Intelligent piezoelectric beam vibration suppression control method based on fuzzy improved active disturbance rejection controller

Abstract

The invention discloses an intelligent piezoelectric beam vibration suppression control method based on a fuzzy improved active disturbance rejection controller. Firstly, a kinetic model and a state-space equation of the intelligent piezoelectric beam are established; thirdly, according to the state-space equation of the intelligent piezoelectric beam, constructing a fuzzy improved active-disturbance-rejection controller, including designing a nonlinear Arcfu function based on an arctan function, and constructing an extended state observer and a nonlinear state error feedback control law based on the nonlinear Arcfu function; the fuzzy controller generates a deviation increment of the vibration displacement tracking error and the vibration speed tracking error according to the deviation of the vibration displacement tracking error and the vibration speed tracking error, and dynamically adjusts a control law parameter by using the deviation increment; finally, the vibration displacement of the intelligent piezoelectric beam is obtained in real time, the fuzzy improved active disturbance rejection controller generates system control quantity according to the vibration displacement, the system control quantity acts on the piezoelectric ceramic piece, and active vibration suppression control is conducted on the intelligent piezoelectric beam. According to the method, high-frequency oscillation is avoided, and the vibration suppression control effect is enhanced.

Description

Technical Field

[0001] This invention belongs to the field of vibration control technology, and in particular relates to an intelligent piezoelectric beam vibration suppression control method based on a fuzzy improved active disturbance rejection controller. Background Technology

[0002] Flexible structures are widely used in engineering fields such as aerospace and precision manufacturing. However, they are prone to continuous vibration under external excitation, which leads to decreased operational accuracy, accelerated fatigue damage, and shortened service life. To solve this problem, active vibration suppression control has become crucial.

[0003] In existing active vibration suppression control systems, PID control has poor adaptability to nonlinear systems and complex disturbances, making it difficult to match the dynamic characteristics of flexible structures; Sliding Mode Control (SMC) suffers from chattering due to discontinuous switching; Robust control and feedback control rely on precise mathematical models, limiting their applicability to multivariable complex systems. Active Disturbance Rejection Control (ADRC) does not require precise mathematical models and is highly adaptable to nonlinear and strongly disturbed systems, but ADRC suffers from limitations due to nonlinearity. fal The non-differentiability of the function at the piecewise points leads to high-frequency oscillations, and the numerous fixed parameters cannot adapt to the dynamic changes of the system, thus affecting the vibration suppression control performance. Therefore, this application proposes an intelligent piezoelectric beam vibration suppression control method based on a fuzzy improved active disturbance rejection controller. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the technical problem this invention aims to solve is to provide an intelligent piezoelectric beam vibration suppression control method based on a fuzzy improved active disturbance rejection controller.

[0005] The present invention solves the aforementioned technical problem by adopting the following technical solution: A method for intelligent piezoelectric beam vibration suppression control based on a fuzzy improved active disturbance rejection controller is characterized by the following steps: Step 1: Establish the dynamic model and state-space equations of the intelligent piezoelectric beam; Step 2: Based on the state-space equation of the smart piezoelectric beam, construct a fuzzy improved active disturbance rejection controller, including an extended state observer, a nonlinear state error feedback control law, and a fuzzy controller. Design of nonlinear functions based on arctan function Arcfal The function, whose expression is: (11) (12) In the formula, Representing nonlinearity Arcfal function, express Vibration displacement tracking error at any given time. It is a nonlinear factor. The length of the linear segment interval. The attenuation coefficient; The discretized expression for the extended state observer is: (13) In the formula, represent The actual value of vibration displacement at any given time. , for , The estimated value of the vibration displacement tracking error at any given time. , for , The estimated value of the vibration velocity tracking error at any given time. , for , The estimated value of the total system disturbance at time t. The sampling step size, , , To extend the state observer gain, As an interference compensation factor, for System control variables at any given time; The discretized expression of the state error feedback control law is: (14) In the formula, for The deviation between the estimated and expected values ​​of the vibration displacement tracking error at any given time. for The deviation between the estimated and expected values ​​of the vibration velocity tracking error at any given time. For the output of the state error feedback control law Time system control quantity and For control law parameters, This is the compensation coefficient; The fuzzy controller generates the deviation increment of the vibration displacement tracking error based on the deviation between the estimated and expected values ​​of the vibration displacement tracking error and the deviation between the estimated and expected values ​​of the vibration velocity tracking error. The deviation increment of vibration velocity tracking error By tuning the control law parameters using the deviation increment, the control law parameters satisfy the following equation: (15) In the formula: These are the initial values ​​for the control law parameters; Step 3: Real-time acquisition of the vibration displacement of the intelligent piezoelectric beam. The extended state observer estimates the vibration displacement tracking error, vibration velocity tracking error, and total system disturbance based on the vibration displacement of the intelligent piezoelectric beam. The fuzzy controller dynamically adjusts the control law parameters based on the deviations between the estimated and expected values ​​of the vibration displacement tracking error and the vibration velocity tracking error. The nonlinear state error feedback control law outputs the system control quantity based on the deviations between the estimated and expected values ​​of the vibration displacement tracking error and the vibration velocity tracking error, as well as the adjusted control law parameters. The system control quantity output by the control law is compensated using the estimated value of the total system disturbance. The compensated system control quantity is then applied to the piezoelectric ceramic sheet to actively suppress vibration in the intelligent piezoelectric beam.

[0006] Compared with the prior art, the beneficial effects of the present invention are: This invention designs nonlinear functions based on the arctan function. Arcfal The function solves the problem of existing nonlinearity. fal The problem of high-frequency oscillations caused by the non-differentiability of a function at piecewise points; based on Arcfal The extended state observer and nonlinear state error feedback control law, designed using a function, organically combine the two. The improved extended state observer can more accurately estimate the system state and the total disturbance acting on the system, while the improved nonlinear state error feedback control law can generate more targeted system control variables. Based on the improved active disturbance rejection controller, a fuzzy controller is introduced, combining the adaptive capability of fuzzy logic with the nonlinear control capability of the nonlinear state error feedback control law to achieve real-time dynamic adjustment of the control law parameters. This enhances the adaptability and stability of the active disturbance rejection controller and effectively strengthens the vibration suppression control effect. Attached Figure Description

[0007] Figure 1 This is a schematic diagram of the structure of the intelligent piezoelectric beam of the present invention; Figure 2 This is a schematic diagram of the control principle of the active disturbance rejection controller of the present invention; Figure 3 This is a control principle diagram of the fuzzy improved active disturbance rejection controller of the present invention; Figure 4 This is a vibration displacement diagram of the intelligent piezoelectric beam of the present invention under no vibration suppression control. Figure 5 The diagram shows the vibration displacement of the self-disturbance rejection controller and the vibration-displacement control without vibration suppression according to the present invention. Figure 6 This is a vibration displacement diagram of the fuzzy improved active disturbance rejection controller and the vibration-damping control under the present invention. Detailed Implementation

[0008] Specific embodiments are given below with reference to the accompanying drawings. These specific embodiments are only used to describe the technical solution of the present invention in detail and are not intended to limit the scope of protection of this application.

[0009] like Figures 1-3 As shown, this invention provides a smart piezoelectric beam vibration suppression control method based on a fuzzy improved active disturbance rejection controller, comprising the following steps: Step 1: Establish the dynamic model and state-space equations of the smart piezoelectric beam based on Euler-Bernoulli beam theory; According to the Euler-Bernoulli beam theory, the Euler-Bernoulli beam equation is: (1) In the formula, The distributed load is the piezoelectric ceramic sheet acting on the beam. for At any given moment, the distance from the origin on the beam is... Lateral displacement at the location Let be the bending stiffness of the beam. The material density of the beam, Let be the cross-sectional area of ​​the beam; Lateral displacement is determined using the modal superposition method. Represented as: (2) In the formula, For the first First-order modal shape function, For the first Principal coordinates; Substituting equation (2) into equation (1), we get: (3) (4) In the formula, The modal shape governing equations, for The second derivative, For the first The natural frequencies of the first mode; According to the modal orthogonality condition, we have: (5) In the formula, The symbol for Kronecker. For the normalized modal shape function, The length of the beam; Substitute equation (4) into equation (3), and multiply both sides of equation (3) by the same factor. and Liang Chang After integration, substituting equation (5) into it, we obtain the vibration control equation of the beam as follows: (6) In the formula, For the first First-order modal damping ratio, for The first derivative; The distributed load of the piezoelectric ceramic sheet acting on the beam is: (7) (8) In the formula, The torque exerted by the piezoelectric ceramic sheet on the beam. For the Heaviside function, The voltage applied to the piezoelectric ceramic sheet, The width of the piezoelectric ceramic sheet. The piezoelectric constant of the piezoelectric ceramic sheet is... The electric field strength of the piezoelectric ceramic sheet. For the thickness of the beam, The thickness of the piezoelectric ceramic sheet. This is the distance from one end of the piezoelectric ceramic sheet to the fixed end of the beam. This is the distance from the other end of the piezoelectric ceramic sheet to the fixed end of the beam.

[0010] Substituting equation (7) into equation (6), we obtain the vibration control equation of the beam under the action of the piezoelectric ceramic sheet as follows: (9) By introducing state-space variables, the state-space equations of the smart piezoelectric beam are established as follows: (10) In the formula, Represents a state variable. Represents the state matrix. Represents the input matrix. Represents system control variables. Represents output quantity. This represents the output matrix.

[0011] Step 2: Based on the state-space equation of the beam, construct a fuzzy improved active disturbance rejection controller, including an extended state observer, a nonlinear state error feedback control law, and a fuzzy controller; (1) Based on the arctan function in fal Designing nonlinear functions based on functions Arcfal Function, nonlinear Arcfal The function is smooth and continuously differentiable, and its expression is: (11) (12) In the formula, represent The vibration displacement tracking error at any given time is the deviation between the tracked vibration displacement value and the actual vibration displacement value. It is a nonlinear factor. The length of the linear segment interval. To adjust the attenuation coefficient of the error gain.

[0012] (2) Based on nonlinearity Arcfal The function designs an extended state observer to estimate the total internal and external disturbances, vibration displacement tracking error, and vibration velocity tracking error of the control system. The discretized expression of the extended state observer is: (13) In the formula, represent The actual value of vibration displacement at any given time. , for , The estimated value of the vibration displacement tracking error at any given time. , for , The estimated value of the vibration velocity tracking error at any given time. , for , The estimated value of the total system disturbance at time t. The sampling step size, , , To extend the state observer gain, As an interference compensation factor, for System control variables at any given time.

[0013] This extended state observer can better treat all disturbances from both inside and outside the system as a total disturbance and expand them into new state variables. This allows it to more accurately estimate the real-time amount of the total disturbance without relying on a specific mathematical model of the disturbance, and to eliminate the impact in advance by using compensation methods.

[0014] (3) Based on nonlinearity Arcfal The nonlinear state error feedback control law, designed using functions, can generate more targeted system control variables. Therefore, the discretized expression of the state error feedback control law is: (14) In the formula, for The deviation between the estimated and expected values ​​of the vibration displacement tracking error at any given time. for The deviation between the estimated and expected values ​​of the vibration velocity tracking error at any given time. For the output of the state error feedback control law Time system control quantity and For control law parameters, This is the compensation coefficient.

[0015] like Figure 2 As shown, based on nonlinearity Arcfal The active disturbance rejection controller of the function is based on nonlinearity Arcfal The organic combination of the extended state observer and the state error feedback control law in this controller enables the extended state observer to more accurately estimate the system state and action and the total disturbance of the system, and feed them back to the state error feedback control law. This allows the state error feedback control law to generate more targeted system control quantities, thereby achieving overall control performance superior to traditional active disturbance rejection controllers or the use of any one component alone.

[0016] (4) Introduce a fuzzy controller to dynamically adjust the control law parameters in real time to improve the control's adaptability and vibration suppression performance; like Figure 3 As shown, the fuzzy controller uses the deviation between the estimated and expected values ​​of the vibration displacement tracking error as the basis for its calculation. The deviation between the estimated and expected values ​​of vibration velocity tracking error Generate the deviation increment of vibration displacement tracking error The deviation increment of vibration velocity tracking error By tuning the control law parameters using the deviation increment, the control law parameters satisfy the following equation: (15) In the formula: These are the initial values ​​for the control law parameters.

[0017] In fuzzy control, the input quantities are fuzzified, including NB (negative large), NS (negative small), ZO (zero), PS (positive small), and PB (positive large). A joint Gaussian membership function is used for the input quantities, and a triangular membership function is used for the output quantities. Based on practical control experience and active disturbance rejection control theory, 25 fuzzy control rules are formulated, as shown in Tables 1 and 2.

[0018] Table 1. Fuzzy control rules for the deviation increment of vibration displacement tracking error

[0019] Table 2. Fuzzy control rules for the deviation increment of vibration velocity tracking error

[0020] Step 3: Real-time acquisition of the vibration displacement of the intelligent piezoelectric beam; the fuzzy improved active disturbance rejection controller generates system control quantity based on the vibration displacement, and applies the system control quantity to the piezoelectric ceramic sheet to actively suppress vibration of the intelligent piezoelectric beam. The extended state observer estimates the vibration displacement tracking error, vibration velocity tracking error, and total system disturbance based on the beam's vibration displacement. The fuzzy controller dynamically adjusts the control law parameters based on the deviations between the estimated and expected values ​​of the vibration displacement tracking error and the vibration velocity tracking error. The nonlinear state error feedback control law outputs the system control quantity based on the deviations between the estimated and expected values ​​of the vibration displacement tracking error and the vibration velocity tracking error, as well as the adjusted control law parameters. It then uses the estimated total system disturbance to compensate for the system control quantity output by the control law, and applies the compensated system control quantity to the piezoelectric ceramic sheet.

[0021] Example This embodiment takes the active vibration suppression control of the intelligent piezoelectric beam at the first modal frequency as an example. The main parameters of the beam and the piezoelectric ceramic sheet are shown in Table 3.

[0022] Table 3 Main parameters of beams and piezoelectric ceramic sheets

[0023] Numerical simulation was performed using MATLAB. A sinusoidal voltage signal with a first-order modal frequency of 16.25 Hz and an amplitude of 10 V was applied to the intelligent piezoelectric beam for 40 seconds, with a sampling time interval of 0.001 s. This yielded the vibration-displacement curve of the intelligent piezoelectric beam without vibration damping control. Figure 4 As shown.

[0024] A laser displacement sensor is used to collect the vibration displacement signal of the free end of the intelligent piezoelectric beam in real time, and the data is transmitted to a data acquisition card. The collected vibration displacement signal is then transmitted to a computer for control. The system control quantity output by the active disturbance rejection controller is amplified by a certain factor through a power amplifier to reach the effective operating voltage of the piezoelectric ceramic, and then applied to the piezoelectric ceramic, thereby realizing active vibration suppression control. The vibration displacement curves under no vibration suppression control and under the active disturbance rejection controller are shown below. Figure 5 As shown, the vibration displacement response curves under no vibration damping control and the fuzzy improved active disturbance rejection controller are as follows: Figure 6 As shown.

[0025] As can be seen from the figure, the nonlinear design based on the arctan function in this invention... Arcfal The function effectively solves the problem caused by nonlinearity. fal The non-differentiability of the function at the piecewise points leads to high-frequency oscillations. Therefore, compared to active disturbance rejection controllers, nonlinear... Arcfal The fuzzy improved active disturbance rejection controller based on function design has better parameter adaptability, vibration suppression performance and stability, and improves the first-order modal vibration suppression performance of the smart piezoelectric beam by 75.38%.

[0026] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for intelligent piezoelectric beam vibration suppression control based on a fuzzy improved active disturbance rejection controller, characterized in that, Includes the following steps: Step 1: Establish the dynamic model and state-space equations of the intelligent piezoelectric beam; Step 2: Based on the state-space equation of the smart piezoelectric beam, construct a fuzzy improved active disturbance rejection controller, including an extended state observer, a nonlinear state error feedback control law, and a fuzzy controller. Design of nonlinear functions based on arctan function Arcfal The function, whose expression is: (11) (12) In the formula, Representing nonlinearity Arcfal function, express Vibration displacement tracking error at any given time. It is a nonlinear factor. The length of the linear segment interval. The attenuation coefficient; The discretized expression for the extended state observer is: (13) In the formula, represent The actual value of vibration displacement at any given time. , for , The estimated value of the vibration displacement tracking error at any given time. , for , The estimated value of the vibration velocity tracking error at any given time. , for , The estimated value of the total system disturbance at time t. The sampling step size, , , To extend the state observer gain, As an interference compensation factor, for System control variables at any given time; The discretized expression of the state error feedback control law is: (14) In the formula, for The deviation between the estimated and expected values ​​of the vibration displacement tracking error at any given time. for The deviation between the estimated and expected values ​​of the vibration velocity tracking error at any given time. For the output of the state error feedback control law Time system control quantity and For control law parameters, The compensation coefficient; The fuzzy controller generates the deviation increment of the vibration displacement tracking error based on the deviation between the estimated and expected values ​​of the vibration displacement tracking error and the deviation between the estimated and expected values ​​of the vibration velocity tracking error. The deviation increment of vibration velocity tracking error By tuning the control law parameters using the deviation increment, the control law parameters satisfy the following equation: (15) In the formula: These are the initial values ​​for the control law parameters; Step 3: The vibration displacement of the intelligent piezoelectric beam is acquired in real time. The extended state observer estimates the vibration displacement tracking error, vibration velocity tracking error, and total system disturbance based on the vibration displacement of the intelligent piezoelectric beam. The fuzzy controller dynamically adjusts the control law parameters based on the deviation between the estimated and expected values ​​of the vibration displacement tracking error and the vibration velocity tracking error. The nonlinear state error feedback control law outputs the system control quantity based on the deviation between the estimated and expected values ​​of the vibration displacement tracking error, the deviation between the estimated and expected values ​​of the vibration velocity tracking error, and the adjusted control law parameters. The system control quantity output by the control law is compensated by the estimated value of the total system disturbance, and the compensated system control quantity is applied to the piezoelectric ceramic sheet to perform active vibration suppression control on the intelligent piezoelectric beam.

2. The intelligent piezoelectric beam vibration suppression control method based on a fuzzy improved active disturbance rejection controller according to claim 1, characterized in that, The fuzzy control rules of the fuzzy controller are shown in Tables 1 and 2: Table 1. Fuzzy control rules for the deviation increment of vibration displacement tracking error ， Table 2. Fuzzy control rules for the deviation increment of vibration velocity tracking error ， in, This represents the deviation between the estimated and expected values ​​of the vibration displacement tracking error. This represents the deviation between the estimated and expected values ​​of the vibration velocity tracking error. NB represents a large negative value, NS represents a small negative value, ZO represents zero, PS represents a small positive value, and PB represents a large positive value.

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