Mechanical arm pulse control transient oscillation analysis method based on forward and feedback channel response characteristics

Abstract

The invention provides a mechanical arm pulse control transient oscillation analysis method based on forward and feedback channel response characteristics. The mechanical arm pulse control transient oscillation analysis method comprises the following steps that 1, unit impulse response of a forward driving channel and a feedback channel is established; 2, deducing a full-time-domain transient output expression under the action of pulse control, and analyzing an oscillation superposition rule; step 3, taking minimization of transient oscillation as a target, combining the dual-channel impulse response characteristics and transient quantitative indexes, and carrying out collaborative optimization on pulse control parameters and feedback adjustment parameters; and step 4, forming an analysis and optimization process of pulse control transient oscillation of the mechanical arm. According to the method, the generation mechanism of transient oscillation is analyzed from the source of system composition, and the technical defect that a traditional model cannot reflect the dynamic characteristics of an actual channel is overcome.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, and in particular relates to a transient oscillation analysis method for pulse control of robotic arms based on the response characteristics of forward and feedback channels. Background Technology

[0002] With the rapid development of industrial informatization, robotic arms are playing an increasingly important role in industrial production and daily life. High-precision control of robotic arms has become a core research topic in the field of robotics, and its control accuracy mainly includes two aspects: steady-state accuracy and transient accuracy. Existing research, while pursuing high steady-state accuracy, generally neglects the control quality of transient processes, i.e., transient accuracy. However, in key application scenarios such as precision gripping of thin-walled components and medical surgical robots, the transient motion smoothness of robotic arms is equally crucial and cannot be ignored.

[0003] As a strongly coupled, highly nonlinear dynamic system, the control performance of robotic arms is susceptible to various uncertainties, including unmodeled dynamics, parameter perturbations, and external disturbances. In recent years, various advanced control strategies have been widely applied to robotic arm trajectory tracking and positioning control, which can be categorized into open-loop control and closed-loop feedback control from a structural perspective. Closed-loop feedback control uses sensors to collect real-time motion information from the robotic arm's end effector, identifying deviations from the desired command and correcting the control input in real time. Considering communication bandwidth, computational overhead, and practical hardware constraints, discontinuous feedback is often used in engineering applications to replace continuous feedback control; pulse feedback control is the most typical implementation method.

[0004] It is worth noting that traditional integer-order differential equations are essentially instantaneous response models. They assume that the output responds immediately when the input changes and stops synchronously when the input terminates. The system response time is approximately zero, which means that the actual physical system is equivalent to an ideal instantaneous impulse response system.

[0005] However, real-world physical systems are not ideal impulse response models; they all possess their own response characteristics. When input signals change alternately, they inevitably induce system oscillations, and robotic arm systems are no exception. Under pulsed, discontinuous actuation, frequently switching control commands directly trigger transient oscillations in the robotic arm, not only generating vibration noise, accelerating mechanical wear, and reducing equipment lifespan, but also significantly deteriorating the system's transient control performance. In scenarios with stringent requirements for motion smoothness, such as precision assembly, flexible grasping, and medical intervention operations, transient oscillations have become a key issue restricting the improvement of control quality.

[0006] From a system dynamics perspective, the root cause of the aforementioned transient oscillations lies in the fact that the actual system is not an ideal instantaneous response system, but rather determined by its inherent dynamic response characteristics. The forward drive channel of the robotic arm can be considered as a dynamic subsystem with independent response characteristics, and the feedback sensing and control channel is also a subsystem with independent response characteristics. Under the coupling effect of the dynamic characteristics of the forward channel and the feedback channel, coupled with the excitation of discontinuous pulse control signals, the robotic arm closed-loop system inevitably generates transient oscillations. Summary of the Invention

[0007] Purpose of the invention: To address the technical pain points in existing transient analysis of robotic arm pulse control, which treats the system as an ideal impulse response system, failing to reflect the actual dynamic characteristics of the forward / feedback channels, resulting in inaccurate analysis of transient oscillation mechanisms, lack of quantitative analysis, and highly arbitrary optimization methods with significant implementation difficulties, this invention constructs a dual-channel impulse response model, a full-time-domain quantitative analysis system, and an intelligent parameter optimization strategy to achieve accurate mechanism analysis, quantitative assessment, and root cause suppression of transient oscillations, reducing implementation costs and providing reliable technical support for improving the transient performance of robotic arm pulse control.

[0008] This invention specifically provides a transient oscillation analysis method for robotic arm pulse control based on the response characteristics of forward and feedback channels. It is specifically applied to pulse-controlled robotic arm systems such as industrial robotic arms and collaborative robots, providing precise mechanism analysis and suppression optimization schemes for transient oscillation problems driven by pulse commands. This method is suitable for scenarios with high requirements for robotic arm positioning accuracy and motion stability.

[0009] This method includes the following steps: Step 1: Establish the unit impulse response of the forward drive channel and the feedback channel; Step 2: Derive the full-time transient output expression under pulse control and analyze the oscillation superposition law; Step 3: With the goal of minimizing transient oscillations, the pulse control parameters and feedback adjustment parameters are optimized in a coordinated manner by combining the dual-channel impulse response characteristics and transient quantization indicators. Step 4: Develop an analysis and optimization process for transient oscillations in the pulse control of the robotic arm.

[0010] Step 1 includes the following steps: Step 1.1, Module decomposition and function definition; Step 1.2, Module impulse response modeling; Step 1.3, Model transformation and parameter identification.

[0011] Step 1.1 includes: dividing the robotic arm control system into a forward channel and a feedback channel. Forward path: includes drive motor and robotic arm, converting power into robotic arm displacement output signal; Feedback channel: includes detection sensors, pulse switches and pulse controllers, which enable the robotic arm output signal to be fed back to the drive motor input through sampling pulses, and error adjustment is achieved through pulse feedback.

[0012] Step 1.2 includes: establishing impulse response models for the forward channel and feedback channel, respectively; Forward channel impulse response model: The dynamic response process of the power output is characterized by an exponentially decaying function, expressed as follows: , in, It is the forward channel unit impulse response; It is the forward channel response amplitude coefficient; t is the forward channel attenuation coefficient; e is time; e is the natural constant. Feedback channel impulse response model: , in It is the unit impulse response of the feedback channel; It is the response amplitude coefficient of the feedback channel; It is the feedback channel attenuation coefficient.

[0013] Step 1.3 includes: Step 1.3.1: Establish the input-output relationship of each module through convolution operation; Construct input-output impulse response convolutional models for the forward and feedback channels respectively: , Among them, symbols The convolution operation is represented by , and j represents the subscripts b and f, respectively, indicating the feedback channel impulse response model and the forward channel impulse response model. This represents the corresponding model input. and These represent the feedback channel output and the forward channel output, respectively. Step 1.3.2, Model Simplification: Transform the convolutional model into an algebraic model using the Legendre transform; Parameter identification: Forward and feedback channel experiments were conducted. Input and output data were collected, and the least squares method was used to identify the unknown parameters of the forward and feedback channel models, thus obtaining the parameters of the forward channel. and feedback channels Impulse response model.

[0014] Step 2 includes: Step 2.1, Pulse control signal modeling; Pulse control input Represented as a delayed pulse sequence: , in Indicates the output of the robotic arm Ideal pulse sampling, For the gain of the j-th pulse, The pulse trigger time, The Dirac impulse function; Step 2.2: Based on the convolution relationship, obtain the output of the feedback channel; The feedback channel output is obtained by considering the response characteristics of the feedback channel: ; Step 2.3: Calculate the robotic arm output based on the forward and feedback channels: ; Step 2.4: Based on the convolutional memory characteristics, the steady-state and transient states are separated according to the trigger time segment, transient analysis is performed, and a transient analysis method is established. When the time is... When within a time period: Robotic arm output: , When time is Within the specified time, the robotic arm outputs: , Introducing a step function Construct window function The starting point of the window function is The destination is The output is: , in, express The output generated by the drive signal within a time period; express The output generated by the drive signal after a certain time; Indicates in The sampled pulse signal at time 10 is fed back through the feedback channel. Output within a time period; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Output after the specified time; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Output after the specified time; The output is divided into steady-state and transient states using a window function: , , in, express The steady-state output of the driving signal after a given time interval; express The driving signal during the time period Transient output after time step; , , in Indicates in The sampling pulse signal at time is fed back through the feedback channel. Steady-state output after time step; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Transient output after time step; The sampled signal at time t equals the historical signal. Steady-state output at the current moment: , When time is Within the specified time, the robotic arm outputs: , Separate transient and steady states: , , , in express The driving signal during the time period Steady-state output after time step; express The driving signal during the time period Transient output after time step; , , in Indicates in The sampling pulse signal at time is fed back through the feedback channel. Steady-state output after time step; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Transient output after time step; , , in Indicates in The sampling pulse signal at time is fed back through the feedback channel. Steady-state output after time step; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Transient output after time step; Sampling signal at time Equals the steady-state output of the historical signal at the current moment: ; When time is When the time limit is reached, the output is obtained as follows: , Separate the steady-state and transient states of the corresponding terms: , in, , , in express The driving signal during the time period Steady-state output after time step; express The driving signal during the time period Transient output after time step; Sampling signal at time Equals the steady-state output of the historical signal at the current moment: ; Step 2.5 yields the transient superposition output: , in express Transient output after a certain time.

[0015] Step 3 includes: Step 3.1, construct the transient cost function cost of the robotic arm output: , Where d represents the differential symbol; Step 3.2: Set constraints based on engineering application limitations; Step 3.3: Optimize the parameters using the particle swarm optimization algorithm: Optimization variables: Optimize control gain and pulse interval; Algorithm parameters: set population size, number of iterations, inertia weight, and learning factor; Optimized output: Obtain the optimal control gain and pulse interval of the robotic arm output, and obtain the optimal control parameters.

[0016] Step 4 includes: integrating steps 1 to 3, developing standardized operating procedures, parameter selection specifications, and experimental verification methods, and forming a standardized process for transient oscillation analysis and optimization of robotic arm pulse control that can be directly applied to engineering practice.

[0017] The present invention also provides an electronic device, including a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method.

[0018] The present invention also provides a storage medium storing a computer program or instructions that, when the computer program or instructions are run on a computer, execute the steps of the method described.

[0019] The present invention has the following beneficial effects: 1. An innovative dual-channel independent impulse response modeling method is proposed, breaking through the limitations of traditional single-system modeling: Unlike existing technologies that establish overall second-order differential equations based on the rigid body dynamics of robotic arms, this invention decomposes the robotic arm closed-loop system into two independent subsystems: a forward drive channel and a feedback adjustment channel. It establishes impulse response models for each channel, accurately characterizing the dynamic response lag and flexible resonance characteristics of the forward channel, as well as the sensing delay and filtering attenuation characteristics of the feedback channel. This invention analyzes the generation mechanism of transient oscillations from the root of the system structure, solving the technical deficiency of traditional models that cannot reflect the actual dynamic characteristics of the channels.

[0020] 2. Construct a full-time-domain transient oscillation quantitative analysis system to achieve accurate characterization of oscillation characteristics: To address the problem that existing technologies cannot quantify key indicators such as transient oscillation amplitude, frequency, and decay rate, this paper derives a superposition formula for transient response under pulse control signal based on a dual-channel impulse response model. A quantitative analysis method for transient oscillations across the entire time domain is established, which can accurately calculate core indicators such as oscillation peak value, overshoot, settling time, and decay rate. The influence weight of the coupling effect between the forward and feedback channels on transient oscillations is clarified, providing precise data support for oscillation suppression optimization.

[0021] 3. A smart and precise parameter optimization strategy is proposed to achieve root cause suppression of transient oscillations: Abandoning the traditional optimization method of blindly adjusting control parameters, this paper designs a targeted intelligent optimization algorithm by combining the dual-channel impulse response characteristics and transient quantization indicators. This algorithm performs coordinated optimization of pulse control signal parameters (pulse amplitude, frequency, duty cycle) and feedback adjustment parameters, realizing closed-loop control of "modeling-quantization-optimization". This reduces transient oscillations caused by dual-channel coupled excitation at the source, while taking into account the steady-state accuracy and transient stability of the system. This solves the problems of poor oscillation suppression and easy impact on steady-state performance of existing optimization methods.

[0022] 4. Adaptable to various engineering applications, highly practical and compatible: The analysis method proposed in this invention does not require large-scale modification of existing robotic arm hardware systems and can be directly adapted to various pulse-controlled robotic arm systems such as industrial robots, collaborative robots, and surgical robots. It is especially suitable for scenarios with stringent requirements for transient stability, such as thin-walled component grasping, precision assembly, and medical intervention. At the same time, it is compatible with various existing pulse feedback control architectures, resulting in low engineering implementation costs and wide adaptability. Attached Figure Description

[0023] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0024] Figure 1 This is a flowchart of the method of the present invention.

[0025] Figure 2 The simulation diagram for Example 1 (pulse interval is 1) shows time on the horizontal axis and the oscillation output of the robotic arm on the vertical axis.

[0026] Figure 3 The simulation diagram for Example 1 (pulse interval is 0.5) shows time on the horizontal axis and the oscillation output of the robotic arm on the vertical axis. Detailed Implementation

[0027] like Figure 1 As shown, this embodiment of the invention provides a method for analyzing transient oscillations in robotic arm pulse control based on the response characteristics of forward and feedback channels, including the following steps: Step 1: Establish the unit impulse response of the forward drive channel and the feedback channel; Step 2: Derive the full-time transient output expression under pulse control and analyze the oscillation superposition law; Step 3: With the goal of minimizing transient oscillations, the pulse control parameters and feedback adjustment parameters are optimized in a coordinated manner by combining the dual-channel impulse response characteristics and transient quantization indicators. Step 4: Develop an analysis and optimization process for transient oscillations in the pulse control of the robotic arm.

[0028] Step 1 includes the following steps: Step 1.1, Module decomposition and function definition; The robotic arm control system is divided into a forward channel and a feedback channel: Forward path: Drive motors, robotic arms, etc., converting power into displacement output signals for the robotic arm; Feedback channel: Detection sensors, pulse switches, pulse controllers, etc., to enable the robotic arm's output signal to be fed back to the drive motor input through sampled pulses, and to achieve error adjustment through pulse feedback; Step 1.2, Module impulse response modeling; Impulse response models for the forward and feedback channels were established separately (avoiding complex physical mechanism modeling, a simplified two-parameter model was established to balance accuracy and engineering feasibility) to characterize the dynamic response characteristics under a unit impulse signal. The specific model is as follows: , in, It is the forward channel unit impulse response; It is the forward channel response amplitude coefficient; t is the forward path attenuation coefficient, reflecting the convergence speed of the drive system response; t is time. Feedback channel impulse response model: , in It is the unit impulse response of the feedback channel; It is the response amplitude coefficient of the feedback channel; It is the feedback channel attenuation coefficient, which reflects the convergence speed of the drive system response.

[0029] Step 1.3, Model Transformation and Parameter Identification; includes the following steps: Step 1.3.1, Establishing Input-Output Relationships: Establish the input-output relationships of each module through convolution operations.

[0030] Construct input-output impulse response convolutional models for the forward and feedback channels respectively: , Among them, symbols The convolution operation is represented by , and j represents the subscripts b and f, respectively, indicating the feedback channel impulse response model and the forward channel impulse response model. This represents the corresponding model input. and These represent the feedback channel output and the forward channel output, respectively. Step 1.3.2, Model Simplification: The model in step 1.3.1 is a long memory decay model. Based on the decay characteristics, the long memory model is truncated to obtain a segment memory convolution model. On this basis, the convolution model is transformed into an algebraic model using the Legendre transform.

[0031] Parameter identification: Experiments were conducted on the forward and feedback channels (with the pulse switch always closed). Input and output data were collected, and the least squares method was used to identify the unknown parameters of the forward and feedback channel models, thus obtaining the parameters of the forward channel. and feedback channels Impulse response model.

[0032] Step 2 includes the following steps: Step 2.1, Pulse control signal modeling; The pulse control input is represented as a delayed pulse sequence: , in Indicates the output of the robotic arm Ideal pulse sampling, For the gain of the j-th pulse, The pulse trigger time, The Dirac impulse function; Step 2.2: Based on the convolution relationship, obtain the output of the feedback channel; The feedback channel output is obtained by considering the response characteristics of the feedback channel (using the convolution delay characteristics of the impulse function): ; Note: Due to the response characteristics of the feedback channel, the pulse feedback input signal is not an ideal sampling signal.

[0033] Step 2.3, robotic arm output; The robotic arm output is calculated based on the forward and feedback channels, including the reference signal. Both the feedback channel output and the forward channel output will affect the forward channel output, and will be calculated separately: ; Step 2.4, Separate transient and steady state (segmented according to trigger time); Based on the memory characteristics of convolution, the steady state and transient state are separated according to the trigger time, and transient analysis is performed to establish a transient analysis method.

[0034] When time is When within a time period: Robotic arm output: , The second item indicates the output of the first sample through the feedback channel.

[0035] When time is Within the specified time, the robotic arm outputs: , Because convolution has memory properties, not only does the past input affect the current output, but the past feedback signal may not necessarily disappear. Depending on the length of the feedback channel memory, it will also affect the current process. The process by which the past input affects the current output is called a transient process.

[0036] Introducing a step function Construct window function The starting point of the window function is The destination is The output is: , in, express The output generated by the drive signal within a time period; express The output generated by the drive signal after a certain time; Indicates in The sampled pulse signal at time 10 is fed back through the feedback channel. The output within a time period acts as feedback on the input. Indicates in The sampling pulse signal at time is fed back through the feedback channel. The output after a certain time has a feedback effect on the input. Indicates in The sampling pulse signal at time is fed back through the feedback channel. The output after a certain time point serves as feedback to the input. Note: Due to the memory characteristics of convolution, and At any moment The output is not necessarily zero; there is also a transient state. Therefore, a window function is used to divide the output into steady-state and transient states: , , in, express The steady-state output of the driving signal after a given time interval; express The driving signal during the time period Transient output after time step; , , in Indicates in The sampling pulse signal at time is fed back through the feedback channel. Steady-state output after time step; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Transient output after time step; The sampled signal at time t equals the historical signal. Steady-state output at the current moment: , When time is Within the specified time, the robotic arm outputs: , Three pulse feedbacks were received within this time period. Based on the previous feedback, a new steady-state value transient needs to be calculated. The transient and steady-state states are then separated: , , , in express The driving signal during the time period Steady-state output after time step; express The driving signal during the time period Transient output after time step; , , in Indicates in The sampling pulse signal at time is fed back through the feedback channel. Steady-state output after time step; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Transient output after time step; , , in Indicates in The sampling pulse signal at time is fed back through the feedback channel. Steady-state output after time step; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Transient output after time step; Sampling signal at time Equals the steady-state output of the historical signal at the current moment: ; When time is Within a given time frame, step by step, the output is obtained: , Separate the steady-state and transient states of the corresponding terms: , in, , , in express The driving signal during the time period Steady-state output after time step; express The driving signal during the time period Transient output after time step; Sampling signal at time Equals the steady-state output of the historical signal at the current moment: ; Step 2.5, transient superposition law; According to step 2.3, the transient oscillation at any given time is the superposition of all transients prior to that time: The robotic arm's output transient is composed of all historical transients, including those generated by historical input signals and historical feedback signals. Therefore, the result is a superimposed output of transients: , in express The transient output after a given time step is related to all historical processes. Due to the system's decay characteristics, historical transients decay over time, and can be ignored when the transient approaches zero. In engineering, based on the decay characteristics, a suitable historical length of transients is selected for study.

[0037] Step 3 includes: The collaborative optimization is based on the optimal transient oscillation amplitude, and optimizes the control parameters: under the premise of given the impulse response of the forward channel and feedback channel of the system, optimize the control parameters such as control gain and pulse control interval, optimize the transient performance of the robotic arm, reduce oscillation, and improve control accuracy.

[0038] Step 3.1: Establish the transient cost function for the robotic arm output; Based on the transient superposition equation established in step 2, construct the cost function cost: , Where d represents the differential symbol; Step 3.2: Set constraints based on engineering application limitations; Step 3.3: Optimize the parameters using the particle swarm optimization algorithm: Optimization variables: Optimize control gain and pulse interval; Algorithm parameters: Population size 30, number of iterations 50, inertia weight 0.7, learning factor .

[0039] Optimized output: Obtain the optimal control gain and pulse interval of the robotic arm output, and obtain the optimal control parameters.

[0040] Step 4 includes: integrating all the steps of dual-channel modeling, full-time transient analysis, and intelligent parameter optimization mentioned above, formulating standardized operating procedures, parameter selection specifications, and experimental verification methods, forming a standardized process for transient oscillation analysis and optimization of robot arm pulse control that can be directly applied to engineering practice; this process does not require large-scale modification of existing robot arm hardware systems and can be directly adapted to various pulse feedback control robot arm systems.

[0041] In a specific embodiment of the present invention, suppose the forward impulse response of a robotic arm is as follows: ; Feedback channel impulse response: ; The pulse control gain is set to 1. The pulse intervals were selected sequentially, and the simulation results are as follows: Figure 2 (Pulse interval 1) Figure 3 (Pulse interval is 0.5) as shown.

[0042] Any closed-loop control system consists of a forward path and a feedback path, both of which are physically constructed and possess their own response characteristics. Due to these response characteristics, pulse control inevitably results in transient responses, causing transient oscillations in the system output. This invention, starting from the response characteristics of a robotic arm, reveals the mechanism of transient generation in pulse control of a robotic arm. Simulation results are consistent with theoretical analysis, verifying the effectiveness of the proposed method.

[0043] This invention proposes a transient analysis method for robotic arm pulse control based on the response characteristics of the forward and feedback channels. While based on robotic arm pulse control, this method relies heavily on the response characteristics of the forward and feedback channels. Almost all pulse feedback control systems consist of forward and feedback channels. Therefore, this invention is not limited to the transient output of robotic arm pulse control but can also be applied to other transient analysis scenarios involving pulse feedback control.

[0044] This invention provides a transient oscillation analysis method for robotic arm pulse control based on the response characteristics of forward and feedback channels. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A transient oscillation analysis method for robotic arm pulse control based on forward and feedback channel response characteristics, characterized in that, Includes the following steps: Step 1: Establish the unit impulse response of the forward drive channel and the feedback channel; Step 2: Derive the full-time transient output expression under pulse control and analyze the oscillation superposition law; Step 3: With the goal of minimizing transient oscillations, the pulse control parameters and feedback adjustment parameters are optimized in a coordinated manner by combining the dual-channel impulse response characteristics and transient quantization indicators. Step 4: Develop an analysis and optimization process for transient oscillations in the pulse control of the robotic arm.

2. The method according to claim 1, characterized in that, Step 1 includes the following steps: Step 1.1, Module decomposition and function definition; Step 1.2, Module impulse response modeling; Step 1.3, Model transformation and parameter identification.

3. The method according to claim 2, characterized in that, Step 1.1 includes: dividing the robotic arm control system into a forward channel and a feedback channel. Forward path: includes drive motor and robotic arm, converting power into robotic arm displacement output signal; Feedback channel: includes detection sensors, pulse switches and pulse controllers, which enable the robotic arm output signal to be fed back to the drive motor input through sampling pulses, and error adjustment is achieved through pulse feedback.

4. The method according to claim 3, characterized in that, Step 1.2 includes: establishing impulse response models for the forward channel and feedback channel, respectively; Forward channel impulse response model: The dynamic response process of the power output is characterized by an exponentially decaying function, expressed as follows: ， in, It is the forward channel unit impulse response; It is the forward channel response amplitude coefficient; t is the forward channel attenuation coefficient; e is time; e is the natural constant. Feedback channel impulse response model: ， in It is the unit impulse response of the feedback channel; It is the response amplitude coefficient of the feedback channel; It is the feedback channel attenuation coefficient.

5. The method according to claim 4, characterized in that, Step 1.3 includes: Step 1.3.1: Establish the input-output relationship of each module through convolution operation; Construct input-output impulse response convolutional models for the forward and feedback channels respectively: ， Among them, symbols The convolution operation is represented by , and j represents the subscripts b and f, respectively, indicating the feedback channel impulse response model and the forward channel impulse response model. This represents the corresponding model input. and These represent the feedback channel output and the forward channel output, respectively. Step 1.3.2, Model Simplification: Transform the convolutional model into an algebraic model using the Legendre transform; Parameter identification: Forward and feedback channel experiments were conducted. Input and output data were collected, and the least squares method was used to identify the unknown parameters of the forward and feedback channel models, thus obtaining the parameters of the forward channel. and feedback channels Impulse response model.

6. The method according to claim 5, characterized in that, Step 2 includes: Step 2.1, Pulse control signal modeling; Pulse control input Represented as a delayed pulse sequence: ， in Indicates the output of the robotic arm Ideal pulse sampling, For the gain of the j-th pulse, The pulse trigger time, The Dirac impulse function; Step 2.2: Based on the convolution relationship, obtain the output of the feedback channel; The feedback channel output is obtained by considering the response characteristics of the feedback channel: ； Step 2.3: Calculate the robotic arm output based on the forward and feedback channels: ； Step 2.4: Based on the convolutional memory characteristics, the steady-state and transient states are separated according to the trigger time segment, transient analysis is performed, and a transient analysis method is established. When the time is within... When within a time period: Robotic arm output: ， When time is Within the specified time, the robotic arm outputs: ， Introducing a step function Construct window function The starting point of the window function is The destination is The output is: ， in, express The output generated by the drive signal within a time period; express The output generated by the drive signal after a certain time; Indicates in The sampled pulse signal at time 10 is fed back through the feedback channel. Output within a time period; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Output after the specified time; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Output after the specified time; The output is divided into steady-state and transient states using a window function: ， ， in, express The steady-state output of the driving signal after a given time interval; express The driving signal during the time period Transient output after time step; ， ， in Indicates in The sampling pulse signal at time is fed back through the feedback channel. Steady-state output after time step; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Transient output after time step; The sampled signal at time t equals the historical signal. Steady-state output at the current moment: ， When time is Within the specified time, the robotic arm outputs: ， Separate transient and steady states: ， ， ， in express The driving signal during the time period Steady-state output after time step; express The driving signal during the time period Transient output after time step; ， ， in Indicates in The sampling pulse signal at time is fed back through the feedback channel. Steady-state output after time step; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Transient output after time step; ， ， in Indicates in The sampling pulse signal at time is fed back through the feedback channel. Steady-state output after time step; Indicates in The sampling pulse signal at time is fed back through the feedback channel. Transient output after time step; Sampling signal at time Equals the steady-state output of the historical signal at the current moment: ； When time is When the time limit is reached, the output is obtained as follows: ， Separate the steady-state and transient states of the corresponding terms: ， in, ， ， in express The driving signal during the time period Steady-state output after time step; express The driving signal during the time period Transient output after time step; Sampling signal at time Equals the steady-state output of the historical signal at the current moment: ； Step 2.5 yields the transient superposition output: ， in express Transient output after a certain time.

7. The method according to claim 6, characterized in that, Step 3 includes: Step 3.1, construct the transient cost function cost of the robotic arm output: ， Where d represents the differential symbol; Step 3.2: Set constraints based on engineering application limitations; Step 3.3: Optimize the parameters using the particle swarm optimization algorithm: Optimization variables: Optimize control gain and pulse interval; Algorithm parameters: set population size, number of iterations, inertia weight, and learning factor; Optimized output: Obtain the optimal control gain and pulse interval of the robotic arm output, and obtain the optimal control parameters.

8. The method according to claim 7, characterized in that, Step 4 includes: integrating steps 1 to 3, developing standardized operating procedures, parameter selection specifications, and experimental verification methods, and forming a standardized process for transient oscillation analysis and optimization of robotic arm pulse control that can be directly applied to engineering practice.

9. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1 to 8.

10. A storage medium, characterized in that, It stores a computer program or instructions that, when run on a computer, perform the steps of the method as described in any one of claims 1 to 8.

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