control the magnetic field) and the q-axis current (used to control torque). This is the foundation for achieving high-performance motor drives.

[0022] In one embodiment, the flexible joint robotic arm model satisfies the following dynamic equations;

[0023] in, This represents the axial displacement output by the joint. This represents the shaft displacement of the permanent magnet synchronous motor. For load inertia, Here, N is the special coefficient for the rotational spring, and N is the hysteresis ratio. Obstacles from the system it carries. The drag ratio of a permanent magnet synchronous motor. The torque that makes the motor rotate. The system disturbance carried by the circuit. This represents the uncertainty term for the permanent magnet synchronous motor.

[0024] In this embodiment, the dynamic equation is a second-order differential equation that describes the dynamic balance between the inertia (J_L), elastic force (K_s), damping force (C_L), and external disturbance (ω_L) at the load end. It accurately characterizes the vibration modes unique to flexible joint systems, namely, that the motor motion and load motion are not completely synchronized, but coupled through springs, which is the physical root cause of end-point jitter.

[0025] In one embodiment, the active disturbance rejection controller includes; A tracking differentiator is used to schedule the transition process and extract the differential signal; Nonlinear state error feedback law is used to combine error signals and generate control quantities; An extended state observer is used to estimate the total system disturbance and perform feedforward compensation.

[0026] In this embodiment, the tracking differentiator (TD) is given a sudden command signal (such as a step signal), and the TD generates a smooth transition curve (v1) and its differential signal (v2). This avoids overshoot and oscillation caused by directly tracking the sudden signal, and embodies the idea of ​​"arranging the transition process". Nonlinear state error feedback (NLSEF) no longer uses the traditional linear weighting (P+I+D). Instead, it uses a nonlinear function (such as fal) to combine the error (e1 = v1 - z1) and the error derivative (e2 = v2 - z2) to generate the initial control quantity u0. Nonlinear combinations can usually provide smoother, faster, and overshoot-free control effects.

[0027] The Extended State Observer (ESO) is the core of ADRC. The ESO treats all unknown components (nonlinearities, couplings) and external disturbances in the system model as a "total disturbance" and expands it into a new state variable (z3) for real-time observation. Regardless of the source of the disturbance, the ESO can estimate and compensate for it, thereby achieving dynamic feedback linearization. In one embodiment, the extended state observer treats both internal system dynamics and external disturbances as a total disturbance and achieves disturbance rejection control through real-time estimation and compensation.

[0028] In this embodiment, the extended state observer does not distinguish whether the disturbance originates from within the system (such as vibration of a flexible joint or inaccurate model parameters) or from external sources (such as load changes). It treats them all as a single "total disturbance" f(t) acting on the controlled object. The extended state observer estimates the real-time effect z3 of the total disturbance using the system's input u and output y. Then, in the control law, z3 / b (where b is the control gain) is directly subtracted, thus canceling the disturbance before it actually affects the system. This is a feedforward compensation concept that achieves "active disturbance rejection" against internal and external disturbances.

[0029] In one embodiment, the parameter tuning module determines the optimal parameters of each module in the active disturbance rejection controller through simulation optimization methods, including the velocity factor of the tracking differentiator, the weighting coefficient of the nonlinear combination, and the bandwidth of the extended state observer.

[0030] In this embodiment, although the active disturbance rejection controller has a clear physical meaning, its parameters (such as r for TD, β series for ESO, and k_p, k_d for NLSEF) still need to be tuned. In the Simulink model, simulations (such as step response and sine tracking tests) are run to observe the system's response curves (such as rise time, overshoot, steady-state error, and disturbance rejection recovery time). Based on the simulation results, the controller parameters are repeatedly adjusted manually or in combination with optimization algorithms (such as genetic algorithms and particle swarm optimization) until the system performance meets all preset indicators. This process finds the set of parameters that makes the controller perform optimally in the current model.

[0031] The present invention also provides a method for self-disturbance rejection control of a flexible joint robotic arm, comprising the following steps: Establish a mathematical model of a permanent magnet synchronous motor and a flexible joint robotic arm; Design a dual-closed-loop active disturbance rejection controller structure; Configure a tracking differentiator, a nonlinear combination, and an extended state observer; Perform controller parameter tuning and simulation verification; Build a system model and perform performance tests in the Simulink environment.

[0032] This method describes the complete workflow for implementing the control strategy of this invention, from theoretical modeling to simulation verification. Its working principle is to systematically decompose complex control problems into a series of executable and verifiable steps, ensuring that high-performance control is ultimately achieved. Each step lays the foundation for the next, forming a complete closed loop from design to verification.

[0033] In one embodiment, the simulation verification includes building a system simulation model in a Matlab / Simulink environment and comparing the performance differences between PID control and active disturbance rejection control in terms of endpoint jitter, response speed, and disturbance rejection capability.

[0034] In this embodiment, a "software-in-the-loop" digital prototype is constructed in Simulink by establishing an accurate model of the controlled object and building a controller model. Under identical controlled object models and test conditions (such as the same commands and disturbances), run an ADRC-based control system and a traditional PID-based control system respectively. By comparing the quantitative indicators of the two response curves (such as overshoot, settling time, jitter amplitude, and disturbance rejection recovery time), the invention (ADRC) objectively and powerfully demonstrates the significant advantages of the present invention (ADRC) over the prior art (PID) in suppressing jitter, improving accuracy, and robustness.

[0035] The present invention also provides a hardware and software platform for implementing the above system, comprising: The computer equipment is configured with an Intel Core i5-9300HF processor, 16GB of memory, and a GTX 1660 Ti graphics card; The software environment includes SOLIDWORKS 2023, Matlab 2017b, PyCharm Community Edition 2022.2.3, Visio 2013, Origin 2018 64Bit, and LTspice; Among them, SOLIDWORKS is used for mechanical structure modeling, Matlab / Simulink is used for control system simulation, PyCharm is used for data processing, Visio is used for flowchart drawing, Origin is used for data visualization, and LTspice is used for circuit simulation.

[0036] Specifically, the aforementioned technical solution involves intimidation. 1. Hardware and software platform setup First, set up the necessary hardware and software environment for simulation and verification. The hardware platform includes a high-performance computer (such as a Lenovo Legion Y7000P2019, configured with an Intel Core i5-9300HF CPU, 16GB RAM, and an NVIDIA GeForce GTX 1660 Ti graphics card) to ensure the smoothness of complex mathematical operations and real-time simulation.

[0037] The software environment includes: SOLIDWORKS 2023: used for 3D structural modeling of permanent magnet synchronous motors and robotic arms to determine precise physical parameters (such as moment of inertia); Matlab 2017b: the core simulation software, used to build the entire control system model using its Simulink module and to write the S-Function of the active disturbance rejection controller; and Visio 2013: used to draw the control system flowchart (e.g., ...). Figure 1 Origin2018: Used to process simulation results data and plot performance comparison curves. LTspice: Optional, used to assist in verifying the design of motor drive circuits.

[0038] 2. Establish a mathematical model of the controlled object. (1) The mathematical model of the permanent magnet synchronous motor (PMSM) is established in Matlab. Based on equations (2-2) and (2-3), the voltage equation of the PMSM in the dq rotating coordinate system is established: u_q=R_s*i_q+p*ψ_q+ω_r*ψ_du_d=R_s*i_d+p*ψ_d-ω_r*ψ_q, where p is the differential operator. The flux linkage equation is usually ψ_d=L_d*i_d+ψ_f, ψ_q=L_q*i_q. The electromagnetic torque equation is T_e=(3 / 2)*p_n*[ψ_f*i_q+(L_d-L_q)*i_d*i_q], where p_n is the number of pole pairs. In this embodiment, a vector control strategy with i_d=0 is adopted to simplify control and achieve maximum torque output.

[0039] (2) Establishment of the Mathematical Model of the Flexible Joint Robotic Arm Based on the formula, a dynamic model of the flexible joint is established in Simulink. Its core equation is: J_L*d²(θ_L) / dt²=K_s*(θ_m / N-θ_L)+C_L*(d(θ_m) / dt / Nd(θ_L) / dt)+ω_L Simultaneously, the motion equation of the motor rotor is: J_m*d²(θ_m) / dt²=τ_m-K_s*(θ_m / N-θ_L)-C_m*d(θ_m) / dt+ω_m where τ_m is the electromagnetic torque output by the motor. These two equations together constitute the complete model of the controlled object, and are constructed using an integrator, gain module, and summation module in Simulink.

[0040] 3. Specific implementation of the dual closed-loop active disturbance rejection controller The core of this invention is a dual-closed-loop ADRC structure. The outer loop is a position loop, controlling the actual output angle θ_L of the robotic arm joint; the inner loop is a current loop (torque loop), controlling the q-axis current i_q of the motor. Taking the design of the position loop ADRC as an example, its specific implementation steps are as follows: (1) Arranging the transition process—The tracking differentiator (TD) receives the given position command θ_ref and arranges a smooth transition process trajectory v1 (tracking signal) for it, while simultaneously providing its differential signal v2 (differentiated signal). The discretization implementation is as follows: v1(k+1) = v1(k) + h*v2(k) v2(k+1)=v2(k)+h*fhan(v1(k)-θ_ref(k),v2(k),r,h0).

[0041] Where h is the integration step size, r is the speed factor that determines the tracking speed, h0 is the filtering factor, and fhan() is the fastest control synthesis function used to avoid overshoot.

[0042] (2) Estimating and compensating for total disturbance – Extended State Observer (ESO) The ESO unifies the uncertainties of the system model, flexible vibrations, and internal and external disturbances ω(t) into a new state variable x3, and performs real-time estimation. For the position loop, the system is approximated as a second-order system ÿ=f(y, ,ω(t),t)+b*u, where y=θ_L, u is the control output. Its third-order ESO discrete form is: e=z1(k)-y(k) / / y(k) is the actual output position feedback. z1(k+1)=z1(k)+h*(z2(k)-β01*e) z2(k+1)=z2(k)+h*(z3(k)-β02*fal(e,α1,δ)+b*u(k)) z3(k+1)=z3(k)+h*(-β03*fal(e,α2,δ)).

[0043] Where z1 tracks the output y, and z2 tracks the output derivative. z3 estimates the total perturbation f(·). β01, β02, and β03 are the observer gains, which can be tuned using the bandwidth method. The fal() function is a nonlinear function, with the form fal(e,α,δ)=|e|^α*sign(e) (|e|>δ) or e / δ^(1-α) (|e|≤δ), used to improve the estimation effect.

[0044] (3) Generate control quantity - Nonlinear state error feedback (NLSEF) NLSEF calculates the initial control quantity based on the error between the transition signal given by TD and the state signal estimated by ESO.

[0045] e1=v1(k)-z1(k) / / position error e2=v2(k)-z2(k) / / differential error u0=k_p*fal(e1,α_p,δ)+k_d*fal(e2,α_d,δ) / / Nonlinear combination.

[0046] Then, the total disturbance z3 estimated by ESO is used for compensation to obtain the final control quantity u: u=(u0-z3) / b; Here, b is the control gain, a key parameter that needs to be estimated and tuned. k_p,k_d,α_p,α_d are adjustable parameters of NLSEF.

[0047] 4. Parameter tuning and simulation verification Parameter tuning: First, based on the approximate models of the motor and robotic arm, the control gain b is initially set. Then, the coefficients β01, β02, β03 of ESO and the coefficients k_p, k_d of NLSEF are initially determined using the "bandwidth method". Finally, in Simulink simulation, by observing the system's step response and anti-interference response, the above parameters and the speed factor r of TD are repeatedly adjusted until the system achieves a fast, overshoot-free control effect that effectively suppresses jitter.

[0048] Simulation Verification: A complete dual-closed-loop ADRC control system was built in Simulink. A desired joint trajectory (such as a sine wave or step signal) was set, and the simulation was run. Simultaneously, a sudden load change or an external torque pulse ω_L was introduced into the system to simulate disturbances. The control effect of this invention was compared with that of a traditional PID controller. The simulation results clearly show that this invention significantly outperforms PID control in suppressing endpoint jitter, tracking accuracy, and disturbance resistance.

[0049] Furthermore, it should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0050] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0051] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory (ROM) / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0052] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A dual-closed-loop active disturbance rejection control system for a flexible joint robotic arm, characterized in that, include: The permanent magnet synchronous motor model module is used to describe the dynamic behavior of the motor; Flexible joint robotic arm model module, used to describe the flexible joint dynamics of the robotic arm; A dual-loop active disturbance rejection controller, comprising inner-loop current control and outer-loop position control; Tracking differentiator, nonlinear state error feedback law, extended state observer module; The parameter tuning module is used to optimize controller parameters; The simulation verification module is used to verify the performance of the control system in the Matlab / Simulink environment.

2. The dual closed-loop self-disturbance rejection control system for a flexible joint robotic arm according to claim 1, characterized in that: The permanent magnet synchronous motor model is established based on the dq axis coordinate system, and its stator voltage equation is: ； ； Where ud, uq are stator voltages; id, iq are stator currents; ψd, ψq are flux linkages; Rs is stator resistance; and ωr is rotor angular velocity.

3. The dual closed-loop self-disturbance rejection control system for a flexible joint robotic arm according to claim 1, characterized in that: The flexible joint robotic arm model satisfies the following dynamic equations; in, This represents the axial displacement output by the joint. This represents the shaft displacement of the permanent magnet synchronous motor. For load inertia, Here, N is the special coefficient for the rotational spring, and N is the hysteresis ratio. Obstacles from the system it carries. The drag ratio of a permanent magnet synchronous motor. The torque that makes the motor rotate. The system disturbance carried by the circuit. This represents the uncertainty term for the permanent magnet synchronous motor.

4. The dual closed-loop self-disturbance rejection control system for a flexible joint robotic arm according to claim 1, characterized in that: The active disturbance rejection controller includes: A tracking differentiator is used to schedule the transition process and extract the differential signal; Nonlinear state error feedback law is used to combine error signals and generate control quantities; An extended state observer is used to estimate the total system disturbance and perform feedforward compensation.

5. The dual closed-loop self-disturbance rejection control system for a flexible joint robotic arm according to claim 4, characterized in that: The extended state observer treats both internal system dynamics and external disturbances as a total disturbance and achieves disturbance rejection control through real-time estimation and compensation.

6. The dual closed-loop self-disturbance rejection control system for a flexible joint robotic arm according to claim 1, characterized in that: The parameter tuning module determines the optimal parameters of each module in the active disturbance rejection controller through simulation optimization methods, including the velocity factor of the tracking differentiator, the weighting coefficient of the nonlinear combination, and the bandwidth of the extended state observer.

7. A method for self-disturbance rejection control of a flexible joint robotic arm, characterized in that, Includes the following steps: Establish a mathematical model of a permanent magnet synchronous motor and a flexible joint robotic arm; Design a dual-closed-loop active disturbance rejection controller structure; Configure a tracking differentiator, a nonlinear combination, and an extended state observer; Perform controller parameter tuning and simulation verification; Build a system model and perform performance tests in the Simulink environment.

8. The self-disturbance rejection control method for a flexible joint robotic arm according to claim 7, characterized in that, The simulation verification includes building a system simulation model in the Matlab / Simulink environment and comparing the performance differences between PID control and active disturbance rejection control in terms of endpoint jitter, response speed and disturbance rejection capability.

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