Preset performance improvement self-adaptive control method of piezoelectric driving active and passive hybrid vibration isolation system

Abstract

The invention discloses a preset performance improvement self-adaptive control method for a piezoelectric driving active and passive hybrid vibration isolation system, and aims to solve the problems that transient and steady state performance constraints and system nonlinear characteristics are difficult to process in an existing vibration suppression method. The method comprises the following specific steps: 1) simplifying a piezoelectric driving active and passive hybrid vibration isolation system into a mass-spring-damping system, and deducing a kinetic equation and a system transfer function of the vibration isolation system; (2) performance constraint is conducted on the vibration isolation system through preset performance control, and then the temporary and steady state performance of the vibration isolation system is improved; 3) performing linear independent mapping expansion on external vibration by adopting FLANN, so that an expanded reference vibration signal has a certain nonlinear component, and improving the processing capability of a controller on the mixed nonlinear characteristic of the system; and 4) based on the steps 1)-3), vibration suppression of the active and passive hybrid vibration isolation system is realized through the improved adaptive convex combination controller.

Description

Technical Field

[0001] The present invention belongs to the technical field of micro-vibration suppression, and more specifically, relates to an adaptive vibration control method for improving the preset performance of a piezoelectric-driven hybrid active and passive vibration isolation system. Background Art

[0002] In recent years, with the rapid development of advanced manufacturing fields such as integrated circuits, optical instruments, and aerospace, how to ensure micro-nano level control accuracy has become the key in the fields of ultra-precision measurement and processing. However, the performance of precision instruments is easily affected by external environments or micro-vibrations inside the instruments. Micro-vibrations refer to vibrations with small amplitudes and high frequencies, usually at the micro-nano level. Although their amplitudes are small, their impact on the reliability and accuracy of precision instrument equipment is significant.

[0003] Currently, the mainly applied vibration isolation methods include passive vibration isolation, active vibration isolation, and hybrid active and passive vibration isolation. Among them, passive vibration isolation has a simple structure and high reliability, but in the low-frequency range, it is usually difficult to achieve ideal vibration suppression. While the active vibration isolation system can effectively suppress external vibrations with lower frequencies, but as the vibration frequency increases, the performance of active vibration isolation will be limited by the capabilities of its sensors and actuators, and it is difficult to meet the vibration isolation requirements. In order to overcome the limitations of passive and active vibration isolation and improve the vibration isolation bandwidth of the system, the hybrid active and passive vibration isolation technology that combines the two has been widely studied.

[0004] In summary, in order to achieve high-performance micro-vibration suppression in a wide frequency band, the present invention constructs a piezoelectric-driven hybrid active and passive vibration isolation system composed of an active vibration isolation element (piezoelectric actuator) and a passive vibration isolation element (rubber passive vibration isolator). And the Filtered-x Least Mean Square (FxLMS) method widely used in the field of vibration isolation is adopted for control. This method has a simple structure, strong self-adaptability, and low requirements for model accuracy, so it is of great significance to conduct research on it.

[0005] However, in practical applications, there are also many problems with the adaptive FxLMS method. For example, its convergence speed and steady-state accuracy restrict each other, and it is difficult to improve both at the same time. In addition, the adaptive FxLMS method realizes vibration suppression through the linear convolution of an external excitation sequence and the controller weight vector. However, affected by the material properties of the active and passive vibration isolation elements, the vibration isolation system will exhibit some non-linear characteristics during operation. Therefore, the hybrid non-linear characteristics of the vibration isolation system composed of the active and passive vibration isolation elements will increase the burden on the controller, and thus affect the vibration suppression performance of the system.

[0006] Therefore, there is no related technology on how to construct an adaptive controller that has both transient and steady-state performance and can handle relatively complex non-linear characteristics, and apply it to the piezoelectric-driven active-passive hybrid vibration isolation system to achieve high-performance micro-vibration suppression. Summary of the Invention

[0007] The purpose of the present invention is to propose a preset performance improvement adaptive control method for the piezoelectric-driven active-passive hybrid vibration isolation system in view of the deficiencies existing in the above-mentioned prior art.

[0008] The specific implementation steps of the technical solution of the present invention are as follows:

[0009] Step 1: Simplify the piezoelectric-driven active-passive hybrid vibration isolation system into a mass-spring-damper system. According to Newton's second law, the dynamic equation of the vibration isolation system is derived as follows:

[0010]

[0011] where m1 is the equivalent mass of the active vibration isolation element and the passive vibration isolation element, and m2 is the mass of the sensitive load. f is the driving force generated by the active vibration isolation element, k1 and c1 represent the equivalent stiffness and equivalent damping of the active vibration isolation element, k2 and c2 represent the equivalent stiffness and equivalent damping of the passive vibration isolation element, x1, x2, and respectively represent the displacement, velocity, and acceleration of the active-passive hybrid vibration isolation system and the sensitive load;

[0012] Perform Laplace transform on the dynamic equation (1) of the vibration isolation system and eliminate x1(s). The system transfer function G(s) can be obtained as:

[0013]

[0014] where s is a complex variable. Through the above dynamic model, the dynamic characteristics of the vibration isolation system can be accurately described.

[0015] Step 2: Perform performance constraint on the vibration isolation system through preset performance control, thereby improving the transient and steady-state performance of the vibration isolation system.

[0016] The preset performance function ρ(t) is:

[0017] ρ(t) = (ρ0 - ρ ∞ )e -lt + ρ ∞ (3)

[0018] where l represents a parameter affecting the convergence speed of the preset performance function, ρ0 and ρ ∞ respectively represent the initial value and the final value of the function, and e represents the residual vibration of the system.

[0019] Therefore, the preset performance constraint interval to be achieved can be described as:

[0020]

[0021] where δ represents the parameter selected according to the residual vibration overshoot during the control process, and δ = 1 is taken.

[0022] Then, error transformation is performed; the transformed conversion error is:

[0023]

[0024] where ε is the transformed conversion error. And when ε is bounded, the system residual vibration error converges; z(t) represents the normalized error:

[0025]

[0026] and satisfies the following conditions:

[0027]

[0028] Step 3: On the basis of the above preset performance constraints, introduce a Functional Link Artificial Neural Network (FLANN) to perform a non-linear mapping expansion on the external vibration, and improve the controller's ability to handle the system's hybrid non-linear characteristics.

[0029] Through expansion in a Trigonometric manner, the expanded system reference vibration signal is expressed as:

[0030]

[0031] where L w is the order of the original input vector of the controller before expansion, and P is the dimension of non-linear expansion using linearly independent functions.

[0032] By convolving the expanded reference vibration signal input vector with the weight vector, the output of FLANN can be obtained as:

[0033] y f (k) = W′ T (k)G(k) (9)

[0034] where W′(k) represents the neural network weight vector and can be expressed as

[0035] Step 4: Based on the above preset performance constraints and FLANN non - linear mapping expansion, vibration suppression of the main - passive hybrid vibration isolation system is achieved through an improved adaptive convex combination controller;

[0036] First, let the objective functions \(J_1(k)\) and \(J_2(k)\) of the two adaptive controllers \(W_1(z)\) and \(W_2(z)\) in the convex combination be respectively:

[0037]

[0038] where \(E[\cdot]\) represents the mathematical expectation, and \(\varepsilon_1(k)\) and \(\varepsilon_2(k)\) respectively represent the transformation errors obtained by converting the residuals \(e_1\) and \(e_2\) of \(W_1(z)\) and \(W_2(z)\).

[0039] In addition, after the external vibration is expanded by non - linear mapping through FLANN, the residuals \(e_1\) and \(e_2\) of the two controllers in the convex combination are expressed as:

[0040]

[0041] where \(U\) i (k)=[u(k),u(k - 1),...,u(k - L n + 1)] T is the output vector of the \(i\) - th \(L\) n - order controller, \(W\) i (k) represents the weight vector of the two adaptive controllers in the convex combination, and \(G′(k)\) represents the reference filtered vector obtained by filtering the reference vibration signal after non - linear expansion through the secondary channel. Its expression is:

[0042]

[0043] where \(*\) represents the convolution operation, represents the impulse response vector of the secondary channel model .

[0044] To make the weight vectors of the above two controllers continuously approach the optimal weights, the LMS algorithm is used to update \(W_1(k)\) and \(W_2(k)\) in real - time to minimize the objective functions \(J_1(k)\) and \(J_2(k)\). Therefore, the update formulas of \(W_1(k)\) and \(W_2(k)\) can be obtained as follows:

[0045]

[0046] where \(\mu\) n1 and \(\mu\) n2 are respectively the normalized step sizes adopted by the two controllers in the convex combination, and \(\rho_1(k)\) and \(\rho_2(k)\) respectively represent the discretized preset performance functions designed according to the characteristics of the external vibration.

[0047] By designing the adaptive parameter τ, the combined weight of the adaptive convex combination of the two controllers is dynamically adjusted, and the output of the combined system controller is:

[0048]

[0049] To ensure the effectiveness of the convex combination, the adaptive parameter needs to satisfy τ ∈ (0, 1). Therefore, its parameter expression can be obtained as:

[0050]

[0051] Among them, a is a parameter that is adjusted in real time according to the residual vibration of the system and plays a decisive role in the magnitude of τ. a is updated in real time by the gradient descent method, that is:

[0052]

[0053] Among them, μ a represents the update step size of the parameter a. In addition, to ensure the self - adaptability of the system convex combination, the value range of a(k) should satisfy the inequality - 4 ≤ a(k) ≤ 4.

[0054] The relevant design parameters are selected according to the following principles:

[0055] Taking into comprehensive consideration of the transient and steady - state performance of the system and the computational complexity, the step sizes of the controllers are selected as: μ 01 = 0.00045, μ 02 = 0.0001, L w1 = L n1 = 50, L w2 = L n2 = 45, P = 1; In addition, to satisfy the inequality μ a > max{μ n1 , μ n2}, take μ a = 0.06. The preset performance function is selected according to the actual performance requirements and the form of external vibration. For 50Hz sinusoidal vibration, since the excitation frequency is relatively close to the resonance frequency of the system, the resonance effect causes a large amplitude. Therefore, the preset performance functions are selected as ρ1(t) = 17.2e -2.7t + 0.8, ρ2(t) = 17.5e -1.9t + 0.5; For other forms of external vibration, the preset performance functions are both taken as ρ1(t) = 15.3e -10.5t + 1, ρ2(t) = 15.5e -8.6t + 0.7.

[0056] The beneficial effects of the present invention are:

[0057] For the piezoelectric-driven active and passive hybrid vibration isolation system, the present invention proposes a preset performance improvement adaptive control method to ensure its vibration suppression performance. This method has the following three main advantages: First, it realizes the feedback reconstruction of the reference vibration signal, enabling effective vibration suppression even when the vibration information is unknown, thus enhancing the applicability of the system; Second, the present invention introduces preset performance constraints on the basis of the adaptive controller, simultaneously improving the convergence speed and steady-state accuracy of the system, and ensuring the overall performance of the system; Third, through FLANN, the external vibration is linearly independent mapped and expanded, so that there are certain non-linear components in the expanded reference vibration signal. While increasing the input dimension of the controller, it enhances the controller's ability to handle the hybrid non-linear characteristics of the system, and thus realizes high-precision vibration suppression.

[0058] The method of the present invention fully considers the transient and steady-state performance constraints faced by the vibration isolation system in practical applications and the problem that it is difficult to handle the hybrid non-linear characteristics of the system, providing a theoretical basis and technical reference for the application of the piezoelectric-driven active and passive hybrid vibration isolation system in practical engineering. Brief Description of the Drawings

[0059] Figure 1 is the control block diagram of the preset performance improvement adaptive control method for the piezoelectric-driven active and passive hybrid vibration isolation system of the present invention;

[0060] Figure 2 is the dynamic analysis diagram of the piezoelectric-driven active and passive hybrid vibration isolation system of the present invention

[0061] Figure 3 is the schematic diagram of the experimental device of the piezoelectric-driven active and passive hybrid vibration isolation system of the present invention;

[0062] Figure 4 is the working principle diagram of the piezoelectric-driven active and passive hybrid vibration isolation system of the present invention;

[0063] Figure 5 is the experimental result diagram when suppressing free vibration of the present invention;

[0064] Figure 6 is the experimental result diagram when suppressing 5 Hz vibration of the present invention;

[0065] Figure 7 is the experimental result diagram when suppressing 50 Hz vibration of the present invention;

[0066] Figure 8 is the experimental result diagram when suppressing 100 Hz vibration of the present invention;

[0067] Figure 9 is the experimental result diagram when suppressing complex vibration of the present invention. Detailed Embodiments

[0068] The following further elaborates on the content of the present invention in conjunction with the accompanying drawings and further verifies the effectiveness of the technical solution through an embodiment.

[0069] In this embodiment, the control block diagram of a preset performance improvement adaptive control method for a piezoelectric-driven main-passive hybrid vibration isolation system is as Figure 1 shown. The specific steps are as follows:

[0070] Step 1: The dynamic analysis of the piezoelectric-driven main-passive hybrid vibration isolation system is as Figure 2 shown. Given that the adaptive controller adopted in the present invention has low requirements for model accuracy, for the convenience of analysis, the piezoelectric-driven main-passive hybrid vibration isolation system is simplified into a mass-spring-damper system. The system from bottom to top is respectively the excitation source, the piezoelectric-driven active vibration isolation element, the passive vibration isolation element based on rubber material, and the load. Therefore, according to Newton's second law, the dynamic equation of the vibration isolation system can be derived as:

[0071]

[0072] where, m1 is the equivalent mass of the active vibration isolation element and the passive vibration isolation element, and m2 is the mass of the sensitive load. f is the driving force generated by the active vibration isolation element, k1 and c1 represent the equivalent stiffness and equivalent damping of the active vibration isolation element, k2 and c2 represent the equivalent stiffness and equivalent damping of the passive vibration isolation element, x1, x2, and respectively represent the displacement, velocity, and acceleration of the main-passive hybrid vibration isolation system and the sensitive load.

[0073] Performing Laplace transform on formula (18) and eliminating x1(s), the system transfer function G(s) can be obtained as:

[0074]

[0075] Through the above dynamic model, the dynamic characteristics of the vibration isolation system can be accurately described.

[0076] Step 2: Perform performance constraints on the vibration isolation system through preset performance control, thereby improving the transient and steady-state performance of the vibration isolation system.

[0077] Preset performance control first needs to design corresponding performance functions according to control requirements to constrain the transient and steady-state performance of the system. Then, to reduce the impact of the constraints on the controller design, error transformation is used to transform the constrained system into an unconstrained system, and thus the original error convergence problem becomes the problem of the boundedness of the transformed error. Generally speaking, the preset performance function ρ(t) needs to be a monotonically decreasing smooth function and satisfy the condition In summary, the preset performance function ρ(t) is designed as:

[0078] ρ(t) = (ρ0 - ρ ∞ )e -lt + ρ ∞ (3)

[0079] where l represents the parameter affecting the convergence speed of the preset performance function, ρ0 and ρ ∞ represent the initial value and the final value of the function respectively, and e represents the residual vibration of the system.

[0080] Therefore, the preset performance constraint interval to be achieved for the residual vibration can be described as:

[0081]

[0082] where δ represents the parameter selected according to the overshoot of the residual vibration during the control process. In this chapter, for the convenience of subsequent controller design, δ = 1 is taken.

[0083] After designing the preset performance function according to the actual control requirements, error transformation can be carried out to realize the subsequent controller design. First, the residual vibration is normalized, that is:

[0084]

[0085] where z represents the error after normalization and satisfies the following conditions:

[0086]

[0087] By performing system error transformation, the transformed conversion error can be obtained as:

[0088]

[0089] where ε is the transformed conversion error. And when ε is bounded, the system residual vibration error converges.

[0090] Step 3: On the basis of the above preset performance constraints, introduce a Functional Link Artificial Neural Network (FLANN) to perform non - linear mapping expansion on the external vibration, and improve the processing ability of the controller for the hybrid non - linear characteristics of the system.

[0091] As a single - layer neural network, FLANN uses a set of linearly independent functions to map the input signal, expands the original input into a vector with a higher dimension, generates multiple linearly independent new samples, and can thus represent the input in a higher dimension. By expanding in the Trigonometric way, the expanded system reference vibration signal can be expressed as:

[0092]

[0093] Among them, L w is the order of the original input vector of the controller before expansion, and P is the dimension of the non-linear expansion using linearly independent functions.

[0094] By convolving the input vector of the expanded reference vibration signal with the weight vector, the output of FLANN can be obtained as:

[0095] y f (k) = W′ T (k)G(k) (9)

[0096] Among them, W′(k) represents the weight vector of the neural network and can be expressed as

[0097] Step 4: Based on the above preset performance constraints and the FLANN non-linear mapping expansion, an improved adaptive convex combination controller can be designed and applied to the vibration suppression of the main passive hybrid vibration isolation system;

[0098] First, the objective functions J1(k) and J2(k) of the two adaptive controllers W1(z) and W2(z) in the convex combination can be set as:

[0099]

[0100] Among them, E[·] represents the mathematical expectation, and ε1(k) and ε2(k) respectively represent the transformation errors obtained by converting the residuals e1 and e2 of W1(z) and W2(z).

[0101] In addition, after the non-linear mapping expansion of the external vibration by FLANN, the residuals e1 and e2 of the two controllers in the convex combination can be expressed as:

[0102]

[0103] Among them, U(k) = [u(k), u(k - 1),..., u(k - L n +1)] T is the output vector of the L n -order controller, W i (k) represents the weight vector of the two adaptive controllers in the convex combination, and G′(k) represents the reference filter vector obtained by filtering the non-linearly expanded reference vibration signal through the secondary channel. Its expression is:

[0104]

[0105] Among them, * represents the convolution operation, represents the impulse response vector of the secondary channel model .

[0106] To make the weight vectors of the above two controllers continuously approach the optimal weights, the LMS algorithm can be used to update W1(k) and W2(k) in real time, minimizing the objective functions J1(k) and J2(k). Therefore, the update formulas for W1(k) and W2(k) can be obtained as follows:

[0107]

[0108] where μ n1 and μ n2 are the normalized step sizes adopted by the two controllers in the convex combination, and ρ1(k) and ρ2(k) respectively represent the discretized preset performance functions designed according to the external vibration characteristics.

[0109] In addition, to achieve the adaptive convex combination of the above two controllers, an adaptive parameter τ can be designed to dynamically adjust the combination weights. Therefore, the output of the combined system controller at this time is:

[0110]

[0111] To ensure the effectiveness of the convex combination, the adaptive parameter needs to satisfy τ ∈ (0, 1). Therefore, its parameter expression can be obtained as:

[0112]

[0113] where a is a parameter that is adjusted in real time according to the residual vibration of the system and plays a decisive role in the magnitude of τ. In summary, a can be updated in real time by the gradient descent method, that is:

[0114]

[0115] where μ a represents the update step size of the parameter a. In addition, to ensure the adaptability of the system convex combination, the value range of a(k) should satisfy the inequality -4 ≤ a(k) ≤ 4.

[0116] The beneficial effects of the present invention are verified by the following specific implementation cases.

[0117] Implementation case:

[0118] Apply the preset performance improved adaptive control method designed by the present invention to the Figure 3 piezoelectric drive main - passive hybrid vibration isolation system shown in the figure for vibration suppression experiments.

[0119] The operation process of the hardware-in-the-loop simulation system based on the piezoelectric-driven active and passive hybrid vibration isolation platform is as follows: First, the corresponding modules of the model and the controller are built in the Matlab / Simulink software of the host computer, and then the corresponding control signals are generated through the Real-Time Windows Target real-time working environment. Then, the control signals are transmitted to the data acquisition card connected to the PC. Through the D / A conversion function of the data acquisition card, the control signals are converted into analog voltage signals, and the signals are transmitted to the drive power supply of the vibration suppression controller for signal amplification, and then used to drive the vibration isolation platform for vibration suppression. After the vibration suppression, the remaining residual vibration is measured by the capacitive displacement sensor, and then after the analog-digital signal conversion is realized through the A / D conversion function of the data acquisition card, the real-time displacement information is fed back to the host computer to realize the closed-loop control of the experimental system.

[0120] The relevant design parameters of the vibration controller are selected according to the following principles:

[0121] Taking into comprehensive consideration of the transient and steady-state performance of the system and the computational complexity, the step sizes of the controller are selected as: μ 01 = 0.00045, μ 02 = 0.0001, L w1 = L n1 = 50, L w2 = L n2 = 45, P = 1; In addition, to satisfy the inequality μ a > max{μ n1 , μ n2}, take μ a = 0.06. The preset performance function is selected according to the actual performance requirements and the form of external vibration. For the 50 Hz sinusoidal vibration, since the excitation frequency is relatively close to the resonance frequency of the system, the resonance effect causes a large amplitude. Therefore, the preset performance functions are selected as ρ1(t) = 17.2e -2.7t + 0.8, ρ2(t) = 17.5e -1.9t + 0.5; For other forms of external vibration, the preset performance functions are both taken as ρ1(t) = 15.3e -10.5t + 1, ρ2(t) = 15.5e -8.6t + 0.7.

[0122] The experimental results are as Figures 5 - 9 shown. Among them, Figure 5 is the experimental result diagram of the free vibration suppression when the impact voltage is 90V. It can be seen that the proposed method can achieve effective vibration suppression in a short time. Figures 6 - 8 is the experimental result diagram when suppressing low, medium and high frequency sinusoidal vibrations. Figure 9For the experimental result diagram when suppressing the composite harmonic vibration \(d = 0.5\sin(2\pi\times10t + 1.5\pi)+0.5\sin(2\pi\times10.5t + 1.5\pi)\), it can also be concluded from the above experimental results that the vibration control method proposed by the present invention has good vibration suppression performance.

Claims

1. An adaptive control method for improving the preset performance of a piezoelectric-driven main-passive hybrid vibration isolation system, characterized in that, The method steps are as follows: Step 1: Simplify the piezoelectric-driven primary and secondary hybrid vibration isolation system into a mass-spring-damper system. According to Newton's second law, the dynamic equation of the vibration isolation system is derived as follows: where, m1 is the equivalent mass of the active vibration isolation element and the passive vibration isolation element, and m2 is the mass of the sensitive load; f is the driving force generated by the active vibration isolation element, k1 and c1 represent the equivalent stiffness and equivalent damping of the active vibration isolation element, and k2 and c2 represent the equivalent stiffness and equivalent damping of the passive vibration isolation element, and respectively represent the displacement, velocity, and acceleration of the hybrid active and passive vibration isolation system and the sensitive load; Perform Laplace transform on the dynamic equation (1) of the vibration isolation system, and eliminate x1(s) to obtain the system transfer function G(s) as: Where s is a complex variable. Through the above dynamic model, the dynamic characteristics of the vibration isolation system can be accurately described; Step 2: Perform performance constraints on the vibration isolation system through preset performance control, thereby improving the transient and steady-state performance of the vibration isolation system; The preset performance function ρ(t) is: ρ(t) = (ρ0 - ρ ∞ )e -lt + ρ ∞ (3) where l represents a parameter that affects the convergence rate of the preset performance function, ρ0 and ρ ∞ represent the initial value and the final value of the function respectively, and e represents the residual vibration of the system; Therefore, the preset performance constraint interval of the residual vibration to be achieved can be described as: Where δ represents the parameter selected according to the residual vibration overshoot during the control process, and take δ = 1; Then perform error transformation; the transformed conversion error is: Where ε is the transformed conversion error; and when ε is bounded, the system residual vibration error converges; z(t) represents the normalized error: And satisfy the following conditions: Step 3: On the basis of the above preset performance constraints, introduce a Functional Link Artificial Neural Network (FLANN) to expand the nonlinear mapping of external vibrations, and enhance the controller's ability to handle the hybrid nonlinear characteristics of the system; Expand through the Trigonometric method, and the expanded system reference vibration signal is expressed as: Among them, L w is the original input vector order of the controller before expansion, and P is the dimension of non-linear expansion using linearly independent functions; By convolving the input vector of the expanded reference vibration signal with the weight vector, the output of FLANN can be obtained as: y f (k) = W′ T (k)G(k) (9) where W′(k) represents the neural network weight vector and can be expressed as Step 4: Based on the above preset performance constraints and FLANN nonlinear mapping expansion, realize the vibration suppression of the primary and secondary hybrid vibration isolation system through an improved adaptive convex combination controller; First, let the objective functions J1(k) and J2(k) of the two adaptive controllers W1(z) and W2(z) in the convex combination be respectively Where E[·] represents the mathematical expectation, and ε1(k) and ε2(k) respectively represent the conversion errors obtained by converting the residuals e1 and e2 of W1(z) and W2(z); In addition, after expanding the nonlinear mapping of external vibrations through FLANN, the residuals e1 and e2 of the two controllers in the convex combination are expressed as: Among them, where U i (k) = [u(k), u(k - 1),..., u(k - L n + 1)] T is the output vector of the i-th L n th-order controller, W i (k) represents the weight vector of the two adaptive controllers in the convex combination, and G′(k) represents the reference filtered vector obtained by filtering the reference vibration signal after nonlinear expansion through the secondary channel. Its expression is: where * represents the convolution operation, represents the impulse response vector of the secondary channel model ; To make the weight vectors of the above two controllers continuously approach the optimal weights, the LMS algorithm is used to update W1(k) and W2(k) in real time to minimize the objective functions J1(k) and J2(k); therefore, the update formulas of W1(k) and W2(k) can be obtained as: where μ n1 and μ n2 are the normalized step sizes adopted by the two controllers in the convex combination, and ρ1(k) and ρ2(k) respectively represent the discretized preset performance functions designed according to the external vibration characteristics; Design an adaptive parameter τ to dynamically adjust the combination weights of the adaptive convex combination of the two controllers, and the output of the combined system controller is: To ensure the effectiveness of the convex combination, the adaptive parameter needs to satisfy τ ∈ (0,1); therefore, its parameter expression can be obtained as: Where a is a parameter that is adjusted in real time according to the system residual vibration and plays a decisive role in the magnitude of τ. a is updated in real time through the gradient descent method, that is: where, μ a represents the update step size of parameter a; in addition, to ensure the self - adaptability of the system's convex combination, the value range of a(k) should satisfy the inequality - 4 ≤ a(k) ≤ 4.

2. The preset performance improvement adaptive control method for the piezoelectric drive main-passive hybrid vibration isolation system according to claim 1, characterized in that The relevant design parameters are selected according to the following principles: Comprehensively weighing the transient and steady-state performance of the system and the computational complexity, the step sizes of the controller are selected as follows: μ 01 = 0.00045, μ 02 = 0.0001, L w1 = L n1 = L w2 = L n2 = 45, P = 1; In addition, to satisfy the inequality μ a > max{μ n1 , μ n2}, μ a is taken as 0.06; the preset performance function is selected according to the actual performance requirements and the form of external vibration. For 50 Hz sinusoidal vibration, since the excitation frequency is relatively close to the system resonance frequency, the resonance effect causes a large amplitude. Therefore, the preset performance function is selected as ρ1(t) = 17.2e -2.7t +0.8, ρ2(t) = 17.5e -1.9t +0.5; for other forms of external vibration, the preset performance functions are both taken as ρ1(t) = 15.3e -10.5t +1, ρ2(t) = 15.5e -8.6t +0.7.

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