Generalized dynamic predictive control method for realizing trajectory tracking of manipulator system

Abstract

The invention discloses a generalized dynamic predictive control method for realizing trajectory tracking of a manipulator system, and relates to the technical field of predictive control of the manipulator system.The generalized dynamic predictive control method comprises the steps that the manipulator system is generated, and a mathematical model is constructed through the manipulator system.The generalized dynamic predictive control method is combined with zero-static-error predictive control; the trajectory tracking control of the controlled manipulator system can realize higher tracking control precision; according to the method, the adaptive transient performance optimization capability of the method can be well guaranteed through a prediction control time domain on-line updating mechanism; according to the method, a design framework based on generalized predictive control is adopted, meanwhile, a concise and clear guidance mechanism is provided for selection of control parameters, and the speeds and position quantities of all joints of the manipulator system are collected through position and speed sensors with good measurement performance, so that the closed-loop manipulator system can adapt to various industrial scenes; moreover, the system has good track adjustment performance, and improves the overall intelligent management level.

Description

Technical Field

[0001] This invention relates to the field of predictive control technology for robotic arm systems, specifically a generalized dynamic predictive control method for achieving trajectory tracking in robotic arm systems. Background Technology

[0002] Robotic arms are commonly used in various scenarios requiring high precision, such as high-end manufacturing, aerospace, and various surgical procedures. They are composed of kinematic chains formed by connected joints. Nowadays, robotic arms are increasingly valued by engineers for assisting in the completion of higher-precision engineering tasks, in which the physical interaction between humans and objects is indispensable. In this process, high-precision control of robotic arm trajectories and flexible movements have received widespread attention. Existing control schemes for robotic arm trajectory adjustment can be summarized as follows: proportional-integral-derivative control (PID), robust control, model predictive control, adaptive neural network control, and sliding mode control, etc. However, these strategies are becoming increasingly inadequate in applications with increasingly higher performance requirements and lower cost requirements.

[0003] Existing control schemes have the following advantages and disadvantages:

[0004] 1. Firstly, regarding traditional PID control, with fewer parameters, it offers a flexible and convenient tuning mechanism, making it highly adaptable to industrial scenarios. The required performance can be flexibly obtained through parameter tuning. However, the parameters used are often suitable for specific scenarios. When the scenarios switch over a wide range, it is difficult to guarantee that the control performance will remain as expected. In other words, the PID parameters are considered to be local optima, which is undesirable in industrial robotic arm applications. Furthermore, the stability and robustness of the closed-loop system under PID strategy control are difficult to explain.

[0005] 2. It is undeniable that lumped uncertainty, comprised of uncertainties in system modeling parameters, unmodeled higher-order dynamic states, and external disturbances, is prevalent in various engineering objects. This inevitably leads to a decline in control performance and even safety issues. Traditional robust control strategies offer hope for solving these problems. They typically obtain simple and easily implemented control laws through thorough theoretical proofs and, given a grasp of the changing working conditions, tune the control parameters to make them suitable for various working conditions of the robotic arm system. However, this design approach does not give much consideration to the dynamic performance optimization of the closed-loop system. When faced with small disturbances, the fixed-parameter controller used under large external force disturbances inevitably causes over-robustness issues within the system. This will undoubtedly lead to the actual control performance of the robotic arm system deviating from the design expectations under different external forces, potentially causing workpiece damage or even worker injury in industrial applications.

[0006] 3. Model predictive controllers have strong control performance optimization capabilities by solving performance function optimization equations in real time, and can achieve position or velocity constraint control of the robot system. However, they require high model accuracy for the robot system and have relatively weak anti-interference capabilities. In industrial application scenarios, robot systems inevitably encounter interference from different external forces. Modeling mismatch or even excessive service life can cause perturbation of internal system parameters. If the controller design process does not consider the model signal mismatch, it will inevitably lead to the loss of model predictive control accuracy and may even cause the system to collapse.

[0007] To mitigate potential robustness redundancy issues in systems, several valuable results have been developed. From a control theory perspective, a tracking error-oriented parameter self-tuning mechanism optimizes the controller parameter tuning of the closed-loop system, thereby adaptively adjusting the system's control performance based on the intensity of disturbances. A natural question arises regarding the potential robustness redundancy problem inherent in traditional predictive control: does a predictive period self-tuning function related to the tracking error exist? This function can calculate the optimal predictive period value for the current operating condition based on changes in the intensity of external forces acting on the manipulator, thus achieving a balance between adaptability and robustness in the controlled manipulator system.

[0008] Therefore, this invention requires the design of a generalized dynamic predictive control method for achieving trajectory tracking in a robotic arm system to solve the aforementioned problems. Summary of the Invention:

[0009] The purpose of this invention is to provide a generalized dynamic predictive control method for trajectory tracking in a robotic arm system, addressing the aforementioned problems. This method resolves the robustness redundancy issues that may arise in the system, as mentioned in the background section. Numerous valuable results have already been developed, utilizing a tracking error-oriented parameter self-tuning mechanism from a control theory perspective to optimize the controller parameter tuning of the closed-loop system. This further allows for adaptive adjustment of the system's control performance based on the intensity of disturbances experienced by the system. Regarding the potential robustness redundancy issues faced by traditional predictive control, a natural question arises: does a predictive period self-tuning function related to the tracking error exist, capable of calculating the optimal predictive period value for the current operating condition based on changes in the intensity of external forces acting on the robotic arm, thereby achieving both adaptability and robustness in the controlled robotic arm system?

[0010] To address the above problems, the present invention provides a technical solution:

[0011] The generalized dynamic predictive control method for achieving trajectory tracking in a robotic arm system includes the following specific steps:

[0012] S1. Generate a robotic arm system, and construct a mathematical model using the robotic arm system;

[0013] S2. Perform the system model interference estimation calculation. Based on step S1, establish a series of nonlinear interference estimators to reconstruct the uncertainty and external interference of the robot arm system.

[0014] S3. Construct the steady-state model and expected output value of the robotic arm system. The steady-state model is established based on the estimation work in steps S1 and S2.

[0015] S4. While performing predictive control through the robotic arm system, steady-state model rolling optimization is performed, and rolling optimization performance indicators are set to adjust the system output to converge to its reference value in a better posture.

[0016] S5. Design a self-adjusting mechanism for the prediction cycle within the robotic arm system to maintain coordinate transformation;

[0017] S6. Design the output execution law, and combine it with the design of the predictive control law to obtain the final input execution rate of the controlled manipulator system. Simultaneously, perform the tuning of the nonlinear disturbance estimator parameter matrix and the tuning of the generalized dynamic predictive controller parameters to obtain the final generalized dynamic predictive control method.

[0018] Preferably, step S1 includes the following specific steps:

[0019] S101. Six joint angle sensors are installed inside the robotic arm system. The angular position q and angular velocity of each joint motor are obtained through the six joint angular velocity sensors. Sampling information,

[0020] S102. Establish the standard mathematical dynamic model M1 of the robotic arm operating system.

[0021] Preferably, after generating the mathematical dynamic model M1, the system state is selected as x1 = q. The state-space model M2 of the controlled manipulator system is obtained as follows:

[0022] M2:

[0023] in:

[0024]

[0025] Preferably, the specific form of the reconstruction in step S2 can be described as follows:

[0026]

[0027] Where k > 0 is the parameter gain matrix of the designed estimator, and p is an internal auxiliary state vector of an estimator; symbol Let d be the estimated vector of the lumped disturbance d.

[0028] Preferably, the steady-state model of the system is established as follows:

[0029]

[0030] Where y d For the desired positions of each joint of the robotic arm, The desired angular velocity.

[0031] Preferably, the reference value in step S4 is:

[0032]

[0033] Where T > 0 represents the prediction period;

[0034] By ignoring the estimation error term in the above η system, its nominal system can be obtained:

[0035]

[0036] Within a prediction period, the tracking deviation expands along the aforementioned nominal system, specifically as follows:

[0037]

[0038] Preferably, in step S5, when performing the coordinate transformation:

[0039] ξ i =η i / L i-1 i = 1, 2,

[0040] Where L(t)≥1 is the introduced auxiliary adaptive parameter;

[0041] Where c>0 is a parameter to be designed.

[0042] As a preferred option, according to the definition in step S1

[0043] u=M -1 (x1)τ;

[0044] The design of the generalized predictive control law in step S4 yields the final input execution rate τ of the controlled robotic arm system as follows:

[0045]

[0046] Preferably, in step S6, when tuning the parameter matrix of the nonlinear disturbance estimator, the constraint condition needs to be met. First, a sufficiently large positive number is given, with a magnitude of about 5-10. The larger the value, the faster the convergence speed of the estimator, and the stronger the robustness of the closed-loop system. The estimation accuracy of the nonlinear disturbance estimator is positively correlated with the set control frequency of the controller design loop. The higher the control frequency, the higher the estimation accuracy, and vice versa.

[0047] Preferably, in step S6, when tuning the parameters of the generalized dynamic predictive controller, the parameters to be tuned are c,T(0). Regarding the selection principle of the controller gain parameter, firstly, the control law gain is optimized, which can be achieved through rolling optimization. The larger the value of c, the faster the convergence speed of T, that is, the faster the convergence speed of the system and the smaller the steady-state error. After the system enters the steady state, the trajectory will show obvious oscillations. The larger T(0), the slower the convergence speed of the robot's closed-loop system and the larger the steady-state error. As T(0) decreases, the adjustment time will increase accordingly.

[0048] The beneficial effects of this invention are:

[0049] 1. This invention combines zero steady-state error predictive control with a feedforward control strategy based on disturbance estimation, enabling the trajectory tracking control of the controlled manipulator system to achieve higher tracking control accuracy.

[0050] 2. This invention, through the mechanism of online updating of predictive control in the time domain, ensures that the adaptive transient performance optimization capability of the robot closed-loop system can be well guaranteed when facing complex external disturbances or high model parameter mismatch.

[0051] 3. This invention, through a design framework based on generalized predictive control, theoretically provides specifications for the selection of control parameters. The selection of control parameters has a concise and clear guiding mechanism, which is more conducive to engineering implementation. High-performance position and velocity sensors are used to collect the velocity and position of each joint of the robotic arm system. The collected information is then integrated to construct a nonlinear disturbance estimator, aiming to obtain the internal uncertainties and external disturbance information of the model as accurately and timely as possible during the operation of the robotic arm system. Mathematical model transformation is then used to transform the physical model of the robotic arm into the state-space model to be designed. Based on the transformed model, a novel adaptive time-domain update mechanism based on generalized predictive control is designed in one step, thereby significantly optimizing the traditional generalized predictive controller. This allows the closed-loop robotic arm system to adapt to various industrial scenarios and has good trajectory adjustment performance, improving the overall level of intelligent management. Attached image description:

[0052] For ease of explanation, the present invention will be described in detail below with reference to specific embodiments and accompanying drawings.

[0053] Figure 1 This is the overall flowchart of the generalized dynamic predictive control method for realizing trajectory tracking of a robotic arm system according to the present invention;

[0054] Figure 2 This is a system block diagram of the non-recursive composite controller of the present invention;

[0055] Figure 3 This is a graph showing the change of d-axis current data of the PI controller under constant disturbance in this invention;

[0056] Figure 4 This is a graph showing the d-axis current data variation of a traditional cascade PI controller under constant disturbance.

[0057] Figure 5 This is a graph of the q-axis current curve of the PI controller under sinusoidal disturbance in this invention;

[0058] Figure 6 This is a graph of the q-axis current of a traditional cascaded PI controller under sinusoidal disturbance. Detailed implementation method:

[0059] like Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown, the specific implementation adopts the following technical solution:

[0060] Example 1:

[0061] The generalized dynamic predictive control method for achieving trajectory tracking in a robotic arm system includes the following specific steps:

[0062] S1. Generate a robotic arm system, and construct a mathematical model using the robotic arm system;

[0063] S2. Perform the system model interference estimation calculation. Based on step S1, establish a series of nonlinear interference estimators to reconstruct the uncertainty and external interference of the robot arm system.

[0064] S3. Construct the steady-state model and expected output value of the robotic arm system. Based on the estimation work in steps S1 and S2, the robotic arm system with unknown dynamics can be corrected to be completely known, and a steady-state model is established.

[0065] S4. While performing predictive control through the robotic arm system, steady-state model rolling optimization is performed, and rolling optimization performance indicators are set to adjust the system output to converge to its reference value in a better posture.

[0066] S5. Design a self-adjusting mechanism for the prediction cycle within the robotic arm system to maintain coordinate transformation;

[0067] S6. Design the output execution law, and combine it with the design of the predictive control law to obtain the final input execution rate of the controlled manipulator system. Simultaneously, perform the tuning of the nonlinear disturbance estimator parameter matrix and the tuning of the generalized dynamic predictive controller parameters to obtain the final generalized dynamic predictive control method.

[0068] Example 2

[0069] like Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown, the specific implementation adopts the following technical solution:

[0070] Preferably, step S1 includes the following specific steps:

[0071] S101. Six joint angle sensors are installed inside the robotic arm system. The angular position q and angular velocity of each joint motor are obtained through the six joint angular velocity sensors. Sampling information,

[0072] S102. Establish a standard mathematical dynamic model M1 for the robotic arm operating system, wherein the mathematical dynamic model M1 is as follows:

[0073] M1:

[0074] in Let τ be the joint angular acceleration of the robotic arm system, denoted as the control input, and M(q) be the inertia matrix, satisfying the positive definiteness condition. Let G(q) be the centripetal force and Coriolis force matrix, G(q) be the gravity of the manipulator system, and τ be the force matrix. d It is represented as uncertain dynamics, which includes the parameterized uncertainty of the system, unmodeled dynamics, and external disturbances.

[0075] Preferably, after generating the mathematical dynamic model M1, the system state is selected as x1 = q. The state-space model M2 of the controlled manipulator system is obtained as follows:

[0076] M2:

[0077] in:

[0078]

[0079] Preferably, the specific form of the reconstruction in step S2 can be described as follows:

[0080]

[0081] Where κ>0 is the parameter gain matrix of the designed estimator, and p is an internal auxiliary state vector of an estimator; symbol Let d be the estimated vector of the lumped disturbance d.

[0082] definition The dynamic system of the observer's estimation error is then:

[0083]

[0084] Preferably, the steady-state model of the system is established as follows:

[0085]

[0086] Where y d For the desired positions of each joint of the robotic arm, Let be the desired angular velocity. Therefore, the trajectory adjustment and control of the robotic arm system in a physical sense can now be transformed into a system output trajectory tracking problem in intelligent control theory, requiring the following coordinate transformation:

[0087]

[0088] The compact form of the system can then be simply written as:

[0089]

[0090] in

[0091]

[0092] Preferably, the reference value in step S4 is:

[0093]

[0094] Where T > 0 represents the prediction period;

[0095] By ignoring the estimation error term in the above η system, its nominal system can be obtained:

[0096]

[0097] Within a prediction period, the tracking deviation expands along the aforementioned nominal system, specifically as follows:

[0098]

[0099] Where r is the control order of the system.

[0100]

[0101]

[0102]

[0103] At this point, the performance function can be further calculated as follows:

[0104]

[0105] in

[0106]

[0107]

[0108]

[0109] Next, make Take the partial derivative with respect to V, and take... In the known Based on this, the optimal control law is derived as follows:

[0110] Therefore, the implementable optimized intermediate control law can be described as follows:

[0111]

[0112] where E=[I n If the control order r is chosen as 0, then the optimal control law can be directly written as [0, ..., 0].

[0113]

[0114] in It can be calculated directly.

[0115] Preferably, in step S5, when performing the coordinate transformation:

[0116] ξ i =η i / Z i-1 i = 1, 2,

[0117] Where L(t)≥1 is the introduced auxiliary adaptive parameter;

[0118] Where c>0 is a parameter to be designed.

[0119] As a preferred option, according to the definition in step S1

[0120] u=M -1 (x1)τ;

[0121] The design of the generalized predictive control law in step S4 yields the final input execution rate τ of the controlled robotic arm system as follows:

[0122]

[0123] Preferably, in step S6, when tuning the parameter matrix of the nonlinear disturbance estimator, constraints need to be met. First, a sufficiently large positive number, around 5-10, is given. Its magnitude directly affects the convergence speed of the estimator. Generally, the larger the value, the faster the estimator converges, corresponding to stronger robustness of the closed-loop system. However, in the early stages of estimator convergence, it can lead to significant overshoot. Therefore, this is a parameter worth coordinating. Based on this, using the "trial and error" approach, the detailed values ​​of the parameter matrix need to be fine-tuned according to the trajectory output by the closed-loop system. The estimation accuracy of the nonlinear disturbance estimator is positively correlated with the set control frequency of the controller's design loop. The higher the control frequency, the higher the estimation accuracy; conversely, the lower the control frequency, the lower the estimation accuracy.

[0124] Preferably, in step S6, when tuning the parameters of the generalized dynamic predictive controller, the parameter to be tuned is c,T(0). The selection principle for the controller gain parameter is to first optimize the control law gain, which can be accurately calculated through rolling optimization. c, as a parameter related to the convergence performance of the prediction period T, is usually adjusted manually through the "trial and error method". Specifically, the larger the value of c, the faster the convergence speed of T, that is, the faster the convergence speed of the system and the smaller the steady-state error. However, the value of c cannot be increased indefinitely. As the value of c gradually increases, the convergence speed of T increases dramatically, and the lower bound of T convergence gradually decreases. The decrease in the lower bound of T will enhance the robustness of the system. When it exceeds a certain critical value, it will cause the robot's closed-loop system to become overly robust, which will lead to a decrease in the transient performance of the closed-loop system, that is, a certain overshoot will occur. Even after the system enters steady state, the trajectory will show obvious oscillations. The larger T(0) is, the slower the convergence speed of the robot's closed-loop system and the larger the steady-state error. As T(0) decreases, the settling time will increase accordingly, but if it is too small, it will cause the problem of robustness redundancy, and the recovery process will have a certain degree of overshoot.

[0125] Example 3:

[0126] like Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6As shown, the specific implementation adopts the following technical solution:

[0127] To verify the superiority and effectiveness of this invention, three operating conditions for permanent magnet synchronous motors were set up:

[0128] 1) Given velocity ω ref =1500rpm, after 1s a sudden disturbance torque of T is applied. L =0.5Nm;

[0129] 2) Given a time-varying velocity given signal ω ref =1500rpm, initial disturbance torque set to T L =0.5Nm, the disturbance torque switches to T after 1s. L =0.5+0.3sin(t)Nm.

[0130] Based on the parameter selection rules given above, and considering the permanent magnet brushless DC motor selected in this example, the control parameters of this invention are set as follows:

[0131]

[0132] Meanwhile, a dual-loop PI controller was selected as a control group to more intuitively demonstrate the effectiveness of the proposed invention and its performance improvement to a certain extent. The dual-loop PI controller can be designed as follows:

[0133] 1) Speed ​​loop PI controller

[0134] 2) Current loop PI controller

[0135] The control parameters are selected as follows:

[0136]

[0137] The developed controller exhibits several advantages. First, the non-smooth, non-recursive controller demonstrates strong adaptability, capable of handling various types of disturbances, while also achieving higher control accuracy. Specifically, when facing sinusoidal loads, the proposed controller exhibits smaller steady-state error and less speed drop during disturbance switching, resulting in higher system robustness. Traditional cascade PI controllers are significantly inferior to the developed non-smooth, non-recursive controller in both aspects. Furthermore, regarding current, the proposed controller shows less pronounced sudden changes in operating conditions compared to traditional PI controllers. This is attributed to the developed self-adjusting control bandwidth mechanism, effectively enhancing the dynamic performance and adaptability of the servo system.

[0138] Specifically, in practical applications, this invention combines zero steady-state error predictive control with a feedforward control strategy based on disturbance estimation, enabling the controlled manipulator system to achieve higher tracking accuracy. Furthermore, the online time-domain update mechanism of predictive control ensures the adaptive transient performance optimization capability of the manipulator closed-loop system even under complex external disturbances or high model parameter mismatch. Finally, this invention, based on a generalized predictive control design framework, theoretically provides guidelines for control parameter selection, offering a concise and clear guiding mechanism for parameter selection, facilitating engineering implementation. This is further enhanced by measuring high-performance position and velocity sensors. The device collects the velocity and position data of each joint of the robotic arm system. Then, by integrating the collected information, a nonlinear disturbance estimator is constructed to obtain the internal uncertainty and external disturbance information of the model as accurately and timely as possible during the operation of the robotic arm system. Then, by using mathematical model transformation, the physical model of the robotic arm is transformed into the state-space model to be designed. Based on the transformed model, a novel adaptive time-domain update mechanism based on generalized predictive control is designed directly in one step, thereby significantly optimizing the traditional generalized predictive controller. This enables the closed-loop robotic arm system to adapt to various industrial scenarios and has good trajectory adjustment performance, improving the overall level of intelligent management.

[0139] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A generalized dynamic predictive control method for trajectory tracking in a robotic arm system, characterized in that, The specific steps include the following: S1. Generate a robotic arm system, and construct a mathematical model using the robotic arm system; S2. Perform the system model interference estimation calculation. Based on step S1, establish a series of nonlinear interference estimators to reconstruct the uncertainty and external interference of the robot arm system. S3. Construct the steady-state model and expected output value of the robotic arm system. The steady-state model is established based on the estimation work in steps S1 and S2. S4. While performing predictive control through the robotic arm system, steady-state model rolling optimization is performed, and rolling optimization performance indicators are set to adjust the system output to converge to its reference value in a better posture. S5. Design a self-adjusting mechanism for the prediction cycle within the robotic arm system to maintain coordinate transformation; S6. Design the output execution law, and combine it with the design of the predictive control law to obtain the final input execution rate of the controlled manipulator system. Simultaneously, perform the tuning of the nonlinear disturbance estimator parameter matrix and the tuning of the generalized dynamic predictive controller parameters to obtain the final generalized dynamic predictive control method.

2. The generalized dynamic predictive control method for trajectory tracking of a robotic arm system according to claim 1, characterized in that, Step S1 includes the following specific steps: S101. Six joint angle sensors are installed inside the robotic arm system to obtain the angular position q and angular velocity of each joint motor through the six joint angular velocity sensors. Sampling information; S102. Establish the standard mathematical dynamic model M1 of the robotic arm operating system.

3. The generalized dynamic predictive control method for trajectory tracking of a robotic arm system according to claim 2, characterized in that: After generating the mathematical dynamic model M1, the system state is selected as... The state-space model M2 of the controlled manipulator system is obtained as follows: in:

4. The generalized dynamic predictive control method for realizing trajectory tracking of a robotic arm system according to claim 1, characterized in that: The specific form of the reconstruction in step S2 can be described as follows: Where κ>0 is the parameter gain matrix of the designed estimator, and p is the internal auxiliary state vector of an estimator; symbol Let d be the estimated vector of the lumped disturbance d.

5. The generalized dynamic predictive control method for realizing trajectory tracking of a robotic arm system according to claim 1, characterized in that, The steady-state model of the system is established as follows: Where y d The desired positions of each joint of the robotic arm. This represents the desired angular velocity.

6. The generalized dynamic predictive control method for realizing trajectory tracking of a robotic arm system according to claim 1, characterized in that, The reference value in step S4 is: Where T > 0 represents the prediction period; By ignoring the estimation error term in the above η system, its nominal system can be obtained: Within a prediction period, the tracking deviation expands along the aforementioned nominal system, specifically as follows:

7. The generalized dynamic predictive control method for trajectory tracking of a robotic arm system according to claim 1, characterized in that, In step S5, when performing coordinate transformation: x i =the i / L i-1 ,i=1,2, Where L(t)≥1 is the introduced auxiliary adaptive parameter; Where c>0 is a parameter to be designed.

8. The generalized dynamic predictive control method for realizing trajectory tracking of a robotic arm system according to claim 1, characterized in that: According to the definition in step S1 u=M -1 (x1)τ; The design of the generalized predictive control law in step S4 yields the final input execution rate τ of the controlled robotic arm system as follows:

9. The generalized dynamic predictive control method for realizing trajectory tracking of a robotic arm system according to claim 1, characterized in that: In step S6, when tuning the parameter matrix of the nonlinear disturbance estimator, the following constraints need to be met: first, a sufficiently large positive number is given, with a magnitude of about 5-10. The larger the value, the faster the convergence speed of the estimator, and the stronger the robustness of the closed-loop system. The estimation accuracy of the nonlinear disturbance estimator is positively correlated with the set control frequency of the controller design loop. The higher the control frequency, the higher the estimation accuracy, and vice versa.

10. The generalized dynamic predictive control method for realizing trajectory tracking of a robotic arm system according to claim 1, characterized in that: In step S6, when tuning the parameters of the generalized dynamic predictive controller, the parameters to be tuned are c and T(0). Regarding the selection principle of the controller gain parameter, the control law gain is optimized first, which can be achieved through rolling optimization. The larger the value of c, the faster the convergence speed of T, that is, the faster the convergence speed of the system and the smaller the steady-state error. After the system enters the steady state, the trajectory will show obvious oscillation. The larger T(0), the slower the convergence speed of the robot closed-loop system and the larger the steady-state error. As T(0) decreases, the adjustment time will increase accordingly.

Images