Adaptive Vibration Reduction Control Method for Multi-Parallel Platforms Based on RBFNN Dynamic Surface

Abstract

This application relates to an adaptive vibration reduction control method for multi-parallel platforms based on RBFNN dynamic surfaces. It includes the following steps: establishing and performing inverse kinematics model for the multi-channel parallel platform; establishing an environmental contact force model to obtain the force error (environmental contact force minus desired force); inputting the force error into a dynamic surface adaptive module based on RBF networks and an impedance control module based on mass-damping-spring to obtain position correction and position compensation values; and adjusting the desired position of the dynamic platform of the multi-channel parallel platform to make the environmental contact force approach the desired force, thereby achieving vibration reduction control of the multi-channel parallel platform. This invention suppresses high-frequency vibration through dynamic surface technology and compensates for nonlinear disturbances using RBFNN (Radial Basis Neural Network), reducing the force error amplitude and effectively suppressing platform vibration, thus improving the system's adaptability to dynamically changing environments.

Description

Technical Field

[0001] This application relates to the field of parallel robot control technology, specifically to an adaptive vibration reduction control method for multiple parallel platforms based on RBFNN dynamic surfaces. Background Technology

[0002] Multi-channel parallel platforms, such as the six-DOF Stewart platform, typically consist of a static platform (lower platform) and a moving platform (upper platform). Multi-DOF motion is achieved by controlling the extension and retraction of each electric cylinder to drive the moving platform. In practical applications, these platforms are susceptible to vibration due to external disturbances and internal parameter uncertainties, which in turn affects their positioning accuracy and stability. Traditional vibration reduction control methods, such as PID control, fuzzy control, and traditional adaptive impedance control, while able to suppress platform vibration to some extent, struggle to handle complex situations involving system nonlinearity, strong coupling, and parameter uncertainties. In recent years, neural network-based adaptive control methods have shown great potential in vibration reduction control due to their powerful self-learning and nonlinear approximation capabilities. Among them, radial basis function (RBF) neural networks have become a research hotspot due to their simple structure, fast convergence speed, and high approximation accuracy.

[0003] However, existing vibration control methods based on RBF networks still have some shortcomings:

[0004] 1. Traditional RBF networks rely on analytical derivatives or numerical differentiation, which easily introduces noise and errors and increases the computational burden;

[0005] 2. Traditional methods are less robust to unmodeled dynamics and external disturbances, making it difficult to guarantee system stability and control accuracy. Summary of the Invention

[0006] The purpose of this invention is to provide an adaptive vibration reduction control method for multiple parallel platforms based on RBFNN dynamic surfaces. This method suppresses high-frequency vibrations through dynamic surface technology and compensates for nonlinear disturbances using RBFNN (Radial Basis Neural Network), thereby reducing the force error amplitude and effectively suppressing platform vibrations, thus improving the system's adaptability to dynamically changing environments.

[0007] The technical solution adopted in this invention is: an adaptive vibration reduction control method for multiple parallel platforms based on RBFNN dynamic surfaces, comprising the following steps:

[0008] S1: Establish an inverse kinematics model for a multi-channel parallel platform, and determine the desired position of the moving platform of the multi-channel parallel platform. The motion is solved by inverse kinematics, and the desired position of the multi-channel parallel platform is obtained. The inverse kinematics is solved into the motion of each individual channel; by controlling the motion of each individual channel, the overall motion control of the multi-channel parallel platform is realized.

[0009] S2: Based on the actual position of the moving platform, the environmental position, the environmental damping coefficient, and the environmental stiffness coefficient of the multi-channel parallel platform, establish an environmental contact force model and obtain the environmental contact force. Environmental contact force Subtract the pre-set expectation force The force error e is obtained by subtracting the expected force from the environmental contact force:

[0010] ;

[0011] S3: Force error By inputting the dynamic surface adaptive module based on RBF network and the impedance control module based on mass-damped-spring, respectively, the position correction amount from the impedance control module is obtained. The position compensation amount u of the dynamic surface adaptive module is used to obtain the total position adjustment amount. Desired position of the moving platform for a multi-channel parallel platform Adjustments are made to obtain the reference position of the moving platform of the multi-channel parallel platform. An adaptive vibration reduction control system is established through cyclic adjustment to reduce environmental contact force. Approaching Expectation Force This enables vibration reduction control of multi-channel parallel platforms and suppresses vibration in such platforms.

[0012] Furthermore, the environmental contact force model is a spring-damped model, specifically expressed as follows:

[0013] ;

[0014] in, X represents the environmental contact force. e Indicates the environmental location, i.e., the actual location on the environmental surface; X represents the actual location of the moving platform of the multi-channel parallel platform; b e k represents the damping coefficient of the environmental contact force model. e This represents the stiffness coefficient of the environmental contact force model. The first derivative represents the location of the environment.

[0015] Furthermore, the position correction amount output by the impedance control module based on mass-damping-spring The specific expression is:

[0016]

[0017] Where, mz b represents the quality coefficient of the impedance control module. z k represents the damping coefficient of the impedance control module. z represents the stiffness coefficient of the impedance control module, and s represents the complex frequency domain variable.

[0018] Furthermore, the dynamic surface adaptive control module based on RBF network includes an input layer, an RBF hidden layer, and an output layer;

[0019] The input to the input layer is the force error e and the first derivative of the force error e. The output is a dynamic surface. ,in, Indicates the gain coefficient. ;RBF hidden layer is ,in, This is a vector composed of the output values ​​of the radial basis functions. Let n be the nth radial basis function output value in the vector formed by the radial basis function output values, where n is a positive integer;

[0020] The portion of the adaptive vibration reduction control system excluding the dynamic adaptive module based on the RBF network is considered as a single system. This system is a nonlinear system, and its specific expression is as follows:

[0021] ;

[0022] in, Let W represent the ideal weight vector, which is a nonlinear system. This represents the transpose of the ideal weight vector. Indicates the approximation error;

[0023] Let the output of the dynamic adaptive module based on the RBF network be... Approximating nonlinear systems The output of the dynamic adaptive module based on the RBF network can be obtained. The specific expression is:

[0024] ;

[0025] in, This represents the estimated vector of the ideal weight vector W. This represents the transpose of the estimated vector of the ideal weight vector;

[0026] Estimated vector of the ideal weight vector of the RBF network To perform an update, the specific expression is:

[0027] ;

[0028] in, The update rate represents the estimated vector of the ideal weight vector W. Let S denote the positive definite gain matrix, and S denote the dynamic surface.

[0029] The specific formula for updating the estimated ideal weight vector is as follows:

[0030] ;

[0031] in, This represents the estimated vector of the ideal weight vector after the (N+1)th update. This represents the estimated vector of the ideal weight vector after the Nth update. N represents the time interval for each update, where N is an integer greater than 0;

[0032] The specific expression for the output position compensation amount u of the output layer is:

[0033] ;

[0034] in, This represents the transpose of the estimated vector of the ideal weight vector. This represents the vector formed by the output values ​​of the radial basis functions, and K represents the feedback gain coefficient.

[0035] Furthermore, the reference position X of the moving platform of the multi-channel parallel platform f The adjustment formula is:

[0036] ;

[0037] Among them, X f Indicates the reference position, and U represents the total position adjustment. represents the position correction amount, and u represents the position compensation amount;

[0038] The cyclic adjustment process is as follows: the reference position of the moving platform of the multi-channel parallel platform obtained after adjustment. The expected motion quantities of each channel are obtained through inverse kinematics. Expected motion volume of each channel The actual motion volume of each channel is controlled through a closed loop. The actual amount of movement in each channel Applying this to a multi-channel parallel platform, we obtain the actual position X of the moving platform; the actual position X of the moving platform of the multi-channel parallel platform is compared with the environmental position. The difference is then input into the environmental contact force model, continuously cycling the entire process, so that the actual position X of the moving platform of the multi-channel parallel platform is different from the environmental position. The difference continuously decreases, thereby reducing the environmental contact force. Its function.

[0039] The beneficial effects of this invention are as follows:

[0040] (1) This invention uses dynamic surface control technology, combined with tracking error and its derivative, to transform the complex system dynamics into a simplified first-order model. This significantly reduces the design complexity of the control module; compared with traditional methods, it eliminates the need to derive high-order error equations step by step, significantly reducing the dimension of parameter adjustment and making the control module easier to implement in engineering; dynamic surface technology can also quickly capture the transient characteristics of the system and automatically suppress external disturbances and model uncertainties during the convergence process, making it particularly suitable for scenarios requiring rapid stabilization and vibration suppression, such as precision machining and high-frequency robot motion.

[0041] (2) The unknown nonlinear dynamics in the system, such as friction, unmodeled dynamics and external disturbances, are approximated with high precision over the entire domain by using the RBF network, which solves the performance bottleneck of the traditional linear control module in strong nonlinear scenarios. The RBF network dynamically generates compensation signals based on the real-time force error information to offset the effects of vibration sources and disturbances.

[0042] (3) The dynamic surface adaptive control module of the RBF network can ensure the precise control of contact force and trajectory through nonlinear dynamic compensation and fast error convergence. Its universality under complex working conditions is significantly better than that of traditional methods. Even if the load inertia is unknown or there is a sudden external force interference, it can still maintain smooth motion and avoid damage to the workpiece. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a control flowchart of an embodiment of the present invention;

[0045] Figure 2 This is a schematic diagram of the network structure of the dynamic surface adaptive control module based on the RBF network in an embodiment of the present invention;

[0046] Figure 3 This is a flowchart of the algorithm for the dynamic surface adaptive control module based on RBF network in an embodiment of the present invention.

[0047] Figure 4The diagrams show a comparison of force errors under step disturbance and sinusoidal disturbance for the traditional adaptive impedance control method and the method described in the embodiments of the present invention, respectively; wherein, (a) is a comparison of force errors under step disturbance and (b) is a comparison of force errors under sinusoidal disturbance.

[0048] Figure 5 This is a simplified diagram of the multi-channel parallel platform structure and a schematic diagram of the reference coordinate system in an embodiment of the present invention;

[0049] Figure 6 This is a schematic diagram of the i-th channel in an embodiment of the present invention. Detailed Implementation

[0050] To better understand the above-described objects, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Many specific details are set forth in the following description to provide a thorough understanding of the invention; however, the invention may be practiced in other ways different from those described herein, and therefore, the invention is not limited to the specific embodiments disclosed below.

[0051] like Figure 1 As shown, the adaptive vibration reduction control method for multiple parallel platforms based on the RBFNN dynamic surface includes the following steps:

[0052] S1: Establish an inverse kinematics model for a multi-channel parallel platform, and determine the desired position of the moving platform of the multi-channel parallel platform. The motion is solved by inverse kinematics, and the desired position of the multi-channel parallel platform is obtained. The inverse kinematics of the system is derived from the motion of each individual channel; by controlling the motion of each individual channel, the overall motion control of the multi-channel parallel platform is achieved. The desired position of the moving platform is... This refers to the target spatial position or trajectory that the end effector of a multi-channel parallel platform expects to reach or track; in this embodiment of the invention, the expected position of the moving platform... The ideal position that the moving platform, representing a multi-channel parallel platform, should reach under conditions of no environmental interference.

[0053] The inverse kinematics process is as follows:

[0054] like Figure 5 As shown, a simplified diagram of the multi-channel parallel platform structure is established, and a reference coordinate system is set at the center point O of the lower platform. B Establish a global coordinate system {B}, with the center point O of the upper platform as the coordinate system. p By establishing a local coordinate system {P}, the coordinates of each point in both the global coordinate system {B} and the local coordinate system {P} can be obtained as follows:

[0055] ;

[0056] in, This represents the coordinates of the i-th point on the platform. This represents the coordinates of the i-th lower platform point. This represents the i-th upper platform point and the upper platform center point O. p The angle between the line connecting the two coordinate systems and the x-axis in the local coordinate system {P}. This represents the i-th lower platform point and the lower platform center point O. B The angle between the line connecting the two coordinate systems and the x-axis in the global coordinate system {B} is R. P R represents the radius of the upper platform. B Indicates the radius of the lower platform.

[0057] The schematic diagram of the i-th channel is as follows: Figure 6 As shown, taking the i-th lower platform point B as an example... i and the i-th platform point P i Establish a local coordinate system B for the origin. i -xyz and local coordinate system P i -xyz, local coordinate system B i -xyz and local coordinate system P i The z-axis of -xyz is along the actuator's axis, defined from the center point O of the lower platform. B Go to point B on the lower platform i The vector is b i From the center point O of the upper platform P Go to the platform point P i The vector is p i From the center point O of the lower platform B Go to the central point O of the platform P Let the vector be t, and the lower platform point be B. i Go to the platform point P i The vector is l i That is, the position and elongation of the actuator in a certain pose are represented by the vector l. i express.

[0058] The rotation matrix R of the upper platform about the z-axis z for:

[0059] ;

[0060] The final rotation matrix R of the upper platform is:

[0061] ;

[0062] in, This represents the angle by which the local coordinate system {P} rotates counterclockwise around the x-axis of the global coordinate system {B}. This represents the angle by which the local coordinate system {P} rotates counterclockwise around the y-axis of the global coordinate system {B}. This represents the angle by which the local coordinate system {P} rotates counterclockwise around the z-axis of the global coordinate system {B}.

[0063] The relationship between the angular velocity of the platform in the global coordinate system {B} and its rotation angle about the ZYX axes in the local coordinate system {P} for:

[0064] ;

[0065] The relationship between the acceleration of the platform in the global coordinate system {B} and its rotation angle about the ZYX axes in the local coordinate system {P} for:

[0066] ;

[0067] in, express The first derivative, express The first derivative, express The first derivative, express The second derivative, express The second derivative, express The second derivative is defined as follows: .

[0068] Finally, the inverse kinematics formulas for the motion vector of a single channel and the positions of the upper and lower platform points can be obtained as follows:

[0069] ;

[0070] in, The length of the module is denoted as .

[0071] Desired motion signal from a single channel The input is fed into a single channel, and the output is the actual motion volume of the single channel. and the actual motion volume of a single channel The actual position X at the end of the multi-channel parallel platform is obtained by inputting the data into the multi-channel parallel platform.

[0072] S2: Based on the actual position of the moving platform, the environmental position, the environmental damping coefficient, and the environmental stiffness coefficient of the multi-channel parallel platform, establish an environmental contact force model and obtain the environmental contact force. Environmental contact force Subtract the pre-set expectation force The force error e is obtained by subtracting the expected force from the environmental contact force:

[0073] .

[0074] The environmental contact force model is a spring-damped model, and its specific expression is as follows:

[0075] ;

[0076] in, X represents the environmental contact force. e Indicates the environmental location, i.e., the actual location on the environmental surface; X represents the actual location of the moving platform of the multi-channel parallel platform; b e k represents the damping coefficient of the environmental contact force model. e This represents the stiffness coefficient of the environmental contact force model. The first derivative represents the location of the environment.

[0077] S3: Force error By inputting the dynamic surface adaptive control module based on RBF network and the impedance control module based on mass-damped-spring, respectively, the position correction amount from the impedance control module is obtained. The position compensation amount u of the dynamic adaptive module is used to obtain the total position adjustment amount. Desired position of the moving platform for a multi-channel parallel platform Adjustments are made to obtain the reference position of the moving platform of the multi-channel parallel platform. An adaptive vibration reduction control system is established through cyclic adjustment to reduce environmental contact force. Approaching Expectation Force This enables vibration reduction control of multi-channel parallel platforms and suppresses vibration in such platforms.

[0078] The position correction amount output by the impedance control module based on mass-damping-spring The specific expression is:

[0079] ;

[0080] Where, m z b represents the quality coefficient of the impedance control module. z k represents the damping coefficient of the impedance control module. z represents the stiffness coefficient of the impedance control module, and s represents the complex frequency domain variable.

[0081] like Figure 2 As shown, the dynamic surface adaptive control module based on RBF network includes an input layer, an RBF hidden layer, and an output layer;

[0082] The input to the input layer is the force error e and the first derivative of the force error e. The output is a dynamic surface. ,in, Indicates the gain coefficient. ;RBF hidden layer is ,in, This is a vector composed of the output values ​​of the radial basis functions. Let n be the nth radial basis function output value in the vector formed by the radial basis function output values, where n is a positive integer;

[0083] The portion of the adaptive vibration reduction control system excluding the RBF-based dynamic surface adaptive control module can be considered as a single system, with force error e as input and position compensation u as output. Since the multi-channel parallel platform itself is highly nonlinear, any system containing multiple parallel channels must also be nonlinear. The specific expression for this system is:

[0084] ;

[0085] in, Let W represent the ideal weight vector, which is a nonlinear system. This represents the transpose of the ideal weight vector. This represents the approximation error.

[0086] Let the output of the dynamic surface adaptive control module based on the RBF network be... Approximating nonlinear systems The output of the dynamic surface adaptive control module based on the RBF network can be obtained. The specific expression is:

[0087] ;

[0088] in, This represents the estimated vector of the ideal weight vector W. This represents the transpose of the estimated vector of the ideal weight vector.

[0089] Estimated vector of the ideal weight vector of the RBF network To perform an update, the specific expression is:

[0090] ;

[0091] in, The update rate represents the estimated vector of the ideal weight vector W. Let S denote the positive definite gain matrix, and let S denote the dynamic surface.

[0092] The specific formula for updating the estimated ideal weight vector is as follows:

[0093] ;

[0094] in, This represents the estimated vector of the ideal weight vector after the (N+1)th update. This represents the estimated vector of the ideal weight vector after the Nth update. N represents the time interval for each update, where N is an integer greater than 0.

[0095] The specific expression for the output position compensation amount u of the output layer is:

[0096] ;

[0097] in, This represents the transpose of the estimated vector of the ideal weight vector. This represents the vector formed by the output values ​​of the radial basis functions, and K represents the feedback gain coefficient.

[0098] Reference position X of the moving platform of the multi-channel parallel platform f The adjustment formula is:

[0099] ;

[0100] Among them, X f Indicates the reference position, and U represents the total position adjustment. represents the position correction amount, and u represents the position compensation amount.

[0101] The cyclic adjustment process is as follows: the reference position of the moving platform of the multi-channel parallel platform obtained after adjustment. The expected motion quantities of each channel are obtained through inverse kinematics. Expected motion volume of each channel The actual motion volume of each channel is controlled through a closed loop. The actual amount of movement in each channel Applying this to a multi-channel parallel platform, we obtain the actual position X of the moving platform; the actual position X of the moving platform of the multi-channel parallel platform is compared with the environmental position. The difference is then input into the environmental contact force model, continuously cycling the entire process, so that the actual position X of the moving platform of the multi-channel parallel platform is different from the environmental position. The difference continuously decreases, thereby reducing the environmental contact force. Its function.

[0102] like Figure 3As shown, the algorithm flow of the dynamic surface adaptive control module based on RBF network is as follows: Step 1: Set the initial weights and parameters; Step 2: Measure and read the force error and its derivative; Step 3: Calculate the dynamic surface; Step 4: Update and estimate the ideal network vector; Step 5: Calculate and update the control input; Step 6: Output the control signal and return to Step 2 for looping.

[0103] like Figure 4 As shown in (a), a vertical step disturbance is applied to the multi-channel parallel platform, and control is performed using both the traditional adaptive impedance control method and the method described in this embodiment of the invention. Figure 4 As can be seen from (a) in the figure, the method of the present invention has a significantly better effect on suppressing force error than the traditional adaptive impedance control method. Figure 4 As shown in (b), a sinusoidal disturbance in the vertical direction is applied to the multi-channel parallel platform, and control is performed using both the traditional adaptive impedance control method and the method described in this embodiment of the invention. Figure 4 As can be seen from (b) in the figure, the method described in the embodiments of the present invention has a significantly better effect on suppressing force errors than the traditional adaptive impedance control method. Therefore, it can be concluded that the vibration reduction effect of the method described in the embodiments of the present invention is better than that of the traditional adaptive impedance control method.

[0104] The RBF network structure used in this embodiment of the invention is simple and requires only a small number of hidden layer nodes to operate efficiently. Combined with the low-order design of dynamic surface technology, the overall algorithm computation is far lower than that of deep learning solutions. The adaptive mechanism reduces the dependence on manual parameter tuning. Engineers only need to set the initial network size and adaptive gain, and the system can automatically optimize through online learning, which greatly reduces the debugging cycle and maintenance costs, providing a cost-effective solution for industrial implementation.

[0105] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-parallel platform adaptive vibration reduction control method based on RBFNN dynamic surfaces, characterized in that, Includes the following steps: S1: Establish an inverse kinematics model for a multi-channel parallel platform, and determine the desired position of the moving platform of the multi-channel parallel platform. The motion is solved by inverse kinematics, and the desired position of the multi-channel parallel platform is obtained. The inverse kinematics is solved into the motion of each individual channel; by controlling the motion of each individual channel, the overall motion control of the multi-channel parallel platform is realized. S2: Based on the actual position of the moving platform, the environmental position, the environmental damping coefficient, and the environmental stiffness coefficient of the multi-channel parallel platform, establish an environmental contact force model and obtain the environmental contact force. Environmental contact force Subtract the pre-set expectation force The force error e is obtained by subtracting the expected force from the environmental contact force: ； S3: Force error By inputting the dynamic surface adaptive module based on RBF network and the impedance control module based on mass-damped-spring, respectively, the position correction amount from the impedance control module is obtained. The position compensation amount u of the dynamic surface adaptive module is used to obtain the total position adjustment amount. Desired position of the moving platform for a multi-channel parallel platform Adjustments are made to obtain the reference position of the moving platform of the multi-channel parallel platform. An adaptive vibration reduction control system is established through cyclic adjustment to reduce environmental contact force. Approaching Expectation Force This enables vibration reduction control of multi-channel parallel platforms and suppresses vibration in such platforms.

2. The adaptive vibration reduction control method for multiple parallel platforms based on RBFNN dynamic surfaces according to claim 1, characterized in that, The environmental contact force model is a spring-damped model, and its specific expression is as follows: ； in, X represents the environmental contact force. e Indicates the environmental location, i.e., the actual location on the environmental surface; X represents the actual location of the moving platform of the multi-channel parallel platform; b e k represents the damping coefficient of the environmental contact force model. e This represents the stiffness coefficient of the environmental contact force model. The first derivative represents the location of the environment.

3. The adaptive vibration reduction control method for multiple parallel platforms based on RBFNN dynamic surfaces according to claim 2, characterized in that, The position correction amount output by the impedance control module based on mass-damping-spring The specific expression is: ； Where, m z b represents the quality coefficient of the impedance control module. z k represents the damping coefficient of the impedance control module. z represents the stiffness coefficient of the impedance control module, and s represents the complex frequency domain variable.

4. The adaptive vibration reduction control method for multiple parallel platforms based on RBFNN dynamic surfaces according to claim 3, characterized in that, The dynamic surface adaptive control module based on RBF network includes an input layer, an RBF hidden layer, and an output layer; The input to the input layer is the force error e and the first derivative of the force error e. The output is a dynamic surface. ,in, Indicates the gain coefficient. ;RBF hidden layer is ,in, This is a vector composed of the output values ​​of the radial basis functions. Let n be the nth radial basis function output value in the vector formed by the radial basis function output values, where n is a positive integer; The portion of the adaptive vibration reduction control system excluding the dynamic adaptive module based on the RBF network is considered as a single system. This system is a nonlinear system, and its specific expression is as follows: ； in, Let W represent the ideal weight vector, which is a nonlinear system. This represents the transpose of the ideal weight vector. Indicates the approximation error; Let the output of the dynamic adaptive module based on the RBF network be... Approximating nonlinear systems The output of the dynamic adaptive module based on the RBF network can be obtained. The specific expression is: ； in, This represents the estimated vector of the ideal weight vector W. This represents the transpose of the estimated vector of the ideal weight vector; Estimated vector of the ideal weight vector of the RBF network To perform an update, the specific expression is: ； in, The update rate represents the estimated vector of the ideal weight vector W. Let S denote the positive definite gain matrix, and S denote the dynamic surface. The specific formula for updating the estimated ideal weight vector is as follows: ； in, This represents the estimated vector of the ideal weight vector after the (N+1)th update. This represents the estimated vector of the ideal weight vector after the Nth update. N represents the time interval for each update, where N is an integer greater than 0; The specific expression for the output position compensation amount u of the output layer is: ； in, This represents the transpose of the estimated vector of the ideal weight vector. This represents the vector formed by the output values ​​of the radial basis functions, and K represents the feedback gain coefficient.

5. The adaptive vibration reduction control method for multiple parallel platforms based on RBFNN dynamic surfaces according to claim 4, characterized in that, Reference position X of the moving platform of the multi-channel parallel platform f The adjustment formula is: ； Among them, X f Indicates the reference position, and U represents the total position adjustment. represents the position correction amount, and u represents the position compensation amount; The cyclic adjustment process is as follows: the reference position of the moving platform of the multi-channel parallel platform obtained after adjustment. The expected motion quantities of each channel are obtained through inverse kinematics. Expected motion volume of each channel The actual motion volume of each channel is controlled through a closed loop. The actual amount of movement in each channel Applying this to a multi-channel parallel platform, we obtain the actual position X of the moving platform; the actual position X of the moving platform of the multi-channel parallel platform is compared with the environmental position. The difference is then input into the environmental contact force model, continuously cycling the entire process, so that the actual position X of the moving platform of the multi-channel parallel platform is different from the environmental position. The difference continuously decreases, thereby reducing the environmental contact force. Its function.

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