SEA frequency analysis and vibration suppression method based on dynamic modeling

Abstract

The invention belongs to the field of robot control, and particularly relates to an SEA frequency analysis and vibration suppression method based on dynamic modeling, which comprises the following steps: S1, establishing a dynamic model of a series elastic actuator SEA, and analyzing the natural vibration frequency and stability of a robot system through the dynamic model of the series elastic actuator SEA to obtain a series elastic actuator SEA model; determining a frequency range which may cause vibration in the input control quantity; s2, designing an observer, and analyzing the dynamic natural vibration frequency, caused by load change, of the kinetic model of the series elastic actuator SEA in real time; and S3, designing a notch filter to filter the input control quantity, and filtering vibration frequency components. The method can effectively solve the problem that in the prior art, vibration is generated due to the fact that the input control quantity contains the natural vibration frequency of a spring system in the motion process of the SEA, and the motion precision and stability of the robot are improved.

Description

Technical Field

[0001] This invention belongs to the field of robot control, specifically a method for SEA frequency analysis and vibration suppression based on dynamic modeling. Background Technology

[0002] Series elastic actuators (SEAs) are widely used in robotics due to their high energy efficiency and good compliance. However, during actual motion, SEAs often exhibit vibration, which severely affects the robot's motion accuracy and stability. Research has found that this vibration is mainly caused by the inclusion of the spring system's natural frequency in the input control quantity, thus triggering system vibration. Currently, although some vibration suppression methods have been proposed, most of them have certain limitations and cannot effectively solve the vibration problem of SEAs under complex load conditions. Summary of the Invention

[0003] The purpose of this invention is to provide a frequency analysis and vibration suppression method for series elastic actuators (SEAs) based on dynamic modeling, in order to solve the problem in the prior art that the SEA vibrates during motion because the input control quantity includes the natural frequency of the spring system.

[0004] The technical solution adopted by this invention to achieve the above objectives is: a SEA frequency analysis and vibration suppression method based on dynamic modeling, comprising the following steps:

[0005] Step S1: Establish a dynamic model of the series elastic actuator (SEA), analyze the natural frequency and stability of the robot system through the dynamic model of the series elastic actuator (SEA), and determine the frequency range that may cause vibration in the input control quantity;

[0006] Step S2: Design an observer to analyze the dynamic natural frequency of the series elastic actuator SEA caused by load changes in real time;

[0007] Step S3: Design a notch filter to filter the input control quantity and remove the vibration frequency component.

[0008] The establishment of the dynamic model for the series elastic actuator SEA is specifically as follows:

[0009] If the series elastic actuator SEA consists of a motor, a spring, and a load, then its motor end equation is:

[0010]

[0011] Its load-side equation is:

[0012]

[0013] Among them, Jm Let be the moment of inertia of the motor rotor. Let b be the angular acceleration of the motor rotor. m This is the damping coefficient at the motor end. τ is the angular velocity of the motor rotor. m k is the electromagnetic torque output by the motor. s θ is the stiffness coefficient of the elastic element. m Let θ be the angular displacement of the motor rotor. t θ is the angular displacement at the load end of the elastic element. m -θ t It represents the deformation of the spring and is proportional to the spring torque;

[0014] The system's natural frequency is obtained by solving the characteristic equation, and the system's stability is determined based on the real part of the eigenvalues.

[0015] The designed observer is specifically as follows:

[0016] S2-1: Set the input of the observer to the displacement, velocity and load change information of the series elastic actuator SEA, and the output to the dynamic natural frequency of the series elastic actuator SEA;

[0017] S2-2: The structure of the observer is then represented as follows:

[0018]

[0019] in, Let L be the output of the observer, I be the gain matrix of the observer, C and K be the matrix coefficients;

[0020] S2-3: Adjust the value of the gain matrix L of the observer to change the dynamic response characteristics of the observer, so that the observer can accurately analyze the dynamic natural frequency of the series elastic actuator SEA caused by load changes in real time.

[0021] The gain matrix L is dynamically adjusted according to the load change rate: when the load change rate exceeds the threshold, the value of L is increased to improve the frequency tracking speed.

[0022] The notch filter design is specifically as follows:

[0023] Based on the natural frequency range obtained from dynamic modeling analysis and the dynamic natural frequency obtained from real-time observation, the parameters of the notch filter are designed; then the transfer function of the notch filter is expressed as:

[0024]

[0025] Where, ω n ζ is the notch frequency, and ζ is the damping ratio;

[0026] The notch filter uses a dual-frequency drive parameter configuration:

[0027] The notch frequency ω of the notch filter n The possible values ​​for include:

[0028] Fundamental frequency: a safe range derived from the dynamic model;

[0029] Real-time frequency: The dynamic natural frequency ω output by the observer. n (t).

[0030] The notch filter is equipped with an online parameter migration mechanism, specifically:

[0031] a. Set the dynamic frequency change threshold Δω = 5% × ω n (t) serves as the trigger condition for updating filter coefficients;

[0032] b. When the real-time frequency ω output by the observer n When the deviation of (t) from the current notch frequency exceeds Δω, the transfer function of the notch filter in the filter is immediately refreshed through the parameter migration channel. Coefficients of terms in the denominator and the terms in the subtotal;

[0033] c. The migration process is completed within a single control cycle, avoiding control interruption.

[0034] It also includes: a closed-loop feedback mechanism, specifically:

[0035] When the vibration suppression effect fails to meet the standard, the residual vibration amplitude at the output end of the series elastic actuator SEA is detected in real time by a torque sensor.

[0036] When the residual amplitude exceeds the safety threshold, a feedback signal is triggered to the observer;

[0037] The observer resets the initial value of the gain matrix L based on the feedback signal and recalculates the dynamic natural frequency ω. n (t) enables closed-loop frequency calibration.

[0038] The filtering of the input control quantity to remove vibration frequency components specifically involves:

[0039] S3-1: By passing the input control quantity through a notch filter, the filtered control quantity τ is obtained. f ,Right now:

[0040] τ f =H(s)τ

[0041] S3-2: Input the filtered control quantity into the series elastic actuator SEA to effectively suppress the vibration of the series elastic actuator SEA.

[0042] The present invention has the following beneficial effects and advantages:

[0043] 1. This invention, through dynamic modeling, can accurately analyze the natural frequency and stability of the SEA, providing a theoretical basis for vibration suppression.

[0044] 2. The observer designed in this invention can monitor load changes in real time and analyze the dynamic natural frequency, enabling the vibration suppression method to adapt to the working state of SEA under different load conditions, thus improving the real-time performance and effectiveness of vibration suppression.

[0045] 3. The notch filter designed in this invention can effectively filter out the vibration frequency components in the input control quantity, thereby significantly reducing the vibration of the SEA and improving the motion accuracy and stability of the robot. Attached Figure Description

[0046] Figure 1 The dynamic modeling and simulation effect diagram of this invention;

[0047] Figure 2 The flowchart of the SEA frequency analysis and vibration suppression method based on dynamic modeling of the present invention;

[0048] Figure 3 Flowchart of dynamic modeling and frequency analysis of the present invention;

[0049] Figure 4 Flowchart of the dynamic frequency observer design of this invention;

[0050] Figure 5 A schematic diagram illustrating the principle of the adaptive notch filter of this invention;

[0051] Figure 6 Schematic diagram of the closed-loop control principle of this invention;

[0052] Figure 7 Flowchart illustrating the principle of the dynamic parameter update mechanism of this invention. Detailed Implementation

[0053] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0054] like Figure 2 The diagram shows a flowchart of the frequency analysis and vibration suppression method of this invention. The main flow of this aspect demonstrates the closed-loop control architecture of the SEA vibration suppression system. Starting with establishing an accurate dynamic model, the system's natural vibration frequency range is determined through theoretical analysis. Subsequently, a load observer is used to sense load changes in real time and calculate the dynamic natural frequency. Finally, based on this frequency, the notch filter parameters are dynamically configured to achieve precise filtering of the control signal.

[0055] This invention discloses a method for SEA frequency analysis and vibration suppression based on dynamic modeling, specifically including the following steps:

[0056] S1: Analyze the system's natural frequencies and stability through dynamic modeling. First, establish a dynamic model of the SEA, which can accurately describe the dynamic characteristics of the SEA under different motion states. Then, use this model to analyze the system's natural frequencies and stability, and determine the frequency range of the input control variables that may cause vibration.

[0057] The frequency analysis and vibration suppression method of this invention achieves the following dynamic modeling and simulation results: Figure 1 As shown, the horizontal axis represents time, the vertical axis of the top graph represents the output angle, and the vertical axis of the bottom graph represents the output torque. The left side shows the state under light load, and the right side shows the state under heavy load. The obvious vibration is consistent with reality, indicating that the model is accurately established.

[0058] S2: Design an observer to analyze the dynamic natural frequency of the SEA caused by load changes in real time. Since the load on the SEA changes continuously during actual operation, its natural frequency will dynamically change. Therefore, design an observer that can monitor load changes in real time and analyze the dynamic natural frequency of the SEA based on these changes, providing accurate frequency information for subsequent vibration suppression.

[0059] S3: Design a notch filter to filter the input control signal, removing frequencies that cause vibration. Based on the natural frequency range obtained from dynamic modeling analysis and the dynamic natural frequency obtained from real-time observation, design a notch filter. This filter can remove frequency components in the input control signal that cause vibration, thereby effectively suppressing the vibration of the SEA.

[0060] Example:

[0061] (I) Dynamic Modeling

[0062] 1-1) Establish the dynamic model of the SEA. Assuming the SEA consists of a motor, springs, and a load, its dynamic equations can be expressed as: Motor end: Load side:

[0063] Among them, J m Moment of inertia of motor rotor (unit: kg·m) 2 This reflects the ability of the motor rotor to resist changes in speed. Angular acceleration of the motor rotor (unit: rad / s) 2 b m Damping coefficient at the motor end (unit: N·m·s / rad) represents losses such as motor bearing friction and wind resistance. Angular velocity of the motor rotor (unit: rad / s). τ m The electromagnetic torque output by the motor (unit: N·m) is the active driving force of the system. s θ: The stiffness coefficient (unit: N·m / rad) of an elastic element (spring), describing the elastic characteristics of the spring. m θ: Angular displacement of the motor rotor (unit: rad). t Angular displacement (unit: rad) at the output end (load end) of the elastic element. (θ) m -θ t ): The deformation of a spring (unit: rad), which is directly proportional to the spring torque.

[0064] 1-2) Use this dynamic model to analyze the system's natural frequencies and stability. By solving the system's characteristic equations, the system's natural frequencies can be obtained. Simultaneously, the stability of the system can be determined based on the real and imaginary parts of its eigenvalues.

[0065] like Figure 3 The diagram shown is a dynamic modeling and frequency analysis diagram. This invention is based on the motor end equations of SEA (including electromagnetic torque τ). m Combine the spring deformation term and the load-end equation (including the gravity disturbance term) to construct the system characteristic equation. Solve for the eigenvalues:

[0066] The sign of the real part determines the stability of the system (if the real part > 0, the system is unstable).

[0067] The range of natural frequencies is obtained by calculating the imaginary part (ω=√(imaginary part)). 2 ))

[0068] The innovation lies in the dual-end coupling modeling: simultaneously considering the motor inertia (J m ) and load nonlinearity (m l gLsinθ l This provides accurate frequency boundary conditions for subsequent filtering.

[0069] (II) Observer Design

[0070] 2-1) Design the structure of the observer, such as Figure 4 As shown, the input of the observer is the displacement, velocity and load change information of the SEA, and the output is the dynamic natural frequency of the SEA.

[0071] The observer employs a multi-source data fusion architecture:

[0072] Input layer: Displacement θ (position sensor), velocity (Encoder differential), load change ΔJ l (Torque sensor)

[0073] Core Algorithm:

[0074] in, Let L be the observer's output, I be the identity matrix, and C and K be the matrix coefficients. The gain matrix L is dynamically compensated through adaptive adjustment, and the (IL) term ensures observation robustness during load abrupt changes.

[0075] Output layer: Real-time natural frequency ωn(t);

[0076] 2-2) Adjust the gain matrix of the observer to enable it to analyze the dynamic natural frequency of the SEA caused by load changes in real time and accurately. By adjusting the value of the gain matrix (L), the dynamic response characteristics of the observer can be changed, enabling it to quickly and accurately track the dynamic natural frequency of the SEA.

[0077] Its innovation lies in the variable gain mechanism: when the load change rate exceeds the threshold, the L value is automatically increased to improve the frequency tracking speed (E judgment box in the figure), and the response time can reach the millisecond level.

[0078] (III) Notch Filter Design

[0079] 3-1) Based on the natural frequency range obtained from dynamic modeling analysis and the dynamic natural frequency obtained from real-time observation, design the parameters of the notch filter. The transfer function of the notch filter can be expressed as: Where, ω n ζ is the notch frequency, and ζ is the damping ratio.

[0080] 3-2) The designed notch filter is applied to the input control quantity to filter out the frequency components that cause vibration. By passing the input control quantity τ through the notch filter, the filtered control quantity τ is obtained. f That is: τ f =H(s)τ, then the filtered control quantity τ f The input is fed into the SEA, thereby effectively suppressing SEA vibration.

[0081] like Figure 5 As shown, the filter implements dual-frequency drive parameter configuration:

[0082] Fundamental frequency: A fixed safety margin derived from the dynamic model (to prevent model errors).

[0083] Real-time frequency: ω output by the observer n (t)(Responding to load disturbances)

[0084] In the transfer function: molecule In ω nA deep notch is generated at the point (>40dB attenuation), and the denominator damping ratio ζ is taken as 0.1-0.5 (to balance the filter depth and phase delay);

[0085] The innovative advantage of this invention in designing a notch filter lies in its online parameter transfer: when ω n When the change in (t) exceeds 5%, the filter coefficients are refreshed in real time (G→B arrow) to avoid the failure of traditional fixed filters.

[0086] According to the overall design of this invention, a real-time adjustment loop of "controller → filter → SEA → observer → filter" is formed, which improves the vibration suppression rate by more than 60% compared with the open-loop system. The specific steps are as follows:

[0087] 1) When the vibration suppression effect fails to meet the standard, the residual vibration amplitude at the output end of the series elastic actuator SEA is detected in real time by a torque sensor;

[0088] 2) When the residual amplitude exceeds the safety threshold, a feedback signal is triggered to the observer;

[0089] 3) The observer resets the initial value of the gain matrix L based on the feedback signal and recalculates the dynamic natural frequency ω. n (t), to achieve frequency calibration closed loop, the closed loop control principle is as follows: Figure 6 As shown.

[0090] like Figure 7 The diagram shown illustrates the principle of the dynamic parameter update mechanism of this invention. The notch filter of this invention is equipped with an online parameter migration mechanism, specifically:

[0091] a. Set the dynamic frequency change threshold Δω = 5% × ω n (t) serves as the trigger condition for updating filter coefficients;

[0092] b. When the real-time frequency ω output by the observer n When the deviation of (t) from the current notch frequency exceeds Δω, the transfer function of the notch filter in the filter is immediately refreshed through the parameter migration channel. Coefficients of terms in the denominator and the terms in the subtotal;

[0093] c. The migration process is completed within a single control cycle, avoiding control interruption.

[0094] In summary, by combining the above embodiments, this invention effectively solves the problem of vibration in the SEA during motion due to the inclusion of the spring system's natural frequency in the input control quantity, thus improving the robot's motion accuracy and stability. The entire process forms a closed loop of "modeling-monitoring-suppression": when vibration suppression fails to meet the standard, the system automatically returns to the observer stage to recalibrate the frequency (feedback loop arrow). This design addresses the pain point of traditional methods being unable to adapt to dynamic load changes, achieving vibration suppression under all working conditions.

[0095] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0096] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A method for SEA frequency analysis and vibration suppression based on dynamic modeling, characterized in that, Includes the following steps: Step S1: Establish a dynamic model of the series elastic actuator (SEA), analyze the natural frequency and stability of the robot system through the dynamic model of the series elastic actuator (SEA), and determine the frequency range that may cause vibration in the input control quantity; Step S2: Design an observer to analyze the dynamic natural frequency of the series elastic actuator SEA caused by load changes in real time; Step S3: Design a notch filter to filter the input control quantity and remove the vibration frequency component.

2. The SEA frequency analysis and vibration suppression method based on dynamic modeling according to claim 1, characterized in that, The establishment of the dynamic model for the series elastic actuator SEA is specifically as follows: If the series elastic actuator SEA consists of a motor, a spring, and a load, then its motor end equation is: Its load-side equation is: Among them, J m Let be the moment of inertia of the motor rotor. Let b be the angular acceleration of the motor rotor. m The damping coefficient at the motor end is... τ is the angular velocity of the motor rotor. m k is the electromagnetic torque output by the motor. s θ is the stiffness coefficient of the elastic element. m Let θ be the angular displacement of the motor rotor. t θ is the angular displacement at the load end of the elastic element. m -θ t It represents the deformation of the spring and is proportional to the spring torque; The system's natural frequency is obtained by solving the characteristic equation, and the system's stability is determined based on the real part of the eigenvalues.

3. The SEA frequency analysis and vibration suppression method based on dynamic modeling according to claim 1, characterized in that, The designed observer is specifically as follows: S2-1: Set the input of the observer to the displacement, velocity and load change information of the series elastic actuator SEA, and the output to the dynamic natural frequency of the series elastic actuator SEA; S2-2: The structure of the observer is then represented as follows: in, Let L be the output of the observer, I be the gain matrix of the observer, C and K be the matrix coefficients; S2-3: Adjust the value of the gain matrix L of the observer to change the dynamic response characteristics of the observer, so that the observer can accurately analyze the dynamic natural frequency of the series elastic actuator SEA caused by load changes in real time. The gain matrix L is dynamically adjusted according to the load change rate: when the load change rate exceeds the threshold, the value of L is increased to improve the frequency tracking speed.

4. The SEA frequency analysis and vibration suppression method based on dynamic modeling according to claim 1, characterized in that, The notch filter design is specifically as follows: Based on the natural frequency range obtained from dynamic modeling analysis and the dynamic natural frequency obtained from real-time observation, the parameters of the notch filter are designed; then the transfer function of the notch filter is expressed as: Where, ω n ζ is the notch frequency, and ζ is the damping ratio.

5. The SEA frequency analysis and vibration suppression method based on dynamic modeling according to claim 4, characterized in that, The notch filter uses a dual-frequency drive parameter configuration: The notch frequency ω of the notch filter n The possible values ​​for include: Fundamental frequency: a safe range derived from the dynamic model; Real-time frequency: The dynamic natural frequency ω output by the observer. n (t).

6. The SEA frequency analysis and vibration suppression method based on dynamic modeling according to claim 4, characterized in that, The notch filter is equipped with an online parameter migration mechanism, specifically: a. Set the dynamic frequency change threshold Δω = 5% × ω n (t) serves as the trigger condition for updating filter coefficients; b. When the real-time frequency ω output by the observer n When the deviation of (t) from the current notch frequency exceeds Δω, the transfer function of the notch filter in the filter is immediately refreshed through the parameter migration channel. Coefficients of terms in the denominator and the terms in the subtotal; c. The migration process is completed within a single control cycle, avoiding control interruption.

7. The SEA frequency analysis and vibration suppression method based on dynamic modeling according to claim 1, characterized in that, It also includes: a closed-loop feedback mechanism, specifically: When the vibration suppression effect fails to meet the standard, the residual vibration amplitude at the output end of the series elastic actuator SEA is detected in real time by a torque sensor. When the residual amplitude exceeds the safety threshold, a feedback signal is triggered to the observer; The observer resets the initial value of the gain matrix L based on the feedback signal and recalculates the dynamic natural frequency ω. n (t) is used to achieve closed-loop frequency calibration.

8. The SEA frequency analysis and vibration suppression method based on dynamic modeling according to claim 1, characterized in that, The filtering of the input control quantity to remove vibration frequency components specifically involves: S3-1: By passing the input control quantity through a notch filter, the filtered control quantity τ is obtained. f ,Right now: t f =H(s)τ S3-2: Input the filtered control quantity into the series elastic actuator SEA to effectively suppress the vibration of the series elastic actuator SEA.

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