Intelligent shafting vibration control system and method

Abstract

The invention discloses an intelligent shafting vibration control system and method. The method comprises the steps that system hardware is set up, an eddy current displacement sensor is installed at a key position to monitor vibration displacement, an electromagnetic actuator is installed on a bearing seat to control bearing rigidity and damping through current, and a data acquisition and analysis system is configured to be connected with the sensor and the actuator and complete parameter setting; the method comprises the following steps: designing a vibration control algorithm, establishing a kinetic model and a noise model, solving an optimal feedback gain matrix and a state estimation value to calculate a control force, optimizing linear quadratic Gaussian (LQG) control parameters by using particle swarm optimization (PSO), defining a target, initializing, calculating fitness, updating particle parameters until conditions are met, and outputting an optimal solution; debugging and optimizing the system according to an actual operation condition, adjusting control parameters, and optimizing an algorithm and a structure to improve control performance and robustness; and finally, system testing and evaluation are carried out, performance and robustness tests such as vibration attenuation rate, control precision, response speed and stability under interference and noise are covered, and efficient and stable vibration control is realized.

Description

Technical Field

[0001] The present invention relates to the field of mechanical system vibration, and in particular to an intelligent vibration control system and method for a shaft system. Background Art

[0002] In many fields of modern industry, such as machinery manufacturing, energy production, aerospace, etc., the shaft system is a key transmission component, and its stable operation is of vital importance to the performance and reliability of the entire system. However, the shaft system will inevitably vibrate during operation. If these vibrations are not effectively controlled, they may cause a series of serious problems.

[0003] Over the past few decades, researchers and engineers have devoted themselves to developing various technologies for shaft vibration control. Early approaches focused on passive control strategies, such as using dampers or springs to absorb and reduce vibration energy. However, this passive control approach has obvious limitations. Their performance often depends on pre-set structural parameters and cannot be adjusted in real time according to actual operating conditions. Therefore, when faced with complex and changing operating conditions, the control effect is difficult to be satisfactory.

[0004] With the advancement of technology, active control technology has gradually attracted people's attention. Active control uses sensors to monitor the vibration state of the shaft system in real time, and then uses actuators to apply corresponding control forces to suppress vibration. However, in practical applications, active control also faces many challenges. On the one hand, accurate vibration monitoring requires high-performance sensors. However, some existing sensors have deficiencies in accuracy, response speed and reliability, resulting in inaccurate and in-time data collected, which affects the control effect. On the other hand, the performance of the actuator and the effectiveness of the control strategy are also directly related to the success or failure of vibration control. Some actuators are difficult to meet the requirements in terms of output force, response speed and control accuracy, and the existing control strategies have many problems in terms of algorithm complexity, computational efficiency and adaptability to system uncertainty. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a shaft system intelligent vibration control system and method.

[0006] First, a high-precision eddy current displacement sensor is used and installed at the key position of the shaft system, such as the cross-critical speed position, so that the vibration displacement can be monitored more accurately in real time. An electromagnetic actuator is installed on the bearing seat where the support parameters need to be adjusted, and the electromagnetic force is changed by flexibly controlling the current size, so as to accurately adjust the support stiffness and damping, and effectively suppress the vibration. In terms of vibration control algorithm design, the present invention innovatively combines particle swarm optimization with linear quadratic Gaussian optimal control. By establishing an accurate dynamic model and noise model, a comprehensive and accurate state equation, input matrix, control matrix, output matrix, noise matrix and observation matrix are determined. Then, by solving the Riccati differential equation and the Kalman filter equation, the optimal feedback gain matrix K and the state estimate are obtained, and then the control force is calculated and output to the actuator, and the particle swarm algorithm is used to optimize the key parameters in the linear quadratic Gaussian optimal control, such as the state weighting matrix and the control weighting matrix, which further improves the performance and adaptability of the control algorithm.

[0007] In the system debugging and optimization phase, the control parameters are finely adjusted according to the actual operation conditions, such as the state weighting matrix and the control weighting matrix, to obtain the best vibration control effect. By continuously optimizing the control algorithm and system structure, the control performance and robustness of the system are further improved.

[0008] The present invention provides an intelligent vibration control system for a shaft system, which integrates an eddy current displacement sensor, an electromagnetic actuator, a data acquisition and analysis system, a control algorithm module, a human-machine interaction interface, and a protection and installation structure component in the shaft system equipment. In the protection and installation structure, the sensor mounting bracket is an aluminum alloy cantilever type to ensure that the sensor is vertical and the spacing is adjustable; the electromagnetic actuator fixed base is made of steel, contains a buffer structure, and is firmly connected to the bearing seat. The system has the functions of intelligent working condition identification, shaft system health assessment prediction, and remote communication. Through hardware and software integration, the control strategy is optimized according to the working conditions, the shaft system health is assessed and remotely managed, and efficient vibration control is achieved.

[0009] The present invention provides a method for a shaft system intelligent vibration control system, and the specific steps are as follows:

[0010] Step 1: Build the system hardware, install eddy current displacement sensors at key locations to monitor vibration displacement in real time; install electromagnetic actuators on the bearing seats to adjust the support stiffness and damping by controlling the current; select a suitable data acquisition and analysis system, connect sensors and actuators, and set parameters;

[0011] Step 2: Design the vibration control algorithm, establish the dynamic model and noise model, solve the optimal feedback gain matrix and state estimation value, and calculate the control force; use PSO to optimize the parameters in LQG control, define the optimization target, initialize the particle swarm, calculate the particle fitness, update the particle speed and position, iterate until the termination condition is met, and output the optimal solution;

[0012] Step 3: System debugging and optimization: according to the actual operation conditions, adjust the control parameters to obtain the best vibration control effect, optimize the control algorithm and system structure, and improve the control performance and robustness;

[0013] Step 4: System testing and evaluation, complete performance testing and robustness testing, including vibration attenuation rate, control accuracy and response speed, stability under interference and noise, etc.

[0014] The present invention is further improved, and the process of building the system hardware in step 1 can be expressed as:

[0015] Step 1.1, install the eddy current displacement sensor. When the sensor probe is close to the shaft surface, eddy currents will be generated on the shaft surface, and the eddy currents will in turn affect the electrical properties of the probe coil, such as inductance and impedance. The changes in these properties correspond to the vibration displacement of the shaft:

[0016] Z=f(d)

[0017] Wherein, Z represents the output voltage of the eddy current displacement sensor, d represents the vibration displacement of the shaft system, and f represents the function of the output voltage and the vibration displacement of the shaft system. The eddy current displacement sensor is installed near the journal of the rotating machinery. Abnormal vibration is prone to occur near this point. During installation, ensure that the sensor probe is perpendicular to the measured surface and maintains a suitable distance.

[0018] Step 1.2, install the electromagnetic actuator. When the electromagnetic actuator is energized with current, it acts on the bearing seat and other structures through electromagnetic force, changing its force characteristics, thereby adjusting the support stiffness and damping. From a mechanical point of view, for a single-degree-of-freedom vibration system, its motion equation can be expressed as:

[0019]

[0020] Where m is the mass, is the acceleration, c is the damping coefficient, is the velocity, k is the stiffness, x is the displacement, and F is the force generated by the electromagnetic actuator. By controlling the current flowing into the electromagnetic actuator, the equivalent values ​​of c and k can be changed, thereby adjusting the vibration response of the system. It will be installed on the bearing seat, because the bearing seat is the key part of the mechanical system that supports the rotating parts and has a great influence on the vibration characteristics of the entire system. The installation must ensure that the actuator is firmly connected to the bearing seat, and the force it generates can be effectively transmitted to the entire supporting structure.

[0021] Step 1.3, data acquisition and analysis system, connect the output end of the eddy current displacement sensor to the corresponding analog input channel of the data acquisition system, and connect the control end of the electromagnetic actuator to the analog output channel of the data acquisition system; in terms of parameter setting, it is necessary to set the gain, sampling frequency, trigger mode and other parameters of the acquisition channel.

[0022] The present invention is further improved, and the process of designing the vibration control algorithm in step 2 can be expressed as follows:

[0023] Step 2.1, establish a dynamic model, discretize the shaft system into units such as disks, shaft segments and bearing seats, and connect each unit through nodes, which are selected at the center of the disk, the center of the journal, etc. For a rigid disk, assume its mass is m and its diameter moment of inertia is J d , the polar moment of inertia is J p , its kinetic energy T d for:

[0024]

[0025] Among them, w x0 、w y0 、w z0 is the three-axis angular velocity of the disk, is the first-order derivative of displacement with respect to time; the differential equation of motion is derived through the second-kind Lagrange equation, which can be expressed as:

[0026]

[0027] Among them, q j is the generalized coordinate, j = 1, 2, 3, 4, is the generalized coordinate differential, T is the kinetic energy of the system, t is the time variable, V is the potential energy of the system, Q j is the generalized coordinate q j For elastic shaft segments, the generalized coordinates are expressed by the displacement of the nodes at both ends of the unit, and the unit kinetic energy T is obtained by displacement interpolation function and other methods. x and bending elastic potential energy V x, and then get its motion equation; the bearing support is simplified to a spring-damper model, considering the influence of its stiffness and damping characteristics on the system; combining the unit equations, the system's motion equation is obtained:

[0028]

[0029] Where [M] is the mass matrix, [C] is the damping matrix, [K] is the stiffness matrix, {U} is the displacement vector, is the velocity vector, is the acceleration vector, {Q} is the generalized force vector

[0030] Step 2.2, establish a noise model. In the actual system, there are random interference and measurement noise, which are expressed as zero-mean Gaussian white noise; for a continuous random linear system, its state equation is:

[0031]

[0032] Z(t)=H(t)x(t)+N(t)

[0033] Among them, x(t) is the state variable of the system, is the differential of the system state variable, A(t), B(t), G(t), H(t) are system matrices, representing the state transfer matrix, control input matrix, noise input matrix and output matrix of the system respectively, u(t) is the control input vector, Z(t) is the measurement output vector representing the eddy current displacement sensor, W(t) and N(t) are zero-mean Gaussian white noise;

[0034] Step 2.3, solve the optimal feedback gain matrix and state estimation value, and calculate the control force;

[0035] Step 2.4, solve the state estimation value. According to the separation theorem, the linear quadratic Gaussian problem is decomposed into the LQR optimal state feedback problem and the state estimation problem with disturbance. For state estimation, the Kalman filter equation is used:

[0036]

[0037] in, is the derivative of the state estimate vector; is the state estimation vector, which includes the estimation of the state variables such as displacement and velocity of each node of the shaft system; A, B, H are the system matrix, control input matrix, and output matrix respectively; u is the control input vector; K c is the Kalman filter gain matrix; Z is the measurement output vector, which is the system output value actually measured by the sensor; the Kalman filter gain matrix is ​​expressed as:

[0038] K c =PHT R -1

[0039] Where P is the state estimation error covariance matrix, which describes the covariance of the error between the state estimation vector and the true state vector; R is the measurement noise variance matrix; when solving, first determine the correlation matrix according to the system model and noise characteristics, then solve the equation by numerical method to obtain P, and then obtain K c ; By continuously updating the state estimate, the accuracy of the estimation of the system state can be improved;

[0040] Step 2.5, calculate the control force. After obtaining the optimal feedback gain matrix and state estimation value, calculate the control force according to the control strategy:

[0041]

[0042] Where L(t) is the system state estimate Related feedback gain;

[0043] Step 2.6, use PSO to optimize the parameters in LQG control.

[0044] The present invention is further improved, and the process of solving the optimal feedback gain matrix and the state estimation value in step 2.3 and calculating the control force can be expressed as follows:

[0045] Step 2.3.1, solve the optimal feedback gain matrix, for the linear system:

[0046]

[0047] Take performance indicators:

[0048]

[0049] Among them, J represents the performance index of the control system, which is used to measure the comprehensive performance of the control system in the entire control process; x is the state vector of the system; t0 and t frepresents the initial time and terminal time respectively, which determine the time interval considered by the performance index; P is the terminal state penalty matrix, which is a symmetric semi-positive definite matrix used to penalize the state of the system at the terminal moment; Q(t) is the state weighting matrix; u(t) is the control input vector, which is the force control signal applied to the shaft system through actuators such as electromagnetic actuators; R(t) is the control weighting matrix, which determines the weight of the control input in the performance index and reflects the restriction or emphasis on the control energy consumption; the control effect and robustness to noise are balanced by reasonably selecting the values ​​of Q(t) and R(t); if the system is more sensitive to the state error, the weight of the corresponding state variable in Q(t) can be appropriately increased to prompt the control strategy to more actively suppress the state fluctuation caused by noise; if the control energy consumption needs to be limited, the value of R(t) can be adjusted;

[0050] Step 2.3.2, derive the optimal control law and construct the Hamiltonian function H:

[0051]

[0052] Among them, λ(t) is the co-state variable, which can be expressed as the sensitivity of the system performance index to the change of the state variable; and according to the co-state equation:

[0053]

[0054] in, is the derivative of the covariate variable with respect to time; the governing equation is:

[0055] u(t)=-R -1 (t)B T (t)λ(t)

[0056] And the transversality condition:

[0057]

[0058] assumed:

[0059] λ(t)=K(t)x(t)

[0060] Where K(t) is the feedback gain matrix. Substituting it into the relevant equation yields the Riccati matrix differential equation:

[0061]

[0062] in, is the time derivative of the feedback gain matrix. Solve the equation backward from the terminal time and let K(t f )=P to get K(t), and then get the optimal control:

[0063] u(t)=-R -1(t)B T (t)K(t)x(t)=-G(t)x(t)

[0064] Among them, G(t) is the feedback gain matrix. In the solution process, due to the existence of noise, there is a deviation between the actual state of the system and the ideal state. By continuously iteratively solving the Riccati equation, the feedback gain matrix G(t) can adapt to the dynamic characteristics of the system under the influence of noise, thereby suppressing the interference of noise on the system to a certain extent and achieving better control effect.

[0065] The present invention is further improved, and the process of optimizing the parameters in LQG control by using PSO in step 2.6 can be expressed as follows:

[0066] Step 2.6.1, define the optimization goal: the optimization goal is to minimize the vibration control effect of the vibration displacement;

[0067] Step 2.6.2, initialize the particle swarm: determine the size of the particle swarm, randomly initialize the position and speed of each particle, the particle is represented by the parameter values ​​of the state weight matrix Q, R control weight matrix, etc., and the upper and lower limits of the particle position and speed are set; among them, the value range of the state weight matrix elements is set to [0.1, 10], and the value range of the control weight matrix elements is set to [0.01, 1]; the upper limit of the speed is set to 0.5, and the lower limit is set to -0.5 to ensure that the parameters are within a reasonable range;

[0068] Step 2.6.3, calculate particle fitness: substitute the current position of each particle into the system model and optimization objective function, and calculate the corresponding fitness value. The fitness value reflects the quality of the system vibration control effect under this set of parameters. The smaller the fitness value, the better the control effect.

[0069] Step 2.6.4, update particle speed and position: calculate the new speed of each particle according to the speed and position update formula of the particle swarm optimization algorithm and location The speed update formula is:

[0070]

[0071] in, is the speed update value, w is the inertia weight, v i is the particle velocity vector, where i represents the i-th particle, c1 and c2 are learning factors, r1 and r2 are random numbers between 0 and 1, and p i is the historical optimal position of the individual particle, g is the global optimal position of the particle swarm; the position update formula is:

[0072]

[0073] in, is the particle position update value;

[0074] Step 2.6.5, repeat the process of calculating particle fitness, updating particle velocity and position until the maximum number of iterations is reached or the fitness value converges to a certain accuracy; at this time, the parameter value corresponding to the global optimal position in the particle swarm is the optimized LQG control parameter, output the optimal solution, and apply it to the LQG control algorithm to improve the vibration control performance of the system.

[0075] The present invention provides a shaft system intelligent vibration control system and method, with beneficial effects: The technical effects of the present invention are:

[0076] 1. The eddy current displacement sensor of the present invention can accurately monitor vibration displacement in real time, provide a basis for the control algorithm, and combine the control force solved by the dynamics and noise models to efficiently control vibration, reduce mechanical damage and extend the life of equipment.

[0077] 2. The PSO of the present invention optimizes the LQG control parameters, improves the control accuracy, can accurately suppress vibration in complex vibration environments, and ensure stable operation of the equipment.

[0078] 3. The present invention takes noise and interference factors into consideration. The noise model and the stability test under interference ensure that the system works stably in a complex environment and the sensor can still be accurately controlled when it is interfered by noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a flow chart of the present invention.

[0080] Figure 2 It is a block diagram of the control system of the present invention.

[0081] Figure 3 It is the vibration displacement response curve under the vibration control of the present invention. DETAILED DESCRIPTION

[0082] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0083] The present invention proposes an intelligent vibration control system and method for a shaft system. The system integrates eddy current displacement sensors, electromagnetic actuators, data acquisition and analysis systems, control algorithm modules, human-machine interaction interfaces, and protection and installation structural components into the shaft system equipment. In the protection and installation structure, the sensor mounting bracket is an aluminum alloy cantilever type to ensure that the sensor is vertical and the spacing is adjustable; the electromagnetic actuator fixed base is made of steel, contains a buffer structure, and is firmly connected to the bearing seat. The system has functions such as intelligent working condition identification, shaft system health assessment prediction, and remote communication. Through hardware and software integration, it optimizes the control strategy according to the working conditions, assesses the health of the shaft system and remotely manages it, thereby achieving efficient vibration control. The invention flow chart is as follows Figure 1As shown, the steps of the present invention are described in detail below.

[0084] Step 1: Build the system hardware, install eddy current displacement sensors at key locations to monitor vibration displacement in real time; install electromagnetic actuators on the bearing seats to adjust the support stiffness and damping by controlling the current; select a suitable data acquisition and analysis system, connect sensors and actuators, and set parameters.

[0085] Step 1.1, install the eddy current displacement sensor. When the sensor probe is close to the shaft surface, eddy currents will be generated on the shaft surface, and the eddy currents will in turn affect the electrical properties of the probe coil, such as inductance and impedance. The changes in these properties correspond to the vibration displacement of the shaft:

[0086] Z=f(d)

[0087] Wherein, Z represents the output voltage of the eddy current displacement sensor, d represents the vibration displacement of the shaft system, and f represents the function of the output voltage and the vibration displacement of the shaft system. The eddy current displacement sensor is installed near the journal of the rotating machinery. Abnormal vibration is prone to occur near this point. During installation, ensure that the sensor probe is perpendicular to the measured surface and maintains a suitable distance.

[0088] Step 1.2, install the electromagnetic actuator. When the electromagnetic actuator is energized with current, it acts on the bearing seat and other structures through electromagnetic force, changing its force characteristics, thereby adjusting the support stiffness and damping. From a mechanical point of view, for a single-degree-of-freedom vibration system, its motion equation can be expressed as:

[0089]

[0090] Where m is the mass, is the acceleration, c is the damping coefficient, is the speed, k is the stiffness, x is the displacement, and F is the force generated by the electromagnetic actuator. By controlling the current flowing into the electromagnetic actuator, the equivalent values ​​of c and k can be changed, thereby adjusting the vibration response of the system; it will be installed on the bearing seat, because the bearing seat is the key part of the mechanical system to support the rotating parts, and has a great influence on the vibration characteristics of the entire system. The installation must ensure that the actuator is firmly connected to the bearing seat, and the force it generates can be effectively transmitted to the entire supporting structure.

[0091] Step 1.3, data acquisition and analysis system, connect the output end of the eddy current displacement sensor to the corresponding analog input channel of the data acquisition system, and connect the control end of the electromagnetic actuator to the analog output channel of the data acquisition system. In terms of parameter setting, it is necessary to set the acquisition channel gain, sampling frequency, trigger mode and other parameters.

[0092] Step 2: Design a vibration control algorithm, establish a dynamic model and a noise model, solve the optimal feedback gain matrix and state estimation value, and calculate the control force; use PSO to optimize the parameters in LQG control, define the optimization goal, initialize the particle swarm, calculate the particle fitness, update the particle speed and position, iterate until the termination condition is met, and output the optimal solution.

[0093] Step 2.1, establish a dynamic model, discretize the shaft system into units such as disk, shaft segment and bearing seat, and connect each unit through nodes, which are selected at the center of the disk, the center of the journal, etc. For a rigid disk, let its mass be m and its diameter moment of inertia be J d , the polar moment of inertia is J p , its kinetic energy T d for:

[0094]

[0095] Among them, w x0 、w y0 、w z0 is the three-axis angular velocity of the disk, is the first-order derivative of displacement with respect to time; the differential equation of motion is derived through the second-kind Lagrange equation, which can be expressed as:

[0096]

[0097] Among them, q j is the generalized coordinate, j = 1, 2, 3, 4, is the generalized coordinate differential, T is the kinetic energy of the system, t is the time variable, V is the potential energy of the system, Q j is the generalized coordinate q j For elastic shaft segments, the generalized coordinates are expressed by the displacement of the nodes at both ends of the unit, and the unit kinetic energy T is obtained by displacement interpolation function and other methods. x and bending elastic potential energy V x , and then get its motion equation. The bearing support is simplified to a spring-damper model, considering the influence of its stiffness and damping characteristics on the system. Combining the equations of each unit, the system's motion equation is obtained:

[0098]

[0099] Where [M] is the mass matrix, [C] is the damping matrix, [K] is the stiffness matrix, {U} is the displacement vector, is the velocity vector, is the acceleration vector, {Q} is the generalized force vector

[0100] Step 2.2, establish the noise model. In the actual system, there are random interference and measurement noise, which are expressed as zero-mean Gaussian white noise. For a continuous random linear system, its state equation is:

[0101]

[0102] Z(t)=H(t)x(t)+N(t)

[0103] Among them, x(t) is the state variable of the system, is the differential of the system state variable, A(t), B(t), G(t), H(t) are system matrices, representing the state transfer matrix, control input matrix, noise input matrix and output matrix of the system respectively, u(t) is the control input vector, Z(t) is the measurement output vector of the eddy current displacement sensor, W(t) and N(t) are zero-mean Gaussian white noise.

[0104] Step 2.3, solve the optimal feedback gain matrix and state estimation value, and calculate the control force.

[0105] Step 2.3.1, solve the optimal feedback gain matrix, for the linear system:

[0106]

[0107] Take performance indicators:

[0108]

[0109] Among them, J represents the performance index of the control system, which is used to measure the comprehensive performance of the control system in the entire control process; x is the state vector of the system; t0 and t f represents the initial time and terminal time respectively, which determine the time interval considered by the performance index; P is the terminal state penalty matrix, which is a symmetric semi-positive definite matrix used to penalize the state of the system at the terminal moment; Q(t) is the state weighting matrix; u(t) is the control input vector, which is the force control signal applied to the shaft system through the actuator such as the electromagnetic actuator; R(t) is the control weighting matrix, which determines the weight of the control input in the performance index and reflects the restriction or emphasis on the control energy consumption. The control effect and robustness to noise are balanced by reasonably selecting the values ​​of Q(t) and R(t). If the system is sensitive to the state error, the weight of the corresponding state variable in Q(t) can be appropriately increased to prompt the control strategy to more actively suppress the state fluctuation caused by noise; if the control energy consumption needs to be limited, the value of R(t) can be adjusted.

[0110] Step 2.3.2, derive the optimal control law and construct the Hamiltonian function H:

[0111]

[0112] Among them, λ(t) is the co-state variable, which can be expressed as the sensitivity of the system performance index to the change of the state variable. And according to the co-state equation:

[0113]

[0114] in, is the derivative of the covariate variable with respect to time. The governing equation is:

[0115] u(t)=-R -1 (t)B T (t)λ(t)

[0116] And the transversality condition:

[0117]

[0118] assumed:

[0119] λ(t)=K(t)x(t)

[0120] Where K(t) is the feedback gain matrix. Substituting it into the relevant equation yields the Riccati matrix differential equation:

[0121]

[0122] in, is the time derivative of the feedback gain matrix. Solve the equation backward from the terminal time and let K(t f )=P to get K(t), and then get the optimal control. The control system block diagram is as follows Figure 2 As shown:

[0123] u(t)=-R -1 (t)B T (t)K(t)x(t)=-G(t)x(t)

[0124] Among them, G(t) is the feedback gain matrix. In the solution process, due to the existence of noise, there is a deviation between the actual state of the system and the ideal state. By continuously iteratively solving the Riccati equation, the feedback gain matrix G(t) can adapt to the dynamic characteristics of the system under the influence of noise, thereby suppressing the interference of noise on the system to a certain extent and achieving a better control effect.

[0125] Step 2.4, solve the state estimation value. According to the separation theorem, the linear quadratic Gaussian problem is decomposed into the LQR optimal state feedback problem and the state estimation problem with disturbance. For state estimation, the Kalman filter equation is used:

[0126]

[0127] in, is the derivative of the state estimate vector; is the state estimation vector, which includes the estimation of the state variables such as displacement and velocity of each node of the shaft system; A, B, H are the system matrix, control input matrix, and output matrix respectively; u is the control input vector; K c is the Kalman filter gain matrix; Z is the measurement output vector, which is the system output value actually measured by the sensor. The gain matrix of the Kalman filter is expressed as:

[0128] K c =PH T R -1

[0129] Among them, P is the state estimation error covariance matrix, which describes the covariance of the error between the state estimation vector and the true state vector; R is the measurement noise variance matrix. When solving, first determine the correlation matrix according to the system model and noise characteristics, then solve the equation by numerical method to obtain P, and then obtain K c . By continuously updating the state estimate, the estimation accuracy of the system state can be improved.

[0130] Step 2.5, calculate the control force. After obtaining the optimal feedback gain matrix and state estimation value, calculate the control force according to the control strategy:

[0131]

[0132] Where L(t) is the system state estimate Related feedback gain.

[0133] Step 2.6: Optimize the parameters in LQG control using PSO

[0134] Step 2.6.1, define the optimization goal: the optimization goal is to minimize the vibration control effect of the vibration displacement.

[0135] Step 2.6.2, initialize the particle swarm: determine the size of the particle swarm, randomly initialize the position and velocity of each particle, and represent the particles as the parameter values ​​of the state weight matrix Q, R control weight matrix, etc., and set the upper and lower limits of the particle position and velocity. Among them, the value range of the state weight matrix elements is set to [0.1, 10], and the value range of the control weight matrix elements is set to [0.01, 1]; the upper limit of the velocity is set to 0.5, and the lower limit is set to -0.5 to ensure that the parameters are within a reasonable range.

[0136] Step 2.6.3, calculate particle fitness: substitute the current position of each particle into the system model and optimization objective function, and calculate the corresponding fitness value. The fitness value reflects the effect of system vibration control under this set of parameters. The smaller the fitness value, the better the control effect.

[0137] Step 2.6.4, update particle speed and position: calculate the new speed of each particle according to the speed and position update formula of the particle swarm optimization algorithm and location The speed update formula is:

[0138]

[0139] in, is the speed update value, w is the inertia weight, v i is the particle velocity vector, where i represents the i-th particle, c1 and c2 are learning factors, r1 and r2 are random numbers between 0 and 1, and p i is the historical optimal position of the individual particle, and g is the global optimal position of the particle swarm. The position update formula is:

[0140]

[0141] in, is the particle position update value.

[0142] Step 2.6.5, repeat the process of calculating particle fitness, updating particle velocity and position until the maximum number of iterations is reached or the fitness value converges to a certain accuracy. At this time, the parameter value corresponding to the global optimal position in the particle swarm is the optimized LQG control parameter, output the optimal solution, and apply it to the LQG control algorithm to improve the vibration control performance of the system.

[0143] Step 3: System debugging and optimization. According to the actual operation conditions, adjust the control parameters to obtain the best vibration control effect, optimize the control algorithm and system structure, improve the control performance and robustness. The vibration displacement response curve under vibration control is as follows: Figure 3 shown.

[0144] Step 3.1, adjust parameters based on real-time monitoring data: The eddy current displacement sensor installed in step 1 will monitor the vibration displacement of key positions of the system in real time. By observing and analyzing the real-time monitored vibration displacement data and comparing it with the desired vibration control target, the state weighting matrix or control weighting matrix can be adjusted.

[0145] Step 3.2, consider parameter adjustment under different working conditions: the system is under different operating conditions: different speeds, loads, its dynamic characteristics will change, then adjust the control parameters according to the actual working conditions. When the system speed increases, the vibration frequency and amplitude of the shaft system may change. According to the vibration data monitored by the sensor at this time, combined with the established dynamic model, the control current of the electromagnetic actuator is adjusted accordingly, and the support stiffness and damping parameters are changed to adapt to the vibration control requirements under the new working conditions to maintain a better vibration control effect.

[0146] Step 4: System testing and evaluation, complete performance testing and robustness testing, including vibration attenuation rate, control accuracy and response speed, stability under interference and noise, etc.

[0147] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. A shaft system intelligent vibration control system, characterized in that: The system integrates eddy current displacement sensors, electromagnetic actuators, data acquisition and analysis systems, control algorithm modules, human-machine interaction interfaces, and protection and installation structural components into shafting equipment. In the protection and installation structure, the sensor mounting bracket is an aluminum alloy cantilever type to ensure that the sensor is vertical and the spacing is adjustable; the electromagnetic actuator fixed base is made of steel, contains a buffer structure, and is firmly connected to the bearing seat. The system has functions such as intelligent working condition identification, shafting health assessment prediction, and remote communication. Through hardware and software integration, it optimizes the control strategy according to the working conditions, assesses the health of the shafting system and remotely manages it, and achieves efficient vibration control.

2. According to the method of the shaft system intelligent vibration control system of claim 1, the specific steps are as follows, characterized in that: Step 1: Build the system hardware, install eddy current displacement sensors at key locations to monitor vibration displacement in real time; install electromagnetic actuators on the bearing seats to adjust the support stiffness and damping by controlling the current; select a suitable data acquisition and analysis system, connect sensors and actuators, and set parameters; Step 2: Design the vibration control algorithm, establish the dynamic model and noise model, solve the optimal feedback gain matrix and state estimation value, and calculate the control force; use PSO to optimize the parameters in LQG control, define the optimization target, initialize the particle swarm, calculate the particle fitness, update the particle speed and position, iterate until the termination condition is met, and output the optimal solution; Step 3: System debugging and optimization: according to the actual operation conditions, adjust the control parameters to obtain the best vibration control effect, optimize the control algorithm and system structure, and improve the control performance and robustness; Step 4: System testing and evaluation, complete performance testing and robustness testing, including vibration attenuation rate, control accuracy and response speed, stability under interference and noise, etc.

3. The method of a shaft system intelligent vibration control system according to claim 2, characterized in that: The process of building the system hardware in step 1 can be expressed as: Step 1.1, install the eddy current displacement sensor. When the sensor probe is close to the shaft surface, eddy currents will be generated on the shaft surface, and the eddy currents will in turn affect the electrical properties of the probe coil, such as inductance and impedance. The changes in these properties correspond to the vibration displacement of the shaft: Z=f(d) Wherein, Z represents the output voltage of the eddy current displacement sensor, d represents the vibration displacement of the shaft system, and f represents the function of the output voltage and the vibration displacement of the shaft system. The eddy current displacement sensor is installed near the journal of the rotating machinery. Abnormal vibration is prone to occur near this point. During installation, ensure that the sensor probe is perpendicular to the measured surface and maintains a suitable distance. Step 1.2, install the electromagnetic actuator. When the electromagnetic actuator is energized with current, it acts on the bearing seat and other structures through electromagnetic force, changing its force characteristics, thereby adjusting the support stiffness and damping. From a mechanical point of view, for a single-degree-of-freedom vibration system, its motion equation can be expressed as: Where m is the mass, is the acceleration, c is the damping coefficient, is the velocity, k is the stiffness, x is the displacement, and F is the force generated by the electromagnetic actuator. By controlling the current flowing into the electromagnetic actuator, the equivalent values ​​of c and k can be changed, thereby adjusting the vibration response of the system. It will be installed on the bearing seat, because the bearing seat is the key part of the mechanical system that supports the rotating parts and has a great influence on the vibration characteristics of the entire system. The installation must ensure that the actuator is firmly connected to the bearing seat, and the force it generates can be effectively transmitted to the entire supporting structure. Step 1.3, data acquisition and analysis system, connect the output end of the eddy current displacement sensor to the corresponding analog input channel of the data acquisition system, and connect the control end of the electromagnetic actuator to the analog output channel of the data acquisition system; in terms of parameter setting, it is necessary to set the gain, sampling frequency, trigger mode and other parameters of the acquisition channel.

4. The method of a shaft system intelligent vibration control system according to claim 2, characterized in that: The process of designing the vibration control algorithm in step 2 can be expressed as follows: Step 2.1, establish a dynamic model, discretize the shaft system into units such as disks, shaft segments and bearing seats, and connect each unit through nodes, which are selected at the center of the disk, the center of the journal, etc. For a rigid disk, assume its mass is m and its diameter moment of inertia is J d , the polar moment of inertia is J p , its kinetic energy T d for: Among them, w x0 、w y0 、w z0 is the three-axis angular velocity of the disk, is the first-order derivative of displacement with respect to time; the differential equation of motion is derived through the second-kind Lagrange equation, which can be expressed as: Among them, q j is the generalized coordinate, j = 1, 2, 3, 4, is the generalized coordinate differential, T is the kinetic energy of the system, t is the time variable, V is the potential energy of the system, Q j is the generalized coordinate q j For elastic shaft segments, the generalized coordinates are expressed by the displacement of the nodes at both ends of the unit, and the unit kinetic energy T is obtained by displacement interpolation function and other methods. x and bending elastic potential energy V x , and then get its motion equation; the bearing support is simplified to a spring-damper model, considering the influence of its stiffness and damping characteristics on the system; combining the unit equations, the system's motion equation is obtained: Where [M] is the mass matrix, [C] is the damping matrix, [K] is the stiffness matrix, {U} is the displacement vector, is the velocity vector, is the acceleration vector, {Q} is the generalized force vector Step 2.2, establish a noise model. In the actual system, there are random interference and measurement noise, which are expressed as zero-mean Gaussian white noise; for a continuous random linear system, its state equation is: Z(t)=H(t)x(t)+N(t) Among them, x(t) is the state variable of the system, is the differential of the system state variable, A(t), B(t), G(t), H(t) are system matrices, representing the state transfer matrix, control input matrix, noise input matrix and output matrix of the system respectively, u(t) is the control input vector, Z(t) is the measurement output vector representing the eddy current displacement sensor, W(t) and N(t) are zero-mean Gaussian white noise; Step 2.3, solve the optimal feedback gain matrix and state estimation value, and calculate the control force; Step 2.4, solve the state estimation value. According to the separation theorem, the linear quadratic Gaussian problem is decomposed into the LQR optimal state feedback problem and the state estimation problem with disturbance. For state estimation, the Kalman filter equation is used: in, is the derivative of the state estimate vector; is the state estimation vector, which includes the estimation of the state variables such as displacement and velocity of each node of the shaft system; A, B, H are the system matrix, control input matrix, and output matrix respectively; u is the control input vector; K c is the Kalman filter gain matrix; Z is the measurement output vector, which is the system output value actually measured by the sensor; the Kalman filter gain matrix is ​​expressed as: K c =PH T R -1 Where P is the state estimation error covariance matrix, which describes the covariance of the error between the state estimation vector and the true state vector; R is the measurement noise variance matrix; when solving, first determine the correlation matrix according to the system model and noise characteristics, then solve the equation by numerical method to obtain P, and then obtain K c ; By continuously updating the state estimate, the accuracy of the estimation of the system state can be improved; Step 2.5, calculate the control force. After obtaining the optimal feedback gain matrix and state estimation value, calculate the control force according to the control strategy: Where L(t) is the system state estimate Related feedback gain; Step 2.6, use PSO to optimize the parameters in LQG control.

5. The method of a shaft system intelligent vibration control system according to claim 2, characterized in that: In step 2.3, the process of solving the optimal feedback gain matrix and state estimation value and calculating the control force can be expressed as follows: Step 2.3.1, solve the optimal feedback gain matrix, for the linear system: Take performance indicators: Among them, J represents the performance index of the control system, which is used to measure the comprehensive performance of the control system in the entire control process; x is the state vector of the system; t0 and t f represents the initial time and terminal time respectively, which determine the time interval considered by the performance index; P is the terminal state penalty matrix, which is a symmetric semi-positive definite matrix used to penalize the state of the system at the terminal moment; Q(t) is the state weighting matrix; u(t) is the control input vector, which is the force control signal applied to the shaft system through actuators such as electromagnetic actuators; R(t) is the control weighting matrix, which determines the weight of the control input in the performance index and reflects the restriction or emphasis on the control energy consumption; the control effect and robustness to noise are balanced by reasonably selecting the values ​​of Q(t) and R(t); if the system is more sensitive to the state error, the weight of the corresponding state variable in Q(t) can be appropriately increased to prompt the control strategy to more actively suppress the state fluctuation caused by noise; if the control energy consumption needs to be limited, the value of R(t) can be adjusted; Step 2.3.2, derive the optimal control law and construct the Hamiltonian function H: Among them, λ(t) is the co-state variable, which can be expressed as the sensitivity of the system performance index to the change of the state variable; and according to the co-state equation: in, is the time derivative of the covariate variable; the governing equation is: u(t)=-R -1 (t)B T (t)λ(t) And the transversality condition: assumed: λ(t)=K(t)x(t) Where K(t) is the feedback gain matrix. Substituting it into the relevant equation yields the Riccati matrix differential equation: in, is the time derivative of the feedback gain matrix. Solve the equation backward from the terminal time and let K(t f )=P to get K(t), and then get the optimal control: u(t)=-R -1 (t)B T (t)K(t)x(t)=-G(t)x(t) Among them, G(t) is the feedback gain matrix. In the solution process, due to the existence of noise, there is a deviation between the actual state of the system and the ideal state. By continuously iteratively solving the Riccati equation, the feedback gain matrix G(t) can adapt to the dynamic characteristics of the system under the influence of noise, thereby suppressing the interference of noise on the system to a certain extent and achieving better control effect.

6. The method of a shaft system intelligent vibration control system according to claim 2, characterized in that: The process of optimizing the parameters in LQG control using PSO in step 2.6 can be expressed as follows: Step 2.6.1, define the optimization goal: the optimization goal is to minimize the vibration control effect of the vibration displacement; Step 2.6.2, initialize the particle swarm: determine the size of the particle swarm, randomly initialize the position and speed of each particle, the particle is represented by the parameter values ​​of the state weight matrix Q, R control weight matrix, etc., and the upper and lower limits of the particle position and speed are set; among them, the value range of the state weight matrix elements is set to [0.1, 10], and the value range of the control weight matrix elements is set to [0.01, 1]; the upper limit of the speed is set to 0.5, and the lower limit is set to -0.5 to ensure that the parameters are within a reasonable range; Step 2.6.3, calculate particle fitness: substitute the current position of each particle into the system model and optimization objective function, and calculate the corresponding fitness value. The fitness value reflects the quality of the system vibration control effect under this set of parameters. The smaller the fitness value, the better the control effect. Step 2.6.4, update particle speed and position: calculate the new speed of each particle according to the speed and position update formula of the particle swarm optimization algorithm and location The speed update formula is: in, is the speed update value, w is the inertia weight, v i is the particle velocity vector, where i represents the i-th particle, c1 and c2 are learning factors, r1 and r2 are random numbers between 0 and 1, and p i is the historical optimal position of the individual particle, g is the global optimal position of the particle swarm; the position update formula is: in, is the particle position update value; Step 2.6.5, repeat the process of calculating particle fitness, updating particle velocity and position until the maximum number of iterations is reached or the fitness value converges to a certain accuracy; at this time, the parameter value corresponding to the global optimal position in the particle swarm is the optimized LQG control parameter, output the optimal solution, and apply it to the LQG control algorithm to improve the vibration control performance of the system.

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