A preset performance improvement adaptive control method for a piezoelectric drive active-passive hybrid vibration isolation system

Abstract

The application discloses a preset performance improvement adaptive control method of a piezoelectric drive active-passive hybrid vibration isolation system, and aims to solve the problems of transient and steady state performance constraints and difficulty in processing system nonlinear characteristics in existing vibration suppression methods. The specific steps comprise the following steps: 1) simplifying the piezoelectric drive active-passive hybrid vibration isolation system into a mass-spring-damper system, and deducing the dynamic equation and the system transfer function of the vibration isolation system; 2) performing performance constraints on the vibration isolation system through preset performance control, and then improving the transient and steady state performance of the vibration isolation system; 3) adopting FLANN to perform linear independent mapping expansion on external vibration, so that the expanded reference vibration signal has certain nonlinear components, and the processing capacity of the controller on the mixed nonlinear characteristics of the system is improved; and 4) based on steps 1) to 3), realizing vibration suppression on the active-passive hybrid vibration isolation system through an improved adaptive convex combination controller.

Description

Technical Field

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

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

[0003] Currently, the main vibration isolation methods include passive vibration isolation, active vibration isolation, and hybrid active-passive vibration isolation. Passive vibration isolation is simple in structure and highly reliable, but it often fails to achieve ideal vibration suppression in the low-frequency range. While active vibration isolation systems can effectively suppress external vibrations at lower frequencies, their performance becomes limited by the capabilities of their sensors and actuators as the vibration frequency increases, making it difficult to meet vibration isolation requirements. To overcome the limitations of passive and active vibration isolation and improve the system's isolation bandwidth, hybrid active-passive vibration isolation technology, combining the two, has been extensively studied.

[0004] In summary, to achieve high-performance micro-vibration suppression over a wide frequency band, this invention constructs a piezoelectric-driven active-passive hybrid vibration isolation system, composed of active vibration isolation elements (piezoelectric actuators) and passive vibration isolation elements (rubber passive isolators). The system employs the widely used adaptive filtered-x least mean square (FxLMS) method for control. This method is simple in structure, highly adaptive, and does not require high model accuracy; therefore, its research is of great significance.

[0005] However, in practical applications, the adaptive FxLMS method also has many problems. For example, its convergence speed and steady-state accuracy are mutually restrictive, making it difficult to improve both simultaneously. Furthermore, the adaptive FxLMS method achieves vibration suppression through the linear convolution of the external excitation sequence and the controller weight vector. However, due to the material properties of the active and passive vibration isolation components, the vibration isolation system exhibits some nonlinear characteristics during operation. Therefore, the mixed nonlinear characteristics of the vibration isolation system composed of both active and passive vibration isolation components increase the burden on the controller, thus affecting the system's vibration suppression performance.

[0006] Therefore, no relevant technology has yet been found on how to construct an adaptive controller that combines transient and steady-state performance and can handle relatively complex nonlinear characteristics, and apply it to a piezoelectric-driven active-passive hybrid vibration isolation system to achieve high-performance micro-vibration suppression. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of the prior art by proposing a pre-set performance improvement adaptive control method for a piezoelectric-driven active-passive hybrid vibration isolation system.

[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-damping system. Based on Newton's second law, derive the dynamic equations of the vibration isolation system as follows:

[0010]

[0011] Where m1 is the equivalent mass of the active and passive vibration isolation elements, 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, and x1, x2, and These represent the displacement, velocity, and acceleration of the active-passive hybrid vibration isolation system and the sensitive load, respectively.

[0012] By performing a Laplace transform on the dynamic equation (1) of the vibration isolation system and eliminating x1(s), the system transfer function G(s) can be obtained as follows:

[0013]

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

[0015] Step 2: By setting performance controls, the vibration isolation system is constrained to improve its transient and steady-state performance.

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

[0017] ρ(t)=(ρ0-ρ ∞ )e -lt +ρ ∞ (3)

[0018] Where l represents the parameters affecting the convergence speed of the preset performance function, ρ0 and ρ ∞ Let represent the initial and final values ​​of the function, respectively, and e represent the residual vibration of the system.

[0019] Therefore, the desired residual vibration preset performance constraint range can be described as follows:

[0020]

[0021] Where δ represents the parameter selected based on residual vibration overshoot during the control process, and δ = 1 is taken.

[0022] Then, an error transformation is performed; the transformation error after transformation is:

[0023]

[0024] Where ε represents the transformation error after transformation. Furthermore, the residual vibration error of the system converges when ε is bounded; z(t) represents the normalized error.

[0025]

[0026] And it meets the following conditions:

[0027]

[0028] Step 3: Based on the above-mentioned preset performance constraints, a Functional Link Artificial Neural Network (FLANN) is introduced to perform nonlinear mapping expansion of external vibrations, thereby improving the controller's ability to handle the mixed nonlinear characteristics of the system.

[0029] Extending the system using the Trigonometric method, the expanded reference vibration signal is represented as follows:

[0030]

[0031] Among them, L w Let P be the order of the original input vector of the controller before expansion, and let P be the dimension of the nonlinear expansion using linearly independent functions.

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

[0033] y f (k)=W′ T (k)G(k) (9)

[0034] Where W′(k) represents the neural network weight vector, it can be expressed as

[0035] Step 4: Based on the above-mentioned preset performance constraints and FLANN nonlinear mapping extension, vibration suppression of the active-passive hybrid vibration isolation system is achieved through an improved adaptive convex combination controller.

[0036] 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:

[0037]

[0038] Where E[·] represents the mathematical expectation, and ε1(k) and ε2(k) represent the transformation errors obtained by transforming the residuals e1 and e2 of W1(z) and W2(z), respectively.

[0039] Furthermore, after performing a nonlinear mapping expansion of the external vibration using FLANN, the residuals e1 and e2 of the two controllers in the convex combination are expressed as:

[0040]

[0041] Among them, U i (k)=[u(k),u(k-1),...,u(kL n +1)] T For the i-th L n The output vector of the first-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 reference vibration signal after nonlinear expansion through the secondary channel. Its expression is:

[0042]

[0043] Where * denotes convolution operation. Representative secondary channel model The impulse response vector.

[0044] To ensure that the weight vectors of the two controllers continuously approach the optimal weights, the LMS algorithm is 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) are as follows:

[0045]

[0046] Where μ n1 and μ n2 ρ1(k) and ρ2(k) represent the normalized step size used by the two controllers in the convex combination, respectively, while ρ1(k) and ρ2(k) represent the discretized preset performance functions designed based on the external vibration characteristics.

[0047] By designing an adaptive parameter τ to dynamically adjust the combined weights of the adaptive convex combination of the two controllers, the output of the combined system controller is:

[0048]

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

[0050]

[0051] Where 'a' is a parameter that is adjusted in real time based on the residual vibration of the system, and it plays a decisive role in the magnitude of τ. 'a' is updated in real time using the gradient descent method, i.e.:

[0052]

[0053] Where, μ a This represents the update step size of parameter a. Furthermore, to ensure the adaptability of the convex combination of the system, the range of values ​​for a(k) should satisfy the inequality -4 ≤ a(k) ≤ 4.

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

[0055] Considering both the transient and steady-state performance of the system and its computational complexity, the step size of the controller is 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 based on actual performance requirements and the external vibration mode. For 50Hz sinusoidal vibration, since the excitation frequency is close to the system resonant frequency, the resonance effect leads to 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; while for other forms of external vibration, the preset performance function is ρ1(t) = 15.3e -10.5t +1, ρ2(t)=15.5e -8.6t +0.7.

[0056] The beneficial effects of this invention are as follows:

[0057] This invention proposes a pre-set performance improvement adaptive control method for piezoelectric-driven active-passive hybrid vibration isolation systems to ensure their vibration suppression performance. This method has three main advantages: First, it achieves feedback reconstruction of the reference vibration signal, enabling effective vibration suppression even when vibration information is unknown, thus improving the system's applicability. Second, this invention introduces pre-set performance constraints based on the adaptive controller, simultaneously improving the system's convergence speed and steady-state accuracy, ensuring overall system performance. Third, it uses FLANN to perform linearly independent mapping expansion of the external vibration, resulting in a certain nonlinear component in the expanded reference vibration signal. This increases the controller's input dimension while enhancing its ability to handle the system's hybrid nonlinear characteristics, thereby achieving high-precision vibration suppression.

[0058] The method of this invention fully considers the transient and steady-state performance constraints and the difficulty in handling the hybrid nonlinear characteristics of the system faced by vibration isolation systems in practical applications, and provides a theoretical basis and technical reference for the application of piezoelectric driven active-passive hybrid vibration isolation systems in practical engineering. Attached Figure Description

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

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

[0061] Figure 3 This is a schematic diagram of the experimental setup for the piezoelectric-driven active-passive hybrid vibration isolation system of the present invention;

[0062] Figure 4 This is a schematic diagram illustrating the working principle of the piezoelectric-driven active-passive hybrid vibration isolation system of the present invention.

[0063] Figure 5 The figure shows the experimental results of suppressing free vibrations according to the present invention;

[0064] Figure 6 The figure shows the experimental results of suppressing 5Hz vibration according to the present invention;

[0065] Figure 7 The figure shows the experimental results of suppressing 50Hz vibration according to the present invention;

[0066] Figure 8 The figure shows the experimental results of suppressing 100Hz vibration according to the present invention;

[0067] Figure 9 The figure shows the experimental results of the present invention in suppressing complex vibrations. Detailed Implementation

[0068] The invention will now be described in more detail with reference to the accompanying drawings, and the effectiveness of the technical solution will be further verified through an implementation example.

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

[0070] Step 1: Dynamic analysis of the piezoelectric-driven active-passive hybrid vibration isolation system, as follows Figure 2 As shown, given that the adaptive controller used in this invention does not require high model accuracy, the piezoelectric-driven active-passive hybrid vibration isolation system is simplified into a mass-spring-damping system for ease of analysis. From bottom to top, the system consists of the excitation source, the piezoelectric-driven active vibration isolation element, the rubber-based passive vibration isolation element, and the load. Therefore, according to Newton's second law, the dynamic equation of the vibration isolation system can be derived as follows:

[0071]

[0072] Where m1 is the equivalent mass of the active and passive vibration isolation elements, 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, and x1, x2, and These represent the displacement, velocity, and acceleration of the active-passive hybrid vibration isolation system and the sensitive load, respectively.

[0073] Applying a Laplace transform to equation (18) and eliminating x1(s), the system transfer function G(s) can be obtained as follows:

[0074]

[0075] The dynamic model described above can accurately describe the dynamic characteristics of the vibration isolation system.

[0076] Step 2: By setting performance controls, the vibration isolation system is constrained to improve its transient and steady-state performance.

[0077] Preset performance control first requires designing a corresponding performance function based on control requirements to constrain the system's transient and steady-state performance. Then, to reduce the impact of constraints on controller design, an error transformation is used to convert the constrained system into an unconstrained system, thereby transforming the original error convergence problem into a transformed bounded error problem. Generally, the preset performance function ρ(t) must be a monotonically decreasing smooth function and satisfy the following conditions. In summary, the preset performance function ρ(t) is designed as follows:

[0078] ρ(t)=(ρ0-ρ ∞ )e -lt +ρ ∞ (3)

[0079] Where l represents the parameters affecting the convergence speed of the preset performance function, ρ0 and ρ ∞ Let represent the initial and final values ​​of the function, respectively, and e represent the residual vibration of the system.

[0080] Therefore, the desired residual vibration preset performance constraint range can be described as follows:

[0081]

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

[0083] After designing a preset performance function based on actual control requirements, error transformation can be performed to realize subsequent controller design. First, the residual vibration is normalized, i.e.:

[0084]

[0085] Where z represents the normalized error, and satisfies the following condition:

[0086]

[0087] By performing a systematic error transformation, the transformed error can be obtained as follows:

[0088]

[0089] Where ε is the transformation error after the transformation. Furthermore, the residual vibration error of the system converges when ε is bounded.

[0090] Step 3: Based on the above-mentioned preset performance constraints, a Functional Link Artificial Neural Network (FLANN) is introduced to perform nonlinear mapping expansion of external vibrations, thereby improving the controller's ability to handle the mixed nonlinear characteristics of the system.

[0091] As a single-layer neural network, FLANN maps the input signal using a set of linearly independent functions, expanding the original input into a higher-dimensional vector and generating multiple linearly independent new samples, thus allowing for higher-dimensional representation of the input. Through trigonometric expansion, the expanded system reference vibration signal can be represented as:

[0092]

[0093] Among them, L w Let P be the order of the original input vector of the controller before expansion, and let P be the dimension of the nonlinear expansion using linearly independent functions.

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

[0095] y f (k)=W′ T (k)G(k) (9)

[0096] Where W′(k) represents the neural network weight vector, it can be expressed as

[0097] Step 4: Based on the above-mentioned preset performance constraints and FLANN nonlinear mapping extension, an improved adaptive convex combination controller can be designed and applied to the vibration suppression of the active-passive hybrid vibration isolation system.

[0098] 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:

[0099]

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

[0101] Furthermore, after performing a nonlinear mapping expansion of the external vibration using 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(kL n +1)] T For L n The output vector of the first-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 reference vibration signal after nonlinear expansion through the secondary channel. Its expression is:

[0104]

[0105] Where * denotes convolution operation. Representative secondary channel model The impulse response vector.

[0106] To ensure that the weight vectors of the 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) are as follows:

[0107]

[0108] Where μ n1 and μ n2 ρ1(k) and ρ2(k) represent the normalized step size used by the two controllers in the convex combination, respectively, while ρ1(k) and ρ2(k) represent the discretized preset performance functions designed based on the external vibration characteristics.

[0109] Furthermore, to achieve the adaptive convex combination of the two controllers, the combination weights can be dynamically adjusted by designing an adaptive parameter τ. Therefore, the output of the combined system controller is:

[0110]

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

[0112]

[0113] Here, 'a' is a parameter that is adjusted in real time based on the residual vibration of the system, and it plays a decisive role in the magnitude of τ. In summary, 'a' can be updated in real time using the gradient descent method, i.e.:

[0114]

[0115] Where, μ a This represents the update step size of parameter a. Furthermore, to ensure the adaptability of the convex combination of the system, the range of values ​​for 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 examples.

[0117] Implementation Case:

[0118] The pre-designed performance improvement adaptive control method of this invention is applied to... Figure 3 The piezoelectric-driven active-passive hybrid vibration isolation system shown was subjected to vibration suppression experiments.

[0119] The operation process of the hardware-in-the-loop simulation system based on the piezoelectric-driven active-passive hybrid vibration isolation platform is as follows: First, the corresponding modules of the model and controller are built in the Matlab / Simulink software on the host computer. Then, the corresponding control signals are generated through the Real-Time Windows Target real-time working environment. The control signals are then transmitted to a data acquisition card connected to the PC. The D / A conversion function of the data acquisition card converts the control signals into analog voltage signals, which are then 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 vibration suppression, the remaining residual vibration is measured by a capacitive displacement sensor, and then converted from analog to digital signal by the A / D conversion function of the data acquisition card. The real-time displacement information is then fed back to the host computer, realizing 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] Considering both the transient and steady-state performance of the system and its computational complexity, the step size of the controller is 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 based on actual performance requirements and the external vibration mode. For 50Hz sinusoidal vibration, since the excitation frequency is close to the system resonant frequency, the resonance effect leads to 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; while for other forms of external vibration, the preset performance function is ρ1(t) = 15.3e -10.5t +1, ρ2(t)=15.5e -8.6t +0.7.

[0122] Experimental results are as follows Figures 5-9 As shown. Among them, Figure 5 The figure shows the experimental results of 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 This is a graph showing the experimental results for suppressing low, medium, and high frequency sinusoidal vibrations. Figure 9The experimental results for suppressing composite harmonic vibration d = 0.5sin(2π×10t+1.5π)+0.5sin(2π×10.5t+1.5π) are shown in the figure. Based on the above experimental results, it can also be concluded that the vibration control method proposed in this invention has good vibration suppression performance.

Claims

1. A pre-set performance improvement adaptive control method for a piezoelectric-driven active-passive hybrid vibration isolation system, characterized in that, The steps of this method are as follows: Step 1: Simplify the piezoelectric-driven active-passive hybrid vibration isolation system into a mass-spring-damping system. Based on Newton's second law, derive the dynamic equations of the vibration isolation system as follows: Where m1 is the equivalent mass of the active and passive vibration isolation elements, 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 These represent the displacement, velocity, and acceleration of the active-passive hybrid vibration isolation system and the sensitive load, respectively. By performing a Laplace transform on the dynamic equation (1) of the vibration isolation system and eliminating x1(s), the system transfer function G(s) is obtained as follows: Where s is a complex variable, the dynamic characteristics of the vibration isolation system can be accurately described by the above dynamic model; Step 2: By setting performance controls, the vibration isolation system is subjected to performance constraints, 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 +r ∞ (3) Where l represents the parameters affecting the convergence speed of the preset performance function, ρ0 and ρ ∞ Let represent the initial and final values ​​of the function, respectively, and e represent the residual vibration of the system; Therefore, the desired residual vibration preset performance constraint range can be described as follows: Where δ represents the parameter selected based on residual vibration overshoot during the control process, and δ = 1 is taken; Then, an error transformation is performed; the transformation error after transformation is: Where ε is the transformation error after transformation; and, when ε is bounded, the residual vibration error of the system converges; z(t) represents the error after normalization: And it meets the following conditions: Step 3: Based on the above-mentioned preset performance constraints, a Functional Link Artificial Neural Network (FLANN) is introduced to perform nonlinear mapping expansion of external vibrations, thereby improving the controller's ability to handle the mixed nonlinear characteristics of the system. Extending the system using the Trigonometric method, the expanded reference vibration signal is represented as follows: Among them, L w Let P be the order of the original input vector of the controller before expansion, and let P be the dimension of the nonlinear expansion using linearly independent functions. By convolving the unfolded reference vibration signal input vector with the weight vector, the FLANN output can be obtained as follows: y f (k)=W′ T (k)G(k) (9) Where W′(k) represents the neural network weight vector, it can be expressed as Step 4: Based on the above-mentioned preset performance constraints and FLANN nonlinear mapping extension, vibration suppression of the active-passive hybrid vibration isolation system is achieved 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) represent the transformation errors obtained by transforming the residuals e1 and e2 of W1(z) and W2(z), respectively; Furthermore, after performing a nonlinear mapping expansion of the external vibration using FLANN, the residuals e1 and e2 of the two controllers in the convex combination are expressed as: Among them, U i (k)=[u(k),u(k-1),...,u(kL n +1)] T For the i-th L n The output vector of the first-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 reference vibration signal after nonlinear expansion through the secondary channel. Its expression is: Where * denotes convolution operation. Representative secondary channel model The impulse response vector; To ensure that the weight vectors of the two controllers continuously approach the optimal weights, the LMS algorithm is 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) are as follows: Where μ n1 and μ n2 ρ1(k) and ρ2(k) represent the normalized step size used by the two controllers in the convex combination, respectively, and the discretized preset performance functions designed based on the external vibration characteristics are respectively. By designing an adaptive parameter τ to dynamically adjust the combined weights of the adaptive convex combination of the two controllers, the output of the combined system controller is: To ensure the effectiveness of the convex combination, the adaptive parameter must satisfy τ∈(0,1); therefore, its parameter expression can be obtained as: Where 'a' is a parameter that is adjusted in real time based on the residual vibration of the system, and it plays a decisive role in the magnitude of τ. 'a' is updated in real time using the gradient descent method, i.e.: Where, μ a This represents the update step size of parameter a; furthermore, to ensure the adaptability of the convex combination of the system, the range of values ​​for a(k) should satisfy the inequality -4≤a(k)≤4.

2. The pre-set performance improvement adaptive control method for the piezoelectric-driven active-passive hybrid vibration isolation system according to claim 1, characterized in that, The relevant design parameters are selected according to the following principles: Considering both the transient and steady-state performance of the system and its computational complexity, the step size of the controller is selected as: μ 01 =0.00045, μ 02 =0.0001, L w1 =L n1 =50, L w2 =L n2 =45, P=1; Furthermore, in order to satisfy the inequality μ a >max{μ n1 ,μ n2 }, take μ a =0.06; The preset performance function is selected based on actual performance requirements and external vibration mode. For 50Hz sinusoidal vibration, since the excitation frequency is close to the system resonant frequency, the resonance effect leads to 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; while for other forms of external vibration, the preset performance function is ρ1(t) = 15.3e -10.5t +1, ρ2(t)=15.5e -8.6t +0.7.

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