An active vibration damping control method based on an adaptive neuro-fuzzy inference system

Abstract

An active vibration damping control method based on an adaptive neuro-fuzzy inference system, belonging to the technical field of vibration isolation control. The method includes: constructing a system model and collecting data; designing an ANFIS model based on the state variables of the platform; the ANFIS model automatically adjusts the parameters of the fuzzy membership function through training with experimental data; training the ANFIS model based on a hybrid learning algorithm; using sensors to obtain the displacement and velocity of the platform in real time and inputting them into the ANFIS model to achieve real-time active vibration damping control. By collecting the displacement and velocity data of the platform in real time and inputting them into the ANFIS model, the system can dynamically calculate the control signal, quickly respond to vibration changes, effectively suppress vibration and reduce the vibration amplitude of the system, ensuring the stability of the platform. Through the feedback loop of the sensor and the control system, it is ensured that the system can automatically adjust the control signal according to the actual vibration state of the platform at any time.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration isolation control, and particularly relates to an active vibration damping control method based on an adaptive neuro-fuzzy inference system. Background Art

[0002] In recent years, as an intelligent control method, the adaptive neuro-fuzzy inference system (ANFIS) has received extensive attention due to its advantage of combining fuzzy logic and neural networks, and has shown remarkable potential especially in the multivariable control and nonlinear modeling of complex systems. ANFIS classifies the system state using fuzzy rules, adaptively learns parameters through a neural network, predicts the future dynamics of the system in real time and outputs accurate control signals, thereby effectively reducing the vibration impact and enhancing the robustness of the system, enabling it to achieve excellent vibration damping effects in complex environments.

[0003] The present invention proposes an air-bearing quasi-zero stiffness active vibration damping method based on the adaptive neuro-fuzzy inference system (ANFIS), which is applicable to the low-frequency vibration suppression of precision manufacturing and optical measurement equipment. Utilizing the low stiffness and high load characteristics of the air bearing, displacement and velocity are used as the ANFIS model inputs, combined with experimental data for system modeling and frequency response identification, and control signals are generated through adaptive learning to control the voice coil motor in real time to suppress vibration. The ANFIS model is trained using a hybrid learning algorithm. In the forward propagation stage, the least squares method is used to optimize the output weights, and in the backpropagation stage, the fuzzy membership functions are adjusted by the gradient descent method. Experimental results show that this method significantly improves the vibration damping effect in the frequency band of 0.5 - 70 Hz and can stably support the operation of precision equipment in complex environments. Summary of the Invention

[0004] The purpose of this part is to outline some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this part, as well as in the abstract and title of the present application, to avoid obscuring the purpose of this part, the abstract, and the title, but such simplifications or omissions shall not be used to limit the scope of the present invention.

[0005] In view of the above or existing problems of the active vibration damping control method based on the adaptive neuro-fuzzy inference system, the present invention is proposed.

[0006] To solve the above technical problems, the present invention provides the following technical solutions:

[0007] An active vibration damping control method based on an adaptive neuro-fuzzy inference system provided by an embodiment of the present invention includes: constructing a system model and collecting data; designing an ANFIS model based on the state variables of the platform; the ANFIS model automatically adjusts the parameters of the fuzzy membership function through training with experimental data; training the ANFIS model based on a hybrid learning algorithm; using sensors to obtain the displacement and velocity of the platform in real time and inputting them into the ANFIS model to achieve real-time active vibration damping control.

[0008] As a preferred embodiment of the active vibration damping control method based on the adaptive neuro-fuzzy inference system of the present invention, where: the constructing a system model and collecting data includes:

[0009] Obtaining the displacement of the platform through a sensor and velocity As input variables of the system, reflecting the current state of the vibration system, the voice coil motor generates a corresponding braking force F according to the control signal to offset the vibration force received by the platform, and constructs the dynamic model of the system to determine the input-output relationship.

[0010] As a preferred embodiment of the active vibration damping control method based on the adaptive neuro-fuzzy inference system of the present invention, where: the dynamic model is used to describe the dynamic behavior of the platform vibration system, and the equation is as follows:

[0011]

[0012] Where M is the equivalent mass matrix of the system, which determines the response intensity of the system to external vibrations; C is the damping coefficient, which characterizes the damping effect of the system; K is the stiffness coefficient, which determines the anti-deformation ability of the system; F(t) is the control force generated by the voice coil motor to offset the vibration of the platform.

[0013] As a preferred embodiment of the active vibration damping control method based on the adaptive neuro-fuzzy inference system of the present invention, where: the designing an ANFIS model based on the state variables of the platform includes:

[0014] Performing non-linear mapping through fuzzy logic rules and the adaptive ability of the neural network to generate the control signal of the system. The ANFIS model selects the displacement and velocity of the platform as input variables, and the output variable is the control signal.

[0015] As a preferred embodiment of the active vibration damping control method based on the adaptive neuro-fuzzy inference system of the present invention, where: the designing an ANFIS model based on the state variables of the platform further includes:

[0016] The input state is defined by fuzzification and fuzzy membership function. The membership function is selected as the generalized bell-shaped function, and its expression is:

[0017]

[0018] where μ(x) is the input state of the input data x, a is the width parameter, which controls the stretching degree of the membership function; b is the shape parameter, which adjusts the curve shape of the membership function; c is the center parameter, which determines the position of the membership function.

[0019] As a preferred solution of the active vibration control method based on the adaptive neuro-fuzzy inference system of the present invention, wherein: the ANFIS model automatically adjusts the parameters of the fuzzy membership function through training with experimental data, including:

[0020] Multiple fuzzy rules R i constitute the ANFIS model. Each rule generates a control output according to the fuzzy states of the input variables and . The fuzzy rules are as follows:

[0021]

[0022] where Ai and Bi represent the fuzzy sets of the input variables; U represents the control signal of the voice coil motor.

[0023] As a preferred solution of the active vibration control method based on the adaptive neuro-fuzzy inference system of the present invention, wherein: according to the fuzzy rules, the activation values of each rule are derived:

[0024]

[0025] where ω i represents the rule activation degree, μA i (x) represents the membership degree of the input x(t) belonging to the fuzzy set Ai, and μBi(x) represents the membership degree of the input x(t) belonging to the fuzzy set B i ;

[0026] The fuzzy results are defuzzified by weighted average to output the final control signal:

[0027]

[0028] where f i represents the output of the i-th fuzzy rule, N represents the total number of rules, and i = 1, 2, 3,..., N.

[0029] As a preferred solution of the active vibration control method based on the adaptive neuro-fuzzy inference system of the present invention, wherein: training the ANFIS model based on the hybrid learning algorithm includes:

[0030] In the forward propagation stage, the least squares method is used to optimize the weights of the linear combination of the outputs to minimize the error between the model output and the actual value. The ANFIS output layer is a linear combination of the activated fuzzy rules, and its calculation formula is:

[0031]

[0032] where U is the control signal of the voice coil motor, and w n is the weight of the fuzzy rule; f n is the output of the nth fuzzy rule, n = 1, 2, 3, …, N; f1 is the output of the first model rule, f2 is the output of the second model rule, and w1 and w2 are the corresponding weights;

[0033] The goal of the least squares method is to adjust w i to minimize the error, and the error is defined as:

[0034]

[0035] where E is the error, m is the number of samples, k represents the numbering from the 1st to the mth sample, is the predicted output value, is the actual output value; In the backpropagation stage, the gradient descent method is used to update the parameters of the fuzzy membership function. By adjusting the shape and position of the membership function, the output of the model is made to approximate the response of the actual system. The update formula is as follows:

[0036]

[0037]

[0038]

[0039] where η is the learning rate, , , is the updated system parameter, , , is the current system parameter.

[0040] As a preferred scheme of the active vibration control method based on the adaptive neuro-fuzzy inference system described in the present invention, wherein: training the ANFIS model based on the hybrid learning algorithm further includes:

[0041] Define the error function of the system. Assume that e(t) is the error at time step t, and it is calculated in the following way:

[0042]

[0043] Among them, y(t) is the actual output value at time t, and y desired (t) is the expected output value at time t;

[0044] Calculate the change rate of the error, that is, the gradient Δe(t) of the error:

[0045]

[0046] If the change rate of the error is large, the system state changes, and the learning rate is increased to accelerate the adjustment; if the change of the error is small, the system tends to be stable and the learning rate is reduced;

[0047] Gradually reduce the learning rate based on the error value or the change rate of the error, as follows:

[0048]

[0049] Among them, η(t) is the learning rate at time t, η0 is the initial learning rate, and λ is the adjustment factor;

[0050] Use the dynamically adjusted learning rate to update the weights and parameters of the neural network, and use the gradient descent method to update the weights.

[0051] As a preferred solution of the active vibration damping control method based on the adaptive neuro-fuzzy inference system of the present invention, wherein: the displacement and speed of the platform are obtained in real time by using sensors and input into the ANFIS model to achieve real-time active vibration damping control, including:

[0052] The ANFIS model combines fuzzy logic and neural networks, calculates the corresponding control signal based on historical data and real-time input, and the control signal drives actuators such as voice coil motors to generate a reverse force to cancel the vibration of the platform.

[0053] The beneficial effects of the present invention are: by collecting the displacement and speed data of the platform in real time and inputting them into the ANFIS model, the system can dynamically calculate the control signal, quickly respond to the vibration change, effectively suppress the vibration and reduce the vibration amplitude of the system, and ensure the stability of the platform. The ANFIS model combines the advantages of fuzzy logic and neural networks, can automatically adjust the control rules according to different vibration states, has strong adaptability and robustness, and can handle complex vibration problems under different environments and working conditions. Through the feedback loop of the sensor and the control system, it is ensured that the system can automatically adjust the control signal according to the actual vibration state of the platform at any time, realizing continuous and stable active vibration damping control. Description of the Drawings

[0054] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0055] Figure 1 It is the ANFIS control flow chart of the active vibration damping device.

[0056] Figure 2 It is the graph of the ANFIS training error varying with the number of training rounds.

[0057] Figure 3 It is the comparison graph of the actual output and the ANFIS predicted output (time domain).

[0058] Figure 4 It is the comparison graph of the auto-power spectral density of the actual output and the ANFIS predicted output.

[0059] Figure 5 It is the displacement response graph before vibration suppression (ANFIS control).

[0060] Figure 6 It is the displacement response graph after vibration suppression (ANFIS control).

[0061] Figure 7 It is the comparison graph of the maximum displacements before and after vibration suppression (ANIFS control). Specific Embodiments

[0062] To make the above objects, features, and advantages of the present invention more apparent and understandable, the following will make a detailed description of the specific embodiments of the present invention in conjunction with the accompanying drawings of the specification.

[0063] In the following description, many specific details are set forth to fully understand the present invention. However, the present invention can also be implemented in other ways different from those described herein. Those skilled in the art can make similar generalizations without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0064] Secondly, the so-called "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that can be included in at least one implementation manner of the present invention. The "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment that mutually excludes other embodiments.

[0065] Embodiment 1

[0066] Refer to Figure 1, which is an embodiment of the present invention. This embodiment provides an active vibration damping control method based on an adaptive neuro-fuzzy inference system, including:

[0067] S1: Build a system model and collect data.

[0068] Preferably, obtain the displacement and velocity of the platform through sensors as the input variables of the system, reflecting the current state of the vibration system. The voice coil motor generates a corresponding braking force F according to the control signal to counteract the vibration force received by the platform, and constructs a dynamic model of the system to determine the input-output relationship.

[0069] Furthermore, the dynamic model is used to describe the dynamic behavior of the platform vibration system, and the equation is as follows:

[0070]

[0071] where M is the equivalent mass matrix of the system, which determines the response intensity of the system to external vibrations; C is the damping coefficient, which characterizes the damping effect of the system; K is the stiffness coefficient, which determines the anti-deformation ability of the system; F(t) is the control force generated by the voice coil motor to counteract the vibration of the platform.

[0072] S2: Design an ANFIS model based on the state variables of the platform.

[0073] Preferably, perform non-linear mapping through fuzzy logic rules and the adaptive ability of neural networks to generate the control signal of the system. The ANFIS model selects the displacement and velocity of the platform as the input variables, and the output variable is the control signal.

[0074] Preferably, define the input state through fuzzy processing and fuzzy membership functions. The membership function selects the generalized bell-shaped function, and the expression is:

[0075]

[0076] where μ(x) is the input state of the input data x, a is the width parameter, which controls the stretching degree of the membership function; b is the shape parameter, which adjusts the curve shape of the membership function; c is the center parameter, which determines the position of the membership function.

[0077] Furthermore, the ANFIS model contains multiple fuzzy rules, and each rule generates a corresponding control signal according to the fuzzified state of the input (such as the membership degrees of displacement and velocity). For example, set the following two fuzzy rules:

[0078] Rule 1: If the displacement x(t) is large and the velocity v(t) is large, then the output control signal U or I is large to generate a strong reverse force;

[0079] Rule 2: If the displacement x(t) is small and the velocity v(t) is small, then the output control signal U or I is small to generate a weak reverse force;

[0080] For each rule, the output F of the control signal i can be expressed by the fuzzy inference formula as:

[0081]

[0082] where w i is the activation weight of the rule, representing the influence degree of the membership degree of the input variable on this rule, and p, q, r are the linear parameters of the model, reflecting the relationship between the input variable and the output control signal;

[0083] Finally, the control signal U or I is the weighted average of the outputs of all rules:

[0084]

[0085] In this way, the ANFIS model generates corresponding control signals according to real-time sensor data and adjusts the reverse force in real time to cancel the vibration of the platform.

[0086] S3: The ANFIS model automatically adjusts the parameters of the fuzzy membership function through experimental data training.

[0087] Preferably, multiple fuzzy rules R i constitute the ANFIS model, and each rule generates a control output according to the fuzzy states of the input variables and , and the fuzzy rules are as follows:

[0088]

[0089] where Ai and Bi represent the fuzzy sets of the input variables; U represents the control signal of the voice coil motor.

[0090] Preferably, according to the fuzzy rules, the activation values of each rule are derived:

[0091]

[0092] where w i represents the rule activation degree, μA i (x) represents the membership degree of the input x(t) belonging to the fuzzy set Ai, and μBi(x) represents the membership degree of the input x(t) belonging to the fuzzy set B i ;

[0093] Perform weighted average defuzzification on the fuzzy results and output the final control signal:

[0094]

[0095] where U is the control signal of the voice coil motor, and f i represents the output of the i-th fuzzy rule, N represents the total number of rules, and i = 1, 2, 3, …, N.

[0096] Furthermore, assume that we have 4 fuzzy rules (N = 4), which respectively define different control signal outputs f i :

[0097] Rule 1: If the displacement is large and the speed is large, then the control signal is large (f1);

[0098] Rule 2: If the displacement is large and the speed is small, then the control signal is medium (f2);

[0099] Rule 3: If the displacement is small and the speed is large, then the control signal is medium (f3);

[0100] Rule 4: If the displacement is small and the speed is small, then the control signal is small (f4);

[0101] For the given input x(t) and v(t), calculate the activation value w i :

[0102] w1 = μlarge(x(t)) ⋅ μlarge(v(t))

[0103] w2 = μlarge(x(t)) ⋅ μsmall(v(t))

[0104] w3 = μsmall(x(t)) ⋅ μlarge(v(t))

[0105] w4 = μsmall(x(t)) ⋅ μsmall(v(t))

[0106] Assume that the membership degrees obtained through the fuzzy membership function are:

[0107] μlarge(x(t)) = 0.8, μlarge(v(t)) = 0.7, μsmall(x(t)) = 0.2, μsmall(v(t)) = 0.3,

[0108] Then the activation values of each rule are obtained:

[0109] w1 = 0.56, w2 = 0.8 ⋅ 0.3 = 0.24, w3 = 0.2 ⋅ 0.7 = 0.14, w4 = 0.2 ⋅ 0.3 = 0.06,

[0110] Next, calculate the fuzzy output f of each rule i, assuming the output of the rule is:

[0111] f1 = 0.9, f2 = 0.5, f3 = 0.5, f4 = 0.1;

[0112] Then the final control signal U is 0.7, and this signal will be used to drive the voice coil motor to generate a braking force opposite to the vibration direction, achieving the effect of active vibration reduction.

[0113] S4: Train the ANFIS model based on the hybrid learning algorithm.

[0114] Preferably, in the forward propagation stage, the least squares method is used to optimize the weights of the linear combination of the outputs to minimize the error between the model output and the actual value. The ANFIS output layer is a linear combination of the activated fuzzy rules, and its calculation formula is:

[0115]

[0116] where U is the control signal of the voice coil motor, w n is the weight of the fuzzy rule; f n is the output of the nth fuzzy rule, n = 1, 2, 3,..., N; f1 is the output of the first model rule, f2 is the output of the second model rule, and w1 and w1 are the corresponding weights; the goal of the least squares method is to adjust w i to minimize the error, and the error is defined as:

[0117]

[0118] where E is the error. In the backpropagation stage, the gradient descent method is used to update the parameters of the fuzzy membership function. By adjusting the shape and position of the membership function, the output of the model is made to approximate the response of the actual system. The update formula is as follows:

[0119]

[0120]

[0121]

[0122] where η is the learning rate.

[0123] Preferably, define the error function of the system. Assume that e(t) is the error at time step t and is calculated as follows:

[0124]

[0125] where y(t) is the output value at the current moment, and y desired (t) is the desired output value;

[0126] Calculate the rate of change of the error, i.e., the gradient of the error:

[0127]

[0128] If the rate of change of the error is large, the system state changes, and the adjustment is accelerated by increasing the learning rate; if the change in error is small, the system tends to be stable and the learning rate is reduced.

[0129] Gradually reduce the learning rate based on the error value or the rate of change of the error as follows:

[0130]

[0131] where η0 is the initial learning rate, λ is the adjustment factor, and e(t) is the current error.

[0132] Use the dynamically adjusted learning rate to update the weights and parameters of the neural network, and use the gradient descent method to update the weights:

[0133]

[0134] where ∇ w E(t) is the gradient of the loss function.

[0135] Furthermore, assume there are N fuzzy rules Ri, the output of each rule is fi, and each rule has a weight wi. Then the calculation formula for the output layer of ANFIS is:

[0136]

[0137] where wi is the weight of rule Ri, representing the activation degree of this rule; fi is the fuzzy output of rule Ri, representing the control signal generated by this rule.

[0138] In the least squares method, the goal is to adjust the weight wi to minimize the error. Define the error as the difference between the model output U and the actual target value U target :

[0139]

[0140] where E is the error function, representing the mean squared error between the model output and the actual target value; U i is the output of the model, and U target is the desired control signal.

[0141] To optimize the weight by minimizing the error, we take the partial derivative of the error function E with respect to the weight wi and update the weight:

[0142]

[0143] Then, the weights can be adjusted according to the gradient descent method:

[0144]

[0145] where η is the learning rate.

[0146] Furthermore, through the gradient descent method, the parameters a, b, and c of the membership function can be updated to minimize the output error. First, define the error as:

[0147]

[0148] Next, calculate the gradient of the error function with respect to the parameters of the membership function. For each parameter, calculate its derivative:

[0149]

[0150] Then, update the parameters of the membership function:

[0151]

[0152] Through the gradient update in the backpropagation stage, the parameters a, b, and c of the membership function will be gradually adjusted to the optimal values, so that the ANFIS model can more accurately fit the dynamic characteristics of the system and output more accurate control signals.

[0153] Furthermore, set the target output y desired (t) as the desired state of the platform, and calculate the error at the current moment e(t)=y desired (t)-y(t);

[0154] Calculate the rate of change of the error:

[0155]

[0156] If the change in the error is large (e.g., de(t) / dt > ϵ, where ϵ is a set threshold), then increase the learning rate;

[0157] Update the parameters of the ANFIS model through the gradient descent method. During the update process, the dynamically adjusted learning rate η(t) will enable the model to quickly learn the correct control signal.

[0158] S5: Use sensors to obtain the displacement and velocity of the platform in real time, input them into the ANFIS model, and achieve real-time active vibration damping control.

[0159] Preferably, the ANFIS model combines fuzzy logic and neural networks, calculates the corresponding control signal based on historical data and real-time input, and the control signal drives actuators such as voice coil motors to generate a reverse force to cancel the vibration of the platform.

[0160] Furthermore, assume that this control system is applied on a platform to reduce the vibration impact during the platform's flight. Accelerometers and laser displacement sensors are installed on the platform, which are respectively used to collect the vibration displacement and velocity of the platform in real time. The sensor data is transmitted to the control system via wireless communication. The ANFIS model in the control system takes the displacement and velocity data received in real time as inputs and calculates the control signal U(t). According to the control signal, the voice coil motor generates a counterforce F(t) to counteract the vibration caused by the external vibration source.

[0161] After several experiments and optimizations, the system can adjust the control signal in real time according to the vibration state of the platform, thereby achieving precise active vibration reduction control.

[0162] Embodiment 2

[0163] Refer to Figures 2 to 7 , which is another embodiment of the present invention.

[0164] Figure 2 It is a graph showing the change of ANFIS training error with the number of training rounds. The training error of the ANFIS model decreases from about 0.17 in the initial round to below 0.1 at the end of training. Specifically, the training error drops sharply in the first 20 training rounds, reaching a stable value near 0.1, and then the fluctuation decreases and remains at a relatively low error level (close to about 0.05). From a quantitative perspective, the decrease in the training error indicates that the model has achieved an error reduction effect of more than 70% after 100 rounds of training, showing a good convergence effect.

[0165] Figure 3 It is a comparison graph of the actual output and the ANFIS predicted output in the time domain. The actual output (red) and the ANFIS predicted output (blue dashed line) are compared in the time domain. Although a large number of points are shown in the graph, from the overall trend, the predicted output of ANFIS can closely follow the fluctuations of the actual output, especially in the signal changes in the high-frequency band, and the two maintain a high degree of similarity. Comparing the numerical fluctuation ranges, the fluctuation range of the ANFIS predicted output is between -0.6 and 0.6, which is basically the same as the fluctuation of the actual output.

[0166] Figure 4 It shows the auto-power spectral density of the actual output and the ANFIS predicted output in the frequency domain. The power spectral density range of the actual output is between -26dB and -44dB, and the power spectral density range of the ANFIS predicted output is also close to this range, indicating that the ANFIS prediction can better maintain the frequency domain characteristics in different frequency bands. Especially in the frequency band from 5Hz to 25Hz, the power spectral density of the ANFIS predicted output and the actual output almost coincide, which reflects the accuracy of the model in the main frequency band.

[0167] Figure 5 and Figure 7 shows the displacement responses before and after vibration suppression under ANFIS control. The amplitude is significantly reduced to between -0.2 m and 0.2 m, a 50% reduction in amplitude. This shows that ANFIS control significantly reduces the displacement response of the system, demonstrating the control effect from a quantitative perspective.

[0168] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. An active vibration damping control method based on an adaptive neuro-fuzzy inference system, characterized in that Including: By constructing a system model and collecting data; Designing an ANFIS model based on the state variables of the platform; The ANFIS model automatically adjusts the parameters of the fuzzy membership function through experimental data training; Training the ANFIS model based on a hybrid learning algorithm; Using sensors to obtain the displacement and velocity of the platform in real time and inputting them into the ANFIS model to achieve real-time active vibration damping control; The construction of the system model and data collection includes: Obtain the displacement of the platform through the sensor and velocity As the input variables of the system, reflecting the current state of the vibration system, the voice coil motor generates corresponding braking forces according to the control signals F , to offset the vibration force received by the platform, to construct the dynamic model of the system, and to determine the input-output relationship; The ANFIS model automatically adjusts the parameters of the fuzzy membership function through experimental data training, including: Multiple fuzzy rules R i constitute the ANFIS model. Each rule generates a control output according to the fuzzy states of the input variables and . The fuzzy rules are shown as follows: Where, Ai and Bi represent the fuzzy sets of input variables; U represents the control signal of the voice coil motor; According to the fuzzy rules, the activation values of each rule are derived: where ω i represents the rule activation degree, and μA i (x) represents the membership degree that the input x(t) belongs to the fuzzy set Ai. μBi(x) represents the membership degree that the input x(t) belongs to the fuzzy set B i ; Perform weighted average defuzzification on the fuzzy results and output the final control signal: where, f i represents the output of the i-th fuzzy rule, N represents the total number of rules, and i = 1, 2, 3, …, N.

2. The active vibration damping control method based on an adaptive neuro-fuzzy inference system according to claim 1, characterized in that, The dynamic model is used to describe the dynamic behavior of the platform vibration system, and the equation is as follows: Where, M is the equivalent mass matrix of the system, which determines the response intensity of the system to external vibrations; C is the damping coefficient, which characterizes the damping effect of the system; K is the stiffness coefficient, which determines the anti-deformation ability of the system; F(t) is the control force generated by the voice coil motor to counteract the vibration of the platform.

3. The active vibration damping control method based on an adaptive neuro-fuzzy inference system according to claim 1, wherein Designing an ANFIS model based on the state variables of the platform includes: Nonlinear mapping is performed through the fuzzy logic rules and the adaptive ability of the neural network to generate the control signal of the system. The displacement of the platform is selected as the input of the ANFIS model. and velocity are used as the input variables, and the output variable is the control signal.

4. The active vibration damping control method based on an adaptive neuro-fuzzy inference system according to claim 1, characterized in that Designing an ANFIS model based on the state variables of the platform also includes: Defining the input state through fuzzy processing and fuzzy membership function, and the membership function selects the generalized bell-shaped function, and the expression is: Where, μ(x) is the input state of the input data x, a is the width parameter, which controls the stretching degree of the membership function; b is the shape parameter, which adjusts the curve shape of the membership function; c is the center parameter, which determines the position of the membership function.

5. The active vibration damping control method based on an adaptive neuro-fuzzy inference system according to claim 1, characterized in that, Training the ANFIS model based on a hybrid learning algorithm includes: In the forward propagation stage, the least squares method is used to optimize the weights of the linear combination of outputs to minimize the error between the model output and the actual value. The output layer of the ANFIS is a linear combination of activated fuzzy rules, and its calculation formula is: Where, U is the control signal of the voice coil motor, wn is the weight of the fuzzy rule; fn is the output of the nth fuzzy rule, n = 1, 2, 3,..., N; f1 is the output of the first model rule, f2 is the output of the second model rule, and w1 and w2 are the corresponding weights; The goal of the least squares method is to adjust wi to minimize the error, and the error is defined as: Where E is the error, m is the number of samples, and k represents the serial numbers of the samples from the 1st to the mth. is the predicted output value, is the actual output value; in the backpropagation stage, the gradient descent method is used to update the parameters of the fuzzy membership function. By adjusting the shape and position of the membership function, the output of the model can be made closer to the response of the actual system. The update formula is as follows: where η is the learning rate, , , are the updated system parameters, , , are the current system parameters.

6. The active vibration damping control method based on an adaptive neuro-fuzzy inference system according to claim 1, characterized in that Training the ANFIS model based on a hybrid learning algorithm also includes: Defining the error function of the system, assuming e(t) is the error at time step t, and it is calculated in the following way: Among them, y(t) is the actual output value at time t, and y desired (t) is the expected output value at time t; Calculating the rate of change of the error, that is, the gradient of the error Δe(t): If the rate of change of the error is large, the system state changes, and the learning rate is increased to accelerate the adjustment; if the error change is small, the system tends to be stable and the learning rate is reduced; Gradually reduce the learning rate based on the error value or the rate of change of the error, as follows: Where, η(t) is the learning rate at time t, η0 is the initial learning rate, and λ is the adjustment factor; Use the dynamically adjusted learning rate to update the weights and parameters of the neural network, and use the gradient descent method to update the weights.

7. The active vibration damping control method based on an adaptive neuro-fuzzy inference system according to claim 1, characterized in that, The displacement and velocity of the platform are obtained in real time by using sensors and input into the ANFIS model to achieve real-time active vibration damping control, including: The ANFIS model combines fuzzy logic and neural networks to calculate the corresponding control signal based on historical data and real-time input. The control signal drives actuators such as voice coil motors to generate a reverse force to counteract the vibration of the platform.

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